1.
Quantum field theory
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QFT treats particles as excited states of the physical field, so these are called field quanta. In quantum theory, quantum mechanical interactions among particles are described by interaction terms among the corresponding underlying quantum fields. These interactions are conveniently visualized by Feynman diagrams, which are a formal tool of relativistically covariant theory, serving to evaluate particle processes. The first achievement of namely quantum electrodynamics, is "still the paradigmatic example of a successful quantum field theory". Ordinarily, quantum mechanics cannot give an account of photons which constitute the prime case of relativistic ‘particles’. The formalism of QFT is needed for an explicit description of photons. However, quantum mechanics did not focus much on problems of radiation. As as the conceptual framework of quantum mechanics was developed, a small group of theoreticians tried to extend quantum methods to electromagnetic fields. A good example is the famous paper by Born, Jordan & Heisenberg. The ideas of QM were thus extended to systems having an infinite number of degrees of freedom, so an infinite array of quantum oscillators. The inception of QFT is usually considered to be Dirac's famous 1927 paper on "The theory of the emission and absorption of radiation". Here Dirac coined the name "electrodynamics" for the part of QFT, developed first. Employing the theory of the quantum oscillator, Dirac gave a theoretical description of how photons appear in the quantization of the electromagnetic radiation field. Later, Dirac's procedure became a model for the quantization of other fields well. These first approaches to QFT were further developed during the following three years.
Quantum field theory
2.
Introduction to quantum mechanics
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Quantum mechanics is the science of the very small. It explains its interactions with energy on the scale of atoms and subatomic particles. By contrast, classical physics only explains energy on a scale familiar to human experience, including the behaviour of astronomical bodies such as the Moon. Classical physics is still used in much of modern technology. However, towards the end of the 19th century, scientists discovered phenomena in both the small worlds that classical physics could not explain. These concepts are described in roughly the order in which they were first discovered. For a more complete history of the subject, see History of quantum mechanics. Light behaves in other respects like waves. Matter -- particles such as atoms -- exhibits wavelike behaviour too. Some light sources, including neon lights, give off only certain frequencies of light. Since one never observes half a photon, a single photon is smallest observable amount, of the electromagnetic field. Many aspects of quantum mechanics can seem paradoxical, because they describe behaviour quite different from that seen at larger length scales. In the words of physicist Richard Feynman, quantum mechanics deals with "nature as She is -- absurd". Thermal radiation is electromagnetic radiation emitted from the surface of an object due to the object's internal energy. If an object is heated sufficiently, it starts to emit light at the red end of the spectrum, as it becomes red hot.
Introduction to quantum mechanics
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Hot metalwork. The yellow-orange glow is the visible part of the thermal radiation emitted due to the high temperature. Everything else in the picture is glowing with thermal radiation as well, but less brightly and at longer wavelengths than the human eye can detect. A far-infrared camera can observe this radiation.
Introduction to quantum mechanics
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Albert Einstein in around 1905.
Introduction to quantum mechanics
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Niels Bohr as a young man
Introduction to quantum mechanics
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Louis de Broglie in 1929. De Broglie won the Nobel Prize in Physics for his prediction that matter acts as a wave, made in his 1924 PhD thesis.
3.
Electron
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The electron is a subatomic particle, symbol e− or β−, with a negative elementary electric charge. The electron has a mass, approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic momentum of a half-integer value, expressed in units of the reduced Planck constant, ħ. As it is a fermion, no two electrons can occupy the same state, in accordance with the Pauli exclusion principle. Like all matter, electrons have properties of both waves: they can collide with other particles and can be diffracted like light. Electromagnetic fields produced from other sources will affect the motion of an electron according to the Lorentz law. Electrons absorb energy in the form of photons when they are accelerated. Laboratory instruments are capable of trapping individual electrons well as electron plasma by the use of electromagnetic fields. Special telescopes can detect plasma in outer space. Electrons are involved in many applications such as electronics, welding, cathode ray tubes, electron microscopes, radiation therapy, lasers, particle accelerators. Interactions involving electrons with subatomic particles are of interest in fields such as chemistry and nuclear physics. The Coulomb interaction between the positive protons within atomic nuclei and the negative electrons without, allows the composition of the two known as atoms. Ionization or differences in the proportions of negative electrons versus positive nuclei changes the binding energy of an atomic system. The sharing of the electrons between two or more atoms is the main cause of chemical bonding. In 1838, natural philosopher Richard Laming first hypothesized the concept of an indivisible quantity of electric charge to explain the chemical properties of atoms.
Electron
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A beam of electrons deflected in a circle by a magnetic field
Electron
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Hydrogen atom orbitals at different energy levels. The brighter areas are where you are most likely to find an electron at any given time.
Electron
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Robert Millikan
Electron
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A lightning discharge consists primarily of a flow of electrons. The electric potential needed for lightning may be generated by a triboelectric effect.
4.
History of quantum mechanics
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The history of quantum mechanics is a fundamental part of the history of modern physics. In the years to follow, this theoretical basis slowly began to be applied to chemical structure, bonding. Ludwig Boltzmann suggested in 1877 that the energy levels such as a molecule, could be discrete. He was a founder of the Austrian Mathematical Society, together with the mathematicians Gustav von Escherich and Emil Müller. The earlier Wien approximation may be derived by assuming h ν ≫ k T. This statement has been called the most revolutionary sentence written by a physicist of the twentieth century. These quanta later came to be called "photons", a term introduced by Gilbert N. Lewis in 1926. They are collectively known as the old theory. The phrase "quantum physics" was first used in Light of Modern Physics. In 1923, the French physicist Louis de Broglie put forward his theory of matter waves by stating that particles can exhibit wave characteristics and vice versa. This theory was for a single particle and derived from relativity theory. Schrödinger subsequently showed that the two approaches were equivalent. The Copenhagen interpretation started to take shape at about the same time. Starting around 1927, Paul Dirac began the process of unifying quantum mechanics with special relativity by proposing the Dirac equation for the electron. The Dirac equation achieves the relativistic description of the wavefunction of an electron that Schrödinger failed to obtain.
History of quantum mechanics
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Max Planck, Albert Einstein, Niels Bohr, Louis de Broglie, Max Born, Paul Dirac, Werner Heisenberg, Wolfgang Pauli, Erwin Schrödinger, Richard Feynman.
History of quantum mechanics
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Ludwig Boltzmann 's diagram of the I 2 molecule proposed in 1898 showing the atomic "sensitive region" (α, β) of overlap.
History of quantum mechanics
5.
Classical mechanics
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In physics, classical mechanics is one of the two major sub-fields of mechanics, along with quantum mechanics. Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the influence of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the largest subjects in science, engineering and technology. It is also widely known as Newtonian mechanics. Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, well as astronomical objects, such as spacecraft, planets, stars, galaxies. Within classical mechanics are fields of study that describe the behavior of solids, liquids and gases and other specific sub-topics. When classical mechanics can not apply, such as at the quantum level with high speeds, quantum field theory becomes applicable. Since these aspects of physics were developed long before the emergence of quantum relativity, some sources exclude Einstein's theory of relativity from this category. However, a number of modern sources do include relativistic mechanics, which in their view represents classical mechanics in its most accurate form. Later, more general methods were developed, leading to reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. They extend substantially beyond Newton's work, particularly through their use of analytical mechanics. The following introduces the basic concepts of classical mechanics. For simplicity, it often models real-world objects as point particles. The motion of a particle is characterized by a small number of parameters: its position, mass, the forces applied to it. Each of these parameters is discussed in turn.
Classical mechanics
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Sir Isaac Newton (1643–1727), an influential figure in the history of physics and whose three laws of motion form the basis of classical mechanics
Classical mechanics
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Diagram of orbital motion of a satellite around the earth, showing perpendicular velocity and acceleration (force) vectors.
Classical mechanics
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Hamilton 's greatest contribution is perhaps the reformulation of Newtonian mechanics, now called Hamiltonian mechanics.
6.
Interference (wave propagation)
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In physics, interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude. Interference effects can be observed for example, light, radio, acoustic, surface waves matter waves. Consider, for example, what happens when two identical stones are dropped into a still pool of water at different locations. Each stone generates a circular wave propagating outwards from the point where the stone was dropped. When the two waves overlap, the net displacement at a particular point is the sum of the displacements of the individual waves. At some points, these will be in phase, will produce a maximum displacement. In other places, the waves will be in anti-phase, there will be no net displacement at these points. Thus, parts of the surface will be stationary -- these are seen to the right as blue-green lines radiating from the center. The above can be demonstrated in one dimension by deriving the formula for the sum of two waves. Constructive interference: If the phase difference is an even multiple of pi: ϕ =. . . − 4 π, − 2 π, 0, 2 π, 4 π. . .
Interference (wave propagation)
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Swimming pool interference
Interference (wave propagation)
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Magnified-image of coloured interference-pattern in soap-film. The black areas ("holes") are areas where the film is very thin and there is a nearly total destructive interference.
Interference (wave propagation)
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Interference fringes in overlapping plane waves
Interference (wave propagation)
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White light interference in a soap bubble
7.
Quantum decoherence
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Quantum decoherence is the loss of quantum coherence. In quantum mechanics, particles such as electrons are described by a wavefunction. These waves can interfere, leading to the peculiar behaviour of quantum particles. Long as there exists a definite phase relation between different states, the system is said to be coherent. This coherence is necessary for the function of quantum computers. However, when a system is not perfectly isolated, but in contact with its surrounding, the coherence decays with time, a process called quantum decoherence. As a result of this process, the behaviour is lost. Decoherence has been a subject of active research since the 1980s. Viewed in isolation, the system's dynamics are non-unitary. Thus the dynamics of the system alone are irreversible. As with any coupling, entanglements are generated between the environment. These have the effect of sharing information with -- or transferring it to -- the surroundings. Decoherence does not generate actual wave collapse. It only provides an explanation for the observation of wave function collapse, into the environment. That is, components of the wavefunction acquire phases from their immediate surroundings.
Quantum decoherence
8.
Quantum entanglement
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Measurements of physical properties such as position, polarization, performed on entangled particles are found to be appropriately correlated. Later, however, the counterintuitive predictions of quantum mechanics were verified experimentally. Recent experiments have measured entangled particles within less than one hundredth of a percent of the travel time of light between them. According to the formalism of quantum theory, the effect of measurement happens instantly. It is not possible, however, to use this effect to transmit classical information at faster-than-light speeds. Research is also focused on the utilization of entanglement effects in communication and computation. In this study, they formulated a experiment that attempted to show that quantum mechanical theory was incomplete. They wrote: "We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete." However, they did not coin the word entanglement, nor did they generalize the special properties of the state they considered. He thereafter published a seminal paper terming it "entanglement." Einstein famously derided entanglement at a distance." The EPR paper inspired much discussion about the foundations of quantum mechanics, but produced little other published work. Until recently each had left open at least one loophole by which it was possible to question the validity of the results. However, in 2015 the first loophole-free experiment was performed, which ruled out a large class of local realism theories with certainty. The work of Bell raised the possibility of using these super-strong correlations as a resource for communication.
Quantum entanglement
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May 4, 1935 New York Times article headline regarding the imminent EPR paper.
Quantum entanglement
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Spontaneous parametric down-conversion process can split photons into type II photon pairs with mutually perpendicular polarization.
9.
Energy level
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A quantum mechanical system or particle, bound—, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels. The spectrum of a system with such discrete energy levels is said to be quantized. The shells are labeled alphabetically with letters used in the X-ray notation. The general formula is that the shell can in principle hold up to 2 electrons. However, this is not a strict requirement: atoms may have two or even three outer shells. For an explanation of why electrons exist in these shells see configuration. If an atom, molecule is at the lowest possible energy level, it and its electrons are said to be in the ground state. If more than quantum mechanical state is at the same energy, the energy levels are "degenerate". They are then called degenerate energy levels. Quantized energy levels result from the relation between its wavelength. For a confined particle such as an electron in an atom, the function has the form of standing waves. Only stationary states with energies corresponding to integral numbers of wavelengths can exist; for other states the waves interfere destructively, resulting in zero density. Elementary examples that show mathematically how energy levels come about are the particle in the quantum harmonic oscillator.
Energy level
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Energy levels for an electron in an atom: ground state and excited states. After absorbing energy, an electron may jump from the ground state to a higher energy excited state.
10.
Quantum state
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In quantum physics, quantum state refers to the state of an isolated quantum system. A state provides a probability distribution for the value of each observable, i.e. for the outcome of each possible measurement on the system. Knowledge of the state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. A mixture of quantum states is again a state. Quantum states that cannot be written as a mixture of other states are called pure quantum states, all other states are called mixed quantum states. Mathematically, a pure state can be represented by a ray in a Hilbert space over the complex numbers. Its phase factor can be chosen freely anyway. Nevertheless, such factors are important when state vectors are added together to form a superposition. It contains all possible pure quantum states of the given system. A mixed state corresponds to a probabilistic mixture of pure states; however, different distributions of pure states can generate equivalent mixed states. Mixed states are described by so-called density matrices. For example, if the spin of an electron is measured in e.g. with a Stern -- Gerlach experiment, there are two possible results: up or down. The Hilbert space for the electron's spin is therefore two-dimensional. A mixed state, in this case, is a 2 × 2 matrix, Hermitian, positive-definite, has 1. This reflects a core difference between classical and quantum physics.
Quantum state
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Probability densities for the electron of a hydrogen atom in different quantum states.
11.
Quantum superposition
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Quantum superposition is a fundamental principle of quantum mechanics. An example of a physically observable manifestation of superposition is interference peaks from an wave in a double-slit experiment. Likewise 1 ⟩ is the state that will always convert to 1. The numbers that describe the amplitudes for different possibilities define the space of different states. The dynamics describes how these numbers change with time. Formally it is an element of a Hilbert space, an infinite dimensional complex vector space. They are mathematically exactly the same except that they are complex numbers. The eigenvalues of the Hermitian matrix H are real quantities which have a physical interpretation as energy levels. But this rotation introduces a linear term. The analogy between probability is very strong, so that there are many mathematical links between them. The analogous expression in quantum mechanics is the integral. The condition is automatically satisfied when n = m, so it has the same form when written as a condition for the transition-probability matrix. The eigenvectors are the same too, except expressed in the rescaled basis. This relationship between stochastic systems and quantum systems sheds much light on supersymmetry. Successful experiments involving superpositions of relatively large objects have been performed.
Quantum superposition
12.
Symmetry in quantum mechanics
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In general, symmetry in physics, conservation laws, are fundamentally important constraints for formulating physical theories and models. In practice, they are powerful methods for predicting what can happen. While conservation laws do not always give the answer to the problem directly, they form the first steps to solving a problem. The notational conventions used in this article are as follows. Boldface indicates vectors, four vectors, vectorial operators, while quantum states use bra -- ket notation. Wide hats are for operators, narrow hats are for unit vectors. The convention on the repeated tensor indices is used, unless stated otherwise. The Minkowski metric signature is. Generally, the correspondence between continuous symmetries and conservation laws is given by Noether's theorem. This can be done for displacements, angles. Additionally, the invariance of certain quantities can be seen by making such changes in angles, which illustrates conservation of these quantities. In what follows, transformations on only one-particle wavefunctions in the form: Ω ^ ψ = ψ are considered, where Ω ^ denotes a unitary operator. Unitarity is generally required for operators representing transformations of space, spin, since the norm of a state must be invariant under these transformations. The inverse is the Hermitian conjugate Ω ^ 1 = Ω ^ †. The results can be extended to many-particle wavefunctions.
Symmetry in quantum mechanics
13.
Quantum tunnelling
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Quantum tunnelling or tunneling refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the Sun. It has important applications to modern devices such as the scanning tunnelling microscope. The effect was predicted in its acceptance as a physical phenomenon came mid-century. Tunnelling is often explained using the wave -- duality of matter. Mechanical concepts are central to the phenomenon, so quantum tunnelling is one of the novel implications of quantum mechanics. Quantum tunnelling was developed from the study of radioactivity, discovered in 1896 by Henri Becquerel. Radioactivity was examined further by Marie Curie and Pierre Curie, for which they earned the Nobel Prize in Physics in 1903. Ernest Rutherford and Egon Schweidler studied its nature, later verified empirically by Friedrich Kohlrausch. The idea of the half-life and the impossibility of predicting decay was created from their work. J. J. Thomson commented the finding warranted further investigation. In 1926, Rother, using a still newer galvanometer of sensitivity 26 pA, measured the emission currents in a "hard" vacuum between closely spaced electrodes. Friedrich Hund was the first to take notice of tunnelling in 1927 when he was calculating the ground state of the double-well potential. Its first application was a mathematical explanation for alpha decay, done independently by Ronald Gurney and Edward Condon. After attending a seminar by Gamow, Max Born recognised the generality of tunnelling.
Quantum tunnelling
14.
Uncertainty principle
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Heisenberg offered such an observer effect as a physical "explanation" of quantum uncertainty. Thus, the principle actually states a fundamental property of quantum systems, is not a statement about the observational success of current technology. Since the principle is such a basic result in quantum mechanics, typical experiments in quantum mechanics routinely observe aspects of it. Certain experiments, however, may deliberately test a particular form of the principle as part of their main research program. These include, for example, tests of number -- uncertainty relations in superconducting or quantum optics systems. Applications dependent on the principle for their operation include extremely low-noise technology such as that required in gravitational wave interferometers. The principle is not readily apparent on the macroscopic scales of everyday experience. So it is helpful to demonstrate how it applies to more easily understood physical situations. Two alternative frameworks for quantum physics offer different explanations for the principle. Its Fourier transform can not both be sharply localized. In matrix mechanics, the mathematical formulation of any pair of non-commuting self-adjoint operators representing observables are subject to similar uncertainty limits. An eigenstate of an observable represents the state of the wavefunction for a certain value. For example, if a measurement of an observable A is performed, then the system is in a particular Ψ of that observable. According to the de Broglie hypothesis, every object in the universe is a wave, i.e. a situation which gives rise to this phenomenon. The position of the particle is described by a wave Ψ.
Uncertainty principle
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Werner Heisenberg and Niels Bohr
Uncertainty principle
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Click to see animation. The evolution of an initially very localized gaussian wave function of a free particle in two-dimensional space, with colour and intensity indicating phase and amplitude. The spreading of the wave function in all directions shows that the initial momentum has a spread of values, unmodified in time; while the spread in position increases in time: as a result, the uncertainty Δx Δp increases in time.
15.
Wave function
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A wave function in quantum mechanics is a description of the quantum state of a system. The probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a function are the Greek letters ψ or Ψ. The function is a function of the degrees of freedom corresponding to some maximal set of commuting observables. Once such a representation is chosen, the function can be derived from the quantum state. The wave function for such particles includes spin as an intrinsic, discrete degree of freedom. Discrete variables can also be included, such as isospin. These values are often displayed in a matrix. The Schrödinger equation determines how wave functions evolve over time. This gives rise to wave -- particle duality. Since the function is complex valued, only its relative phase and relative magnitude can be measured. The equations represent wave -- duality for both massless and massive particles. In the 1930s, quantum mechanics was developed using calculus and linear algebra. Those who used the techniques of calculus included Louis de Broglie, others, developing "wave mechanics". Those who applied the methods of linear algebra included Werner Heisenberg, others, developing "matrix mechanics".
Wave function
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The electron probability density for the first few hydrogen atom electron orbitals shown as cross-sections. These orbitals form an orthonormal basis for the wave function of the electron. Different orbitals are depicted with different scale.
16.
Afshar experiment
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Afshar's experiment uses a variant of Thomas Young's double-slit experiment to create interference patterns to investigate complementarity. Such interferometer experiments typically paths a photon may take. The results were published as conference proceeding by the International Society for Optical Engineering. The experiment was featured as the story in the July 24, 2004 edition of New Scientist. Afshar presented his work also at the American Physical Society meeting in late March 2005. His peer-reviewed paper was published in January 2007. Afshar claims that his experiment has far-reaching implications for the understanding of quantum mechanics, challenging the Copenhagen interpretation. According to Cramer, Afshar's results challenge the many-worlds interpretation of quantum mechanics. This claim has not been published in a peer reviewed journal. The experiment uses a setup similar to that for the double-slit experiment. In Afshar's variant, light generated by a laser passes through two closely spaced circular pinholes. After the dual pinholes, a lens refocuses the light so that the image of each pinhole falls on separate photon-detectors. Because of quantum interference one can observe that there are regions that the photons avoid, called dark fringes. Some of the light will be blocked by the wires. Consequently, the quality is reduced.
Afshar experiment
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Fig.1 Experiment without obstructing wire grid
17.
Bell test experiments
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Under local realism, correlations between outcomes of different measurements performed on separated physical systems have to satisfy certain constraints, called Bell inequalities. John Bell derived the first inequality of this kind in his paper "On the Einstein-Podolsky-Rosen Paradox". Bell's Theorem states that the predictions of concerning correlations, being inconsistent with Bell's inequality, can not be reproduced by any local hidden variable theory. However, this doesn't disprove variable theories that are nonlocal such as Bohmian Mechanics. A Bell experiment is one designed to test whether or not the real world satisfies local realism. The property of interest is, in the polarisation direction, though other properties can be used. Such experiments fall depending on whether the analysers used have one or two output channels. The diagram shows a optical experiment of the two-channel kind for which Alain Aspect set a precedent in 1982. Coincidences are recorded, the results being categorised as' + +',' + −',' − +' or' − corresponding counts accumulated. Four separate subexperiments are conducted, corresponding to the four terms E in the test statistic S. For each selected value of a and b, the numbers of coincidences in each category are recorded. The experimental estimate for E is then calculated as: E = /. Once all four E's have been estimated, an experimental estimate of the statistic S = E − E + E + E can be found. If S is numerically greater than 2 it has infringed the CHSH inequality. The experiment ruled out all local hidden variable theories.
Bell test experiments
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Scheme of a "two-channel" Bell test The source S produces pairs of "photons", sent in opposite directions. Each photon encounters a two-channel polariser whose orientation can be set by the experimenter. Emerging signals from each channel are detected and coincidences counted by the coincidence monitor CM.
18.
Double-slit experiment
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A simpler form of the double-slit experiment was performed originally by Thomas Young in 1801. He believed it demonstrated that the wave theory of light was correct and his experiment is sometimes referred to as Young's experiment or Young's slits. Changes in the path lengths of both waves result in a phase shift, creating an interference pattern. Another version is the Mach–Zehnder interferometer, which splits the beam with a mirror. Furthermore, versions of the experiment that include detectors at the slits find that each detected photon passes through one slit, not through both slits. However, such experiments demonstrate that particles do not form the interference pattern if one detects which slit they pass through. These results demonstrate the principle of wave–particle duality. Other atomic-scale entities such as electrons are found to exhibit the same behavior when fired towards a double slit. Additionally, the detection of individual discrete impacts is observed to be inherently probabilistic, inexplicable using classical mechanics. The experiment can be done with entities much larger than electrons and photons, although it becomes more difficult as size increases. The largest entities for which the double-slit experiment has been performed were molecules that each comprised 810 atoms. However, when this "single-slit experiment" is actually performed, the pattern on the screen is a diffraction pattern in which the light is spread out. The smaller the slit, the greater the angle of spread. More bands can be seen with a more highly refined apparatus. Diffraction explains the pattern as being the result of the interference of light waves from the slit.
Double-slit experiment
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Same double-slit assembly (0.7 mm between slits); in top image, one slit is closed. In the single-slit image, a diffraction pattern (the faint spots on either side of the main band) forms due to the nonzero width of the slit. A diffraction pattern is also seen in the double-slit image, but at twice the intensity and with the addition of many smaller interference fringes.
Double-slit experiment
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Photons or particles of matter (like an electron) produce a wave pattern when two slits are used
Double-slit experiment
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Electron buildup over time
Double-slit experiment
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A laboratory double-slit assembly; distance between top posts approximately 2.5 cm (one inch).
19.
Popper's experiment
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Popper's experiment is an experiment proposed by the philosopher Karl Popper. As early as 1934 he was proposing experiments to test, the Copenhagen interpretation, a popular subjectivist interpretation of quantum mechanics. Popper's experiment is a realization of an argument similar to the thought experiment of Einstein, Podolsky and Rosen although not as well known. There are various interpretations of quantum mechanics that do not agree with each other. Despite their differences, they are experimentally nearly indistinguishable from each other. The most widely known interpretation of quantum mechanics is the Copenhagen interpretation put forward by Niels Bohr. It says that observations lead to a collapse, thereby suggesting the counter-intuitive result that two well separated, non-interacting systems require action-at-a-distance. Popper argued that non-locality conflicts with common sense, also with what was known at the time from astronomy and the "technical success of physics." "hey all suggest the exclusion of action at a distance." While Einstein's EPR argument involved a experiment, Popper proposed a physical experiment to test for such action-at-a-distance. Popper first proposed an experiment that would test indeterminacy in quantum mechanics in two works of 1934. In the 1950s he formulated this later experiment, finally published in 1982. There are one each in the paths of the two particles. Behind the slits are semicircular arrays of counters which can detect the particles after they pass through the slits. "These counters are coincident counters that they only detect particles that have passed through A and B."
Popper's experiment
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Fig.1 Experiment with both slits equally wide. Both the particles should show equal scatter in their momenta.
20.
Quantum eraser experiment
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Next, the experimenter marks through which slit each photon went, without disturbing its wavefunction, demonstrates that thereafter the interference pattern is destroyed. This stage indicates that it is the existence of the "which-path" information that causes the destruction of the interference pattern. Third, the "which-path" information is "erased," whereupon the interference pattern is recovered. A key result is that it does not matter whether the eraser procedure is done before or after the photons arrive at the detection screen. Quantum erasure technology can be used to increase the resolution of advanced microscopes. The experiment described in this article is a variation of Thomas Young's double-slit experiment. It establishes that when action is taken to determine which slit a photon has passed through, the photon cannot interfere with itself. When a stream of photons is marked in this way, then the interference fringes characteristic of the Young experiment will not be seen. This experiment involves an apparatus with two main sections. After two entangled photons are created, each is directed into its own section of the apparatus. In doing so, the experimenter restores interference without altering the double-slit part of the experimental apparatus. In delayed-choice experiments quantum effects can mimic an influence of future actions on past events. However, the temporal order of measurement actions is not relevant. First, a photon is shot through a specialized nonlinear optical device: a beta barium borate crystal. This crystal converts the single photon into two entangled photons of lower frequency, a process known as spontaneous parametric down-conversion.
Quantum eraser experiment
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Figure 1. Crossed polarizations prevent interference fringes
21.
Delayed choice quantum eraser
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The experiment was designed to investigate peculiar consequences of the double-slit experiment in quantum mechanics, as well as the consequences of quantum entanglement. The delayed choice quantum experiment investigates a paradox. If a photon manifests itself as though it had come by two indistinguishable paths, then it must have entered the double-slit device as a wave. Recent experiments have supported it. In the double slit experiment, a beam of light is directed perpendicularly towards a wall pierced by two parallel slit apertures. Atomic-scale entities such as electrons are found to exhibit the same behavior when fired toward a double slit. By decreasing the brightness of the source sufficiently, individual particles that form the pattern are detectable. This is an idea that contradicts our everyday experience of discrete objects. This which-way experiment illustrates the complementarity principle that photons can behave as either waves, but not both at the same time. However, technically feasible realizations of this experiment were not proposed until the 1970s. The visibility of interference fringes are hence complementary quantities. However, in 1982, Scully and Drühl found a loophole around this interpretation. They proposed a "quantum eraser" to obtain which-path information without scattering the particles or otherwise introducing uncontrolled phase factors to them. Lest there be any misunderstanding, the pattern does disappear when the photons are so marked. Since 1982, multiple experiments have demonstrated the validity of the so-called quantum "eraser."
Delayed choice quantum eraser
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Figure 1. Experiment that shows delayed determination of photon path
22.
Wheeler's delayed choice experiment
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Wheeler's intent was to investigate the time-related conditions under which a photon makes this transition between alleged states of being. His work has been productive of revealing experiments. However, himself seems to be very clear on this point. Either it was a particle; either it went both ways around the galaxy or only one way. Actually, quantum phenomena are intrinsically undefined until the moment they are measured. In a sense, the British philosopher Bishop Berkeley was right when he asserted two centuries ago "to be is to be perceived." This line of experimentation proved very difficult to carry out when it was first conceived. Nevertheless, it has proven very valuable over the years since it has led researchers to provide "increasingly sophisticated demonstrations of the wave -- duality of single quanta." As one experimenter explains, "Wave and behavior can coexist simultaneously." "Wheeler's delayed choice experiment" refers to a series of thought experiments in quantum physics, the first being proposed by him in 1978. Another prominent version was proposed in 1983. All of these experiments try to get in quantum physics. According to the complementarity principle, a photon can manifest properties of a wave, but not both at the same time. What characteristic is manifested depends on whether experimenters use a device intended to observe waves. Detection of a photon is a destructive process because a photon can never be seen in flight.
Wheeler's delayed choice experiment
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Double quasar known as QSO 0957+561, also known as the "Twin Quasar", which lies just under 9 billion light-years from Earth.
Wheeler's delayed choice experiment
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Open and Closed
23.
Mathematical formulation of quantum mechanics
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The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. Many of these structures are drawn from a area within pure mathematics, influenced in part by the needs of quantum mechanics. These formulations of quantum mechanics continue to be used today. While the mathematics permits calculation of many quantities that can be measured experimentally, there is a definite theoretical limit to values that can be simultaneously measured. Probability theory was used in statistical mechanics. Geometric intuition played a strong role in the first two and, accordingly, theories of relativity were formulated entirely in terms of geometric concepts. The most sophisticated example of this is the Sommerfeld -- Wilson -- Ishiwara rule, formulated entirely on the classical space. Planck postulated a direct proportionality between the frequency of radiation and the quantum of energy at that frequency. The proportionality constant, h, is now called Planck's constant in his honor. In 1905, Einstein explained certain features of the photoelectric effect by assuming that Planck's energy quanta were actual particles, which were later dubbed photons. All of these developments were phenomenological and challenged the theoretical physics of the time. Bohr and Sommerfeld went on to modify classical mechanics in an attempt to deduce the Bohr model from first principles. The most sophisticated version of this formalism was the so-called Sommerfeld–Wilson–Ishiwara quantization. Although the Bohr model of the hydrogen atom could be explained in this way, the spectrum of the helium atom could not be predicted. The mathematical status of quantum theory remained uncertain for some time.
Mathematical formulation of quantum mechanics
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Quantum mechanics
24.
Phase space formulation
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The phase space formulation of quantum mechanics places the position and momentum variables on equal footing, in phase space. In contrast, the Schrödinger picture uses the position or momentum representations. This formulation offers logical connections between classical statistical mechanics, enabling a natural comparison between the two. The conceptual ideas underlying the development of quantum mechanics in space have branched into mathematical offshoots such as noncommutative geometry. The phase f of a quantum state is a quasiprobability distribution. There are several different ways to represent the distribution, all interrelated. The most noteworthy is the Wigner representation, W, discovered first. Other representations include Born-Jordan representations. These alternatives are most useful when the Hamiltonian takes a particular form, such as normal order for the Glauber–Sudarshan P-representation. Since the Wigner representation is the most common, this article will usually stick to it, unless otherwise specified. The distribution possesses properties akin to the probability density in a 2n-dimensional phase space. For example, it is real-valued, unlike the generally complex-valued wave function. If Â is an operator representing an observable, it may be mapped to phase space as A through the Wigner transform. Conversely, this operator may be recovered via the Weyl transform. The value of the observable with respect to the phase distribution is ⟨ A ^ ⟩ = ∫ A W d p d x.
Phase space formulation
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The Wigner quasiprobability distribution F n (u) for the simple harmonic oscillator with a) n = 0, b) n = 1, and c) n = 5.
Phase space formulation
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Time evolution of combined ground and 1st excited state Wigner function for the simple harmonic oscillator. Note the rigid motion in phase space corresponding to the conventional oscillations in coordinate space.
25.
Path integral formulation
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The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics. Unlike previous methods, the path-integral allows a physicist to easily change coordinates between very different canonical descriptions of the same quantum system. Possible downsides of the approach include that unitarity of the S-matrix is obscure in the formulation. The path-integral approach has been proved to be equivalent to the other formalisms of theory. Thus, by deriving either approach from the other, problems associated with one or the other approach go away. This idea was extended to the use of the Lagrangian in quantum mechanics by P. A. M. Dirac in his 1933 paper. The complete method was developed in 1948 by Richard Feynman. Some preliminaries were worked out earlier in his doctoral work under the supervision of John Archibald Wheeler. The original motivation stemmed from the desire to obtain a quantum-mechanical formulation for the Wheeler–Feynman absorber theory using a Lagrangian as a starting point. In quantum mechanics, as in classical mechanics, the Hamiltonian is the generator of time-translations. The Hamiltonian in classical mechanics is derived from a Lagrangian, a more fundamental quantity relative to special relativity. The Hamiltonian indicates how to march forward in time, but the time is different in different reference frames. So the Hamiltonian is different in different frames, this type of symmetry is not apparent in the original formulation of quantum mechanics. The Hamiltonian is a function of the position and momentum at one time, it determines the position and momentum a little later. The Lagrangian is a function of the position now and the position a little later.
Path integral formulation
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These are just three of the paths that contribute to the quantum amplitude for a particle moving from point A at some time t 0 to point B at some other time t 1.
26.
Dirac equation
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In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. Including electromagnetic interactions, it describes all spin-1 / 2 massive particles such as electrons and quarks for which parity is a symmetry. It was validated by accounting for the fine details of the spectrum in a completely rigorous way. The equation also implied the existence of a new form of antimatter, previously unsuspected and unobserved and, experimentally confirmed several years later. Moreover, in the limit of zero mass, the Dirac equation reduces to the Weyl equation. This accomplishment has been described as fully before him. In the context of quantum theory, the Dirac equation is reinterpreted to describe quantum fields corresponding to spin-1 / 2 particles. The p1, p2, p3 are the components of the momentum, understood to be the operator in the Schrödinger equation. Also, ħ is the Planck constant divided by 2π. These physical constants reflect special relativity and quantum mechanics, respectively. His rather modest hope was that the corrections introduced this way might have a bearing on the problem of atomic spectra. The four-component wave function ψ. There are four components in ψ because the evaluation of it at any given point in space is a bispinor. It is interpreted as a superposition of a spin-up electron, a spin-down electron, a spin-down positron. The form of the wave function have a deep mathematical significance.
Dirac equation
27.
Rydberg formula
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The Rydberg formula is used in atomic physics to describe the wavelengths of spectral lines of many chemical elements. It was formulated by the Swedish physicist Johannes Rydberg, presented on 5 November 1888. In 1880, Rydberg worked on a formula describing the relation between the wavelengths in spectral lines of alkali metals. He noticed that lines came in series and he found that he could simplify his calculations by using the wavenumber as his unit of measurement. He plotted the wavenumbers of successive lines in each series against consecutive integers which represented the order of the lines in that particular series. Finding that the resulting curves were similarly shaped, he sought a single function which could generate all of them, when appropriate constants were inserted. This did not work very well. Rydberg therefore rewrote Balmer's formula in terms of wavenumbers, as n = n 0 − 4 n 0 m 2. The term Co was found to be a universal constant common to all elements, equal to 4/h. M' is known as the defect. As stressed by Niels Bohr, expressing results in terms of wavenumber, not wavelength, was the key to Rydberg's discovery. The fundamental role of wavenumbers was also emphasized by the Rydberg-Ritz combination principle of 1908. The fundamental reason for this lies in quantum mechanics. Rydberg's 1888 classical expression for the form of the spectral series was not accompanied by a physical explanation. In Bohr's conception of the atom, the integer Rydberg n numbers represent electron orbitals at different integral distances from the atom.
Rydberg formula
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Rydberg's formula as it appears in a November 1888 record
28.
Interpretations of quantum mechanics
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An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to thorough experimental testing, many of these experiments are open to different interpretations. This question is to philosophers of physics as physicists continue to show a strong interest in the subject. The definition such as wavefunctions and matrix mechanics, progressed through many stages. Although the Copenhagen interpretation was originally most popular, decoherence has gained popularity. Thus the many-worlds interpretation has been gaining acceptance. The authors reference a similarly informal poll carried out at the "Fundamental Problems in Quantum Theory" conference in August 1997. In Tegmark's poll, the Everett interpretation received 17% of the vote, similar to the number of votes in our poll." A general law is a regularity of outcomes, whereas a causal mechanism may regulate the outcomes. A phenomenon can receive interpretation either epistemic. For instance, indeterminism may be explained as a real existing maybe encoded in the universe. In a broad sense, scientific theory might be perceived with antirealism. A stance seeks the epistemic and the ontic, whereas an antirealist stance seeks epistemic but not the ontic. In the 20th century's first half, antirealism was mainly logical positivism, which sought to exclude unobservable aspects of reality from scientific theory. The view is carried by the famous quote of David Mermin, "Shut up and calculate", often misattributed to Richard Feynman.
Interpretations of quantum mechanics
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Schrödinger
Interpretations of quantum mechanics
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Born
Interpretations of quantum mechanics
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Everett
29.
Many-worlds interpretation
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The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction and denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternate histories and futures are real, each representing an actual "world". The theory is also referred to as MWI, the relative state formulation, the Everett interpretation, the theory of the universal wavefunction, many-universes interpretation, or just many-worlds. The original relative state formulation is due to Hugh Everett in 1957. Later, this formulation was popularized and renamed many-worlds by Bryce Seligman DeWitt in the 1960s and 1970s. The decoherence approaches to interpreting quantum theory have been further explored and developed, becoming quite popular. MWI is one of many multiverse hypotheses in physics and philosophy. It is currently considered a mainstream interpretation along with the other decoherence interpretations, collapse theories, hidden variable theories such as the Bohmian mechanics. Before many-worlds, reality had always been viewed as a single unfolding history. Many-worlds, however, views reality as a many-branched tree, wherein every possible quantum outcome is realised. Many-worlds reconciles the observation of non-deterministic events, such as random radioactive decay, with the fully deterministic equations of quantum physics. It was that, when his Nobel equations seem to be describing several different histories, they are "not alternatives but all really happen simultaneously". This is the earliest known reference to the many-worlds. "Under scrutiny of the environment, only pointer states remain unchanged. Other states decohere into mixtures of stable pointer states that can persist, and, in this sense, exist: They are einselected."
Many-worlds interpretation
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Hugh Everett III (1930–1982) was the first physicist who proposed the many-worlds interpretation (MWI) of quantum physics, which he termed his "relative state" formulation.
Many-worlds interpretation
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The quantum-mechanical " Schrödinger's cat " paradox according to the many-worlds interpretation. In this interpretation, every event is a branch point; the cat is both alive and dead, even before the box is opened, but the "alive" and "dead" cats are in different branches of the universe, both of which are equally real, but which do not interact with each other.
30.
Relational quantum mechanics
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This article is intended for those already familiar with quantum mechanics and its attendant interpretational difficulties. Readers who are new to the subject may first want to read the introduction to quantum mechanics. This interpretation has since been expanded upon by a number of theorists. The physical content of the theory is not to the relations between them. However, it is held by RQM that this applies to all physical objects, whether or not they are macroscopic. Any "event" is seen simply as an ordinary physical interaction, an establishment of the sort of correlation discussed above. David Mermin has contributed to the relational approach in his "interpretation." The moniker "Zero Worlds" has been popularized by Garret to contrast with the Many Worlds Interpretation. This problem was initially discussed in Everett's thesis, The Theory of the Universal Wavefunction. Consider observer O, measuring the state of the system S. We assume that O can write down the wavefunction | ψ ⟩ describing it. Now, the O wishes to make a measurement on the system. For our purposes here, we can assume that in a single experiment, the outcome is the eigenstate | ↑ ⟩. This is observer O's description of the event. Now, any measurement is also a physical interaction between two or more systems.
Relational quantum mechanics
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The EPR thought experiment, performed with electrons. A radioactive source (center) sends electrons in a singlet state toward two spacelike separated observers, Alice (left) and Bob (right), who can perform spin measurements. If Alice measures spin up on her electron, Bob will measure spin down on his, and vice versa.
31.
Scale relativity
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Scale relativity is a geometrical and fractal space-time theory. The idea of a space-time theory was first introduced by Garnet Ord, by Laurent Nottale in a paper with Jean Schneider. The proposal to combine space-time theory with relativity principles was made by Nottale. The resulting scale theory is an extension of the concept of relativity found in special relativity and general relativity to physical scales. Noticing the relativity as noticing the other forms of relativity is just a first step. Scale theory proposes to extend this insight by introducing an explicit "state of scale" in coordinate systems. To describe scale transformations requires the use of fractal geometries, which are typically concerned with scale changes. Scale relativity is thus an extension of relativity theory to the concept of scale, using fractal geometries to study scale transformations. The construction of the theory is similar to previous relativity theories, with three different levels: Galilean, general. The development of a general scale relativity is not finished yet. Richard Feynman developed a path integral formulation of quantum mechanics before 1966. Searching for the most important paths relevant for quantum particles, Feynman noticed that such paths were very irregular on small scales, non-differentiable. This means that in between two points, a particle can have not an infinity of potential paths. This can be illustrated with a concrete example. Imagine that you are free to walk wherever you like.
Scale relativity
32.
Quantum information science
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Quantum information science is an area of study based on the idea that information science depends on quantum effects in physics. It includes theoretical issues in computational models well as more experimental topics in quantum physics including what can not be done with information. The term quantum information theory is sometimes used, but it fails to encompass experimental research in the area. No-communication theorem Quantum decision tree complexity Quantum capacity Quantum communication channel Entanglement-assisted classical capacity Nielsen, M.A. and Chuang, I.L. Quantum computation and quantum information. Cambridge University Press, 2000. ISBN 0-521-63235-8 Quantiki – quantum information science portal and wiki. ERA-Pilot QIST WP1 European roadmap on Quantum Information Processing and Communication QIIC – Quantum Information, Imperial College London. QIP – Quantum Information Group, University of Leeds. The group at the University of Leeds is engaged in researching a wide spectrum of aspects of information. This ranges from algorithms, quantum computation, to physical implementations of information processing and fundamental issues in quantum mechanics. Also contains some basic tutorials for the lay audience. MathQI Research Group on Mathematics and Quantum Information. CQT Centre for Quantum Technologies at the National University of Singapore
Quantum information science
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General
33.
Quantum computing
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Quantum computing studies theoretical computation systems that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from binary digital electronic computers based on transistors. A quantum Turing machine is a theoretical model of such a computer, is also known as the universal quantum computer. Quantum computers share theoretical similarities with non-deterministic and probabilistic computers. A quantum computer with spins as quantum bits was also formulated for use as a quantum space–time in 1968. There exist quantum algorithms, such as Simon's algorithm, that run faster than any possible probabilistic classical algorithm. Given sufficient computational resources, a classical computer could in theory simulate any quantum algorithm, as quantum computation does not violate the Church–Turing thesis. On the other hand, quantum computers may be able to efficiently solve problems which are not practically feasible on classical computers. A classical computer has a memory made up of bits, where each bit is represented by either a one or a zero. A quantum computer maintains a sequence of qubits. In general, a quantum computer with n qubits can be in an arbitrary superposition of up to 2 n different states simultaneously. The sequence of gates to be applied is called a quantum algorithm. The outcome can therefore be at most n classical bits of information. Quantum algorithms are often probabilistic, in that they provide the correct solution only with a certain known probability. An example of an implementation of qubits of a quantum computer could start with the use of particles with two spin states: "down" and "up".
Quantum computing
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Photograph of a chip constructed by D-Wave Systems Inc., mounted and wire-bonded in a sample holder. The D-Wave processor is designed to use 128 superconducting logic elements that exhibit controllable and tunable coupling to perform operations.
Quantum computing
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The Bloch sphere is a representation of a qubit, the fundamental building block of quantum computers.
34.
Quantum chaos
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Quantum chaos is a branch of physics which studies how chaotic classical dynamical systems can be described in terms of quantum theory. The primary question that chaos seeks to answer is: "What is the relationship between quantum mechanics and classical chaos?" The principle states that classical mechanics is the classical limit of quantum mechanics. If this is true, then there must be quantum mechanisms underlying classical chaos; although this may not be a fruitful way of examining classical chaos. Correlating statistical descriptions of eigenvalues with the classical behavior of the same Hamiltonian. Semiclassical methods such as periodic-orbit theory connecting the classical trajectories of the dynamical system with quantum features. Direct application of the correspondence principle. During the first half of the twentieth century, chaotic behavior in mechanics was recognized, but not well-understood. Other phenomena show up in its response to various types of external forces. Such as acoustics or microwaves, wave patterns are directly observable and exhibit irregular amplitude distributions. Quantum chaos typically deals with systems whose properties need to be calculated using either numerical techniques or approximation schemes. Finding constants of motion so that this separation can be performed can be a analytical task. Solving the classical problem can give valuable insight into solving the problem. Other approaches have been developed in recent years. One is to express the Hamiltonian in coordinate systems in different regions of space, minimizing the non-separable part of the Hamiltonian in each region.
Quantum chaos
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Quantum chaos is the field of physics attempting to bridge the theories of quantum mechanics and classical mechanics. The figure shows the main ideas running in each direction.
Quantum chaos
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Experimental recurrence spectra [disambiguation needed] of lithium in an electric field showing birth of quantum recurrences corresponding to bifurcations of classical orbits.
Quantum chaos
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Comparison of experimental and theoretical recurrence spectra [disambiguation needed] of lithium in an electric field at a scaled energy of.
Quantum chaos
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Computed regular (non-chaotic) Rydberg atom energy level spectra of hydrogen in an electric field near n=15. Note that energy levels can cross due to underlying symmetries of dynamical motion.
35.
Density matrix
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A density matrix is a matrix that describes a quantum system in a mixed state, a statistical ensemble of several quantum states. This should be contrasted with a single vector that describes a system in a pure state. The matrix is the quantum-mechanical analogue to a phase-space measure in classical statistical mechanics. Mixed states arise in situations where the experimenter does not know which particular states are being manipulated. Examples include a system with an uncertain or randomly varying history. The matrix is also a crucial tool in quantum theory. The matrix is a representation of a linear operator called the operator. The close relationship between matrices and operators is a basic concept in linear algebra. In practice, operator are often used interchangeably. Both operator may be infinite-dimensional. In quantum mechanics, the state of a system is represented by a vector | ψ ⟩. A system with a vector | ψ ⟩ is called a pure state. This system would be in a mixed state. The matrix is especially useful for mixed states, because any state, mixed, can be characterized by a single density matrix. A mixed state is different from a quantum superposition.
Density matrix
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The incandescent light bulb (1) emits completely random polarized photons (2) with mixed state density matrix 。 After passing through vertical plane polarizer (3), the remaining photons are all vertically polarized (4) and have pure state density matrix 。
36.
Scattering theory
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In mathematics and physics, scattering theory is a framework for studying and understanding the scattering of waves and particles. Wave scattering corresponds to the collision and scattering of a wave with some material object, for instance sunlight scattered by rain drops to form a rainbow. The direct scattering problem is the problem of determining the distribution of scattered radiation/particle flux basing on the characteristics of the scatterer. The inverse scattering problem is the problem of determining the characteristics of an object from measurement data of radiation or particles scattered from the object. The concepts used in scattering theory go by different names in different fields. The object of this section is to point the reader to common threads. Hence one converts between these quantities via Q = 1/λ = ησ = ρ/τ, as shown in the figure at left. For example, coefficient is variously called opacity, attenuation coefficient. In mathematical physics, scattering theory is a framework for studying and understanding the interaction or scattering of solutions to partial differential equations. In the case of classical electrodynamics, the differential equation is again the wave equation, the scattering of light or radio waves is studied. In particle physics, the equations are those of Quantum electrodynamics, Quantum chromodynamics and the Standard Model, the solutions of which correspond to fundamental particles. The solutions of interest describe the long-term motion of free atoms, protons. The scenario is that several particles come together from an infinite distance away. These reagents then collide, optionally reacting, getting destroyed or creating new particles. The products and unused reagents then fly away to infinity again.
Scattering theory
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Equivalent quantities used in the theory of scattering from composite specimens, but with a variety of units.
37.
Yakir Aharonov
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Yakir Aharonov is an Israeli physicist specializing in quantum physics. He is the James J. Farley Professor of Natural Philosophy at Chapman University in California. He is also a professor emeritus at Tel Aviv University in Israel. He is president of The Israeli Institute for Advanced Research. Yakir Aharonov was born in Haifa. He received his undergraduate education in Haifa graduating with a BSc in 1956. His research interests are topological effects in quantum mechanics, quantum field theories and interpretations of quantum mechanics. In 1959, David Bohm proposed the Aharonov -- Bohm effect for which he co-received the 1998 Wolf Prize. In 1988 Aharonov et al. published their theory of weak values. Verifying a present effect of a future cause requires a measurement, which would ordinarily destroy coherence and ruin the experiment. His colleagues claim that they were able to use weak measurements and verify the present effect of the future cause. 2010: National Medal of Science, awarded and presented by President Barack Obama.
Yakir Aharonov
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Yakir Aharonov
38.
John Stewart Bell
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John Stewart Bell FRS was a Northern Irish physicist, the originator of Bell's theorem, an important theorem in quantum physics regarding hidden variable theories. John Bell was born in Northern Ireland. Both sides of his family were of Ulster Scots roots. When he was 11 years old, he at 16 graduated from Belfast Technical High School. Bell then obtained a bachelor's degree in experimental physics in 1948, one in mathematical physics a year later. He went on specialising in nuclear physics and quantum field theory. In 1954, he married Mary Ross, also a physicist, whom he had met while working at Malvern, UK. Bell became a vegetarian in his teen years. According to his wife, Bell was an atheist. Bell's career began near Harwell, Oxfordshire, known as AERE or Harwell Laboratory. After several years he moved to work for the European Organization in Geneva, Switzerland. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1987. Bell was a proponent of pilot theory. In this work, he showed that carrying forward EPR's analysis permits one to derive the famous Bell's theorem. The resultant inequality, derived from certain assumptions, is violated by theory.
John Stewart Bell
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John Bell receiving an Honorary degree at Queen's University Belfast, July 1988
John Stewart Bell
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Blue plaque honouring John Bell at the Queen's University of Belfast
39.
Patrick Blackett
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Blackett also made a major contribution in World War II developing operational research. His left-wing views saw an outlet in influencing policy in the Labour Government of the 1960s. He was born in the son of Arthur Stuart Blackett, a stockbroker, his wife Caroline Maynard. His younger sister was the psychoanalyst Marion Milner. Brother of Edmund Blacket the Australian architect, was for many years Vicar of Croydon. Charles Maynard was an officer in the Royal Artillery at the time of the Indian Mutiny. The Blackett family lived successively at Kensington, Kenley, Woking and Guildford, Surrey, where Blackett went to preparatory school. His main hobbies were crystal radio. Blackett was spent two years there before moving on to Dartmouth where he was "usually head of his class". In August 1914 on the outbreak of World War I Blackett was assigned as a midshipman. Blackett was present at the Battle of the Falkland Islands. Blackett saw much action at the Battle of Jutland. While on HMS Barham, he was co-inventor of a gunnery device on which the Admiralty took out a patent. His application was refused. Blackett had decided to leave the Navy.
Patrick Blackett
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Patrick Blackett, ca. 1950
40.
Felix Bloch
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Felix Bloch was a Swiss physicist, working mainly in the U.S. Edward Mills Purcell were awarded the 1952 Nobel Prize for "their development of new ways and methods for nuclear magnetic precision measurements." In 1954–1955, he served for one year as the first Director-General of CERN. Bloch was born to Jewish parents Gustav and Agnes Bloch. He was educated in Zürich. Initially studying engineering he soon changed to physics. A fellow student in these seminars was John von Neumann. Graduating in 1927 he continued his physics studies with Werner Heisenberg gaining his doctorate in 1928. His doctoral thesis established the theory of solids, using Bloch waves to describe the electrons. In 1940 he married Lore Misch. In 1933, immediately after Hitler came to power, he left Germany because he was Jewish. He emigrated to work at Stanford University in 1934. In the fall of 1938, Bloch began working with the University of California at Berkeley 37" cyclotron to determine the magnetic moment of the neutron. Bloch went on to become the first professor for theoretical physics at Stanford. In 1939, he became a naturalized citizen of the United States.
Felix Bloch
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Felix Bloch
Felix Bloch
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Felix Bloch in the lab, 1950s
41.
David Bohm
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To complement it, Bohm developed a physical theory of "implicate" and "explicate" order. In this, his epistemology mirrored his ontology. Due to his Communist affiliations, he was the subject of a federal government investigation in 1949, prompting him to leave the United States. Bohm pursued his scientific career in several countries, becoming first a Brazilian and then a British citizen. He was born to a Hungarian Jewish immigrant father, Samuel Bohm, a Lithuanian Jewish mother. Bohm was raised mainly by his father, assistant of the local rabbi. Despite being raised in a Jewish family, Bohm became an agnostic in his teenage years. He attended Pennsylvania State College, graduating in 1939, then the California Institute of Technology, for one year. Bohm then transferred at the University of California, Berkeley where he obtained his doctorate. He with them became increasingly involved in radical politics. Bohm was active including the Young Communist League, the Campus Committee to Fight Conscription, the Committee for Peace Mobilization. During World War II, the Manhattan Project mobilized much of Berkeley's research in the effort to produce the first atomic bomb. He remained in Berkeley, teaching physics, until he completed his Ph.D. by an unusual circumstance. According to Peat, "the scattering calculations that he had completed were immediately classified. To satisfy the university, Oppenheimer certified that Bohm had successfully completed the research.
David Bohm
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David Bohm
David Bohm
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Sites
42.
Niels Bohr
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Bohr was also a philosopher and a promoter of scientific research. Although the Bohr model has been supplanted by other models, its underlying principles remain valid. The notion of complementarity dominated Bohr's thinking in both science and philosophy. Bohr founded the Institute of Theoretical Physics at the University of Copenhagen, now known as the Niels Bohr Institute, which opened in 1920. He collaborated with physicists including Hans Kramers, Oskar Klein, Werner Heisenberg. He predicted the existence of a new zirconium-like element, named hafnium, after the Latin name for Copenhagen, where it was discovered. Later, the element bohrium was named after him. During the 1930s, Bohr helped refugees from Nazism. After Denmark was occupied by the Germans, Bohr had a famous meeting with Heisenberg, who had become the head of the nuclear project. In September 1943, word reached Bohr that he was about to be arrested by the Germans, he fled to Sweden. After the war, Bohr called for international cooperation on nuclear energy. Bohr had a younger brother Harald. Jenny became a teacher, while Harald became a mathematician and Olympic footballer who played for the Danish national team at the 1908 Summer Olympics in London. The two brothers played several matches for the Copenhagen-based Akademisk Boldklub, as goalkeeper. Bohr was educated at Gammelholm Latin School, starting when he was seven.
Niels Bohr
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Bohr in 1922
Niels Bohr
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Niels Bohr as a young man
Niels Bohr
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Niels Bohr and Margrethe Nørlund on their engagement in 1910.
Niels Bohr
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The Niels Bohr Institute
43.
Max Born
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Max Born was a German physicist and mathematician, instrumental in the development of quantum mechanics. He also supervised the work of a number of notable physicists in the 1920s and 1930s. Born won the 1954 Nobel Prize in the statistical interpretation of the wave function". He wrote his Ph.D. thesis on the subject of "Stability of Elastica in a Plane and Space", winning the University's Philosophy Faculty Prize. In 1905, he subsequently wrote his habilitation thesis on the Thomson model of the atom. In 1921, Born returned to Göttingen, arranging another chair for colleague James Franck. Under Born, Göttingen became one of the world's foremost centres for physics. In 1925, Werner Heisenberg formulated the matrix mechanics representation of quantum mechanics. His influence extended far beyond his own research. In January 1933, Born, Jewish, was suspended. Max Born became a British subject on 31 August 1939, one day before World War II broke out in Europe. He remained until 1952. He died in a hospital in Göttingen on 5 January 1970. She died when Max was four years old, on 29 August 1886. Max had a half-brother, Wolfgang, from his father's second marriage, to Bertha Lipstein.
Max Born
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Max Born (1882–1970)
Max Born
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Solvay Conference, 1927. Born is second from the right in the second row, between Louis de Broglie and Niels Bohr.
Max Born
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Born's gravestone in Göttingen is inscribed with the uncertainty principle, which he put on rigid mathematical footing.
44.
Satyendra Nath Bose
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Satyendra Nath Bose, FRS was an Indian physicist from Bengal specialising in theoretical physics. A Fellow of the Royal Society, he was awarded India's second highest civilian award, the Padma Vibhushan in 1954 by the Government of India. The class of particles that obey Bose–Einstein statistics, bosons, was named after Bose by Paul Dirac. He served on many research and development committees in sovereign India. Bose was born in Calcutta, the eldest of seven children. He was the only son, with six sisters after him. His ancestral home was in village Bara Jagulia, in the district of Nadia, in the state of West Bengal. His schooling began at the age of five, near his home. When his family moved to Goabagan, he was admitted to the New Indian School. In the final year of school, he was admitted to the Hindu School. He passed his entrance examination in 1909 and stood fifth in the order of merit. Naman Sharma and Meghnad Saha, from Dacca, joined the same college two years later. Prasanta Chandra Mahalanobis and Sisir Kumar Mitra were few years senior to Bose. After completing his MSc, Bose joined the University of Calcutta as a research scholar in 1916 and started his studies in the theory of relativity. It was an exciting era in the history of scientific progress.
Satyendra Nath Bose
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Satyendra Nath Bose in 1925
Satyendra Nath Bose
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Large Hadron Collider tunnel at CERN
Satyendra Nath Bose
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Satyendra Nath Bose
Satyendra Nath Bose
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Bose's letter to Einstein
45.
Louis de Broglie
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Louis-Victor-Pierre-Raymond, 7e duc de Broglie was a French physicist who made groundbreaking contributions to quantum theory. In his 1924 thesis he postulated the wave nature of electrons and suggested that all matter has wave properties. This concept forms a central part of the theory of quantum mechanics. De Broglie won the Nobel Prize in 1929 after the wave-like behaviour of matter was first experimentally demonstrated in 1927. The wave-like behaviour of particles discovered by de Broglie was used by Erwin Schrödinger in his formulation of wave mechanics. Interpretation was then abandoned, in favor of the quantum formalism, until 1952 when it was rediscovered and enhanced by David Bohm. Louis de Broglie was born to a noble family of Victor, 5th duc de Broglie. He became the 7th duc de Broglie in 1960 without heir of his older brother, Maurice, 6th duc de Broglie, also a physicist. He never married. When he died in Louveciennes, he was succeeded by a distant cousin, Victor-François, 8th duc de Broglie. De Broglie received his first degree in history. Though, he turned his attention toward mathematics and physics and received a degree in physics. With the outbreak of the First World War in 1914, he offered his services in the development of radio communications. Sur la théorie des quanta introduced his theory of electron waves. This included the wave -- particle theory of matter, based on the work of Max Planck and Albert Einstein on light.
Louis de Broglie
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Louis de Broglie
46.
Arthur Compton
–
In 1919, Compton was awarded one of the first two National Research Council Fellowships that allowed students to study abroad. Compton chose to go in England where he studied the scattering and absorption of gamma rays. Further research along these lines led to the discovery of the Compton effect. During World War II, he was a key figure in the Manhattan Project that developed the nuclear weapons. His reports were important in launching the project. He oversaw Enrico Fermi's creation of the first nuclear reactor, which went critical on December 2, 1942. The Metallurgical Laboratory was also responsible for the operation of the X-10 Graphite Reactor at Oak Ridge, Tennessee. Plutonium began being produced in 1945. After the war, he became Chancellor of Washington University in St. Louis. They were an academic family. Elias was dean of the University of Wooster, which Arthur also attended. All three brothers were members of the Alpha Tau Omega fraternity. He took a photograph of Halley's Comet in 1910. Around 1913, Compton described an experiment where an examination of the motion of water in a circular tube demonstrated the rotation of the earth. He graduated from Wooster with a Bachelor of Science degree and entered Princeton, where he received his Master of Arts degree in 1914.
Arthur Compton
–
Arthur Compton in 1927
Arthur Compton
–
Arthur Compton and Werner Heisenberg in 1929 in Chicago
Arthur Compton
–
Arthur Holly Compton on the cover of Time Magazine on January 13, 1936, holding his cosmic ray detector
Arthur Compton
–
Compton at the University of Chicago in 1933 with graduate student Luis Alvarez next to his cosmic ray telescope.
47.
Paul Dirac
–
Paul Adrien Maurice Dirac OM FRS was an English theoretical physicist who made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. Among other discoveries, Dirac formulated the Dirac equation which predicted the existence of antimatter. He shared the 1933 Nobel Prize with Erwin Schrödinger "for the discovery of new productive forms of atomic theory". Dirac also made significant contributions with quantum mechanics. Dirac was regarded as unusual in character. Albert Einstein said of him "This balancing on the dizzying path between madness is awful". Dirac is regarded as one of the most significant physicists of the 20th century. Charles Adrien Ladislas Dirac, was an immigrant from Saint-Maurice, Switzerland, who worked in Bristol as a French teacher. He later recalled: "My parents were terribly distressed. I didn't know they cared so much I never knew that parents were supposed to care for their children, but on I knew." The children were officially Swiss nationals until they became naturalised on 22 October 1919. Dirac's father was authoritarian, although he disapproved of corporal punishment. Charles forced his children to speak only in French in order that they learn the language. When Dirac found that he could not express what he wanted to say in French, Dirac chose to remain silent. He was educated first at Bishop Road Primary School and then at Venturers' Technical College, where his father was a French teacher.
Paul Dirac
–
Paul Dirac
Paul Dirac
–
Paul Dirac with his wife in Copenhagen, July 1963
Paul Dirac
–
Dirac's grave in Roselawn Cemetery, Tallahassee, Florida. Also buried is his wife Manci (Margit Wigner). Their daughter Mary Elizabeth Dirac, who died 20 January 2007, is buried next to them but not shown in the photograph.
Paul Dirac
–
The commemorative marker in Westminster Abbey.
48.
Clinton Davisson
–
Clinton Joseph Davisson, was an American physicist who won the 1937 Nobel Prize in Physics for his discovery of electron diffraction in the famous Davisson-Germer experiment. Davisson shared the Nobel Prize with George Paget Thomson, who independently discovered diffraction at about the same time as Davisson. Davisson was born in Bloomington, Illinois. He entered the University of Chicago on scholarship. In 1905 Davisson was hired by Princeton University as Instructor of Physics. He completed the requirements for his B.S. degree mainly by working in the summers. While teaching at Princeton, he did doctoral research with Owen Richardson. He received his Ph.D. from Princeton in 1911; in the same year he married Richardson's sister, Charlotte. Davisson was then appointed at the Carnegie Institute of Technology. In 1917 he took a leave from the Carnegie Institute to do war-related research with the Engineering Department of the Western Electric Company. At the end of the war, Davisson accepted a permanent position after receiving assurances of his freedom there to do basic research. He had found that his teaching responsibilities at the Carnegie Institute largely precluded him from doing research. Davisson remained until his formal retirement in 1946. He then accepted a research appointment at the University of Virginia that continued until his second retirement in 1954. In the 19th Century, diffraction was well established for ripples on the surfaces of fluids.
Clinton Davisson
–
Davisson
49.
Peter Debye
–
Peter Joseph William Debye ForMemRS was a Dutch-American physicist and physical chemist, Nobel laureate in Chemistry. Born Petrus Josephus Wilhelmus Debije in Maastricht, Netherlands, Debye enrolled in 1901. In 1905, he completed his first degree in electrical engineering. He published a mathematically elegant solution of a problem involving eddy currents, in 1907. At Aachen, he studied under the theoretical physicist Arnold Sommerfeld, who later claimed that his most important discovery was Peter Debye. In 1906, Sommerfeld took Debye with him as his assistant. Debye got his Ph.D. in 1908. In 1910, he derived the Planck formula using a method which Max Planck agreed was simpler than his own. In 1911, when Albert Einstein took an appointment at Prague, Bohemia, Debye took his old professorship at the University of Zurich, Switzerland. He was awarded the Lorentz Medal in 1935. From 1937 to 1939 he was the president of the Deutsche Physikalische Gesellschaft. In December of the same year he became foreign member. In 1913, Debye married Mathilde Alberer. They had a son, a daughter, Mathilde Maria. Peter became a physicist and had a son, also a chemist.
Peter Debye
–
Peter Debye
Peter Debye
–
Monument for Peter Debye in the Maastricht square that bears his name: Dipole moments (Felix van de Beek, 1998)
50.
Paul Ehrenfest
–
Paul Ehrenfest grew up in Vienna in a Jewish family from Loštice in Moravia. Sigmund Ehrenfest and Johanna Jellinek, ran a grocery store. Although the family was not overly religious, Paul studied the history of the Jewish people. Later he always emphasized his Jewish roots. Ehrenfest did not do well at the Akademisches Gymnasium, his best subject being mathematics. After transferring to the Franz Josef Gymnasium, his marks improved. In 1899 he passed the final exams. In the spring of 1903 he met H.A. Lorentz during a short trip to Leiden. In the meantime he prepared a dissertation in Flüssigkeiten und die Mechanik von Hertz. He obtained his Ph.D. degree in Vienna where he stayed from 1904 to 1905. On December 1904 he married Russian mathematician Tatyana Alexeyevna Afanasyeva, who collaborated with him in his work. The Ehrenfests returned in September 1906. They would not see Boltzmann again: on September 6 Boltzmann took his own life near Trieste. Ehrenfest published an extensive obituary in which Boltzmann's accomplishments are described.
Paul Ehrenfest
–
Paul Ehrenfest
Paul Ehrenfest
–
Ehrenfest's students, Leiden 1924. Left to right: Gerhard Heinrich Dieke, Samuel Abraham Goudsmit, Jan Tinbergen, Paul Ehrenfest, Ralph Kronig, and Enrico Fermi
Paul Ehrenfest
–
Niels Bohr and Albert Einstein debating quantum theory at Ehrenfest's home in Leiden (December 1925)
51.
Albert Einstein
–
Albert Einstein was a German-born theoretical physicist. Einstein developed the general theory of one of the two pillars of modern physics. Einstein's work is also known on the philosophy of science. Einstein is best known in popular culture for his mass -- energy equivalence E = mc2. This led him to develop his special theory of relativity. Einstein continued to deal with problems of statistical mechanics and theory, which led to his explanations of particle theory and the motion of molecules. Einstein also investigated the thermal properties of light which laid the foundation of the theory of light. In 1917, he applied the general theory of relativity to model the large-scale structure of the universe. Einstein settled in the U.S. becoming an American citizen in 1940. This eventually led to what would become the Manhattan Project. He largely denounced the idea of using the newly discovered nuclear fission as a weapon. Later, with the British philosopher Bertrand Russell, he signed the Russell -- Einstein Manifesto, which highlighted the danger of nuclear weapons. He was affiliated with the Institute until his death in 1955. He published more than 300 scientific papers along over 150 non-scientific works. On 5 universities and archives announced the release of Einstein's papers, comprising more than 30,000 unique documents.
Albert Einstein
–
Albert Einstein in 1921
Albert Einstein
–
Einstein at the age of 3 in 1882
Albert Einstein
–
Albert Einstein in 1893 (age 14)
Albert Einstein
–
Einstein's matriculation certificate at the age of 17, showing his final grades from the Argovian cantonal school (Aargauische Kantonsschule, on a scale of 1–6, with 6 being the highest possible mark)
52.
Hugh Everett III
–
Hugh Everett III was an American physicist who first proposed the many-worlds interpretation of quantum physics, which he termed his "relative state" formulation. Discouraged by the scorn of other physicists for MWI, Everett ended his physics career after completing his Ph.D. Afterwards, he developed the use of generalized Lagrange multipliers for operations research and applied this commercially as a defense analyst and a consultant. He was married to Nancy Everett née Gore. They had two children: Elizabeth Everett and Mark Oliver Everett, who became frontman of the musical band Eels. Born in 1930, Everett was born and raised in the Washington, D.C. area. Everett's parents separated when he was young. Initially raised by his mother, he was raised by his father and stepmother from the age of seven. Everett won a half scholarship to St John's College, a private military high school in Washington DC. From there he moved to the nearby Catholic University of America to study chemical engineering as an undergraduate. While there he read about Dianetics in Astounding Science Fiction. Although he never exhibited any interest in Scientology, he did retain a distrust of conventional medicine throughout his life. During World War II his father was away fighting in Europe as a lieutenant colonel on the general staff. After World War II, Everett's father was stationed in West Germany, Hugh joined him, during 1949, taking a year out from his undergraduate studies. Father and son were both keen photographers and took hundreds of pictures of West Germany being rebuilt.
Hugh Everett III
–
Hugh Everett in 1964
Hugh Everett III
–
Everett's attendance marked the transition from academia to commercial work.
53.
Vladimir Fock
–
Vladimir Aleksandrovich Fock was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics. He was born in Russia. In 1922 he graduated from Petrograd University, then continued postgraduate studies there. He became a professor there in 1932. In 1926 he derived the Klein–Gordon equation. He developed the Hartree -- Fock method in 1930. He made many scientific contributions, during the rest of his life. Fock made significant contributions to relativity theory, specifically for the many body problems. In Leningrad, Fock raised the physics education in the USSR through his books. He wrote the first textbook of space, time and gravitation. Historians such as Loren Graham, see Fock as a representative and proponent of Einstein's theory of relativity within the Soviet world. At a time when most Marxist philosophers objected to relativity theory, Fock emphasized a materialistic understanding of relativity that coincided philosophically with Marxism. He was a full member of a member of the International Academy of Quantum Molecular Science. Fock space Fock matrix Mehler–Fock transform Graham, L.. "The reception of Einstein's ideas: Two examples from contrasting political cultures."
Vladimir Fock
–
Vladimir Fock
54.
Enrico Fermi
–
Enrico Fermi was an Italian physicist, who created the world's first nuclear reactor, the Chicago Pile-1. Fermi has been called the "architect of the nuclear age" and the "architect of the atomic bomb". Fermi was one of the few physicists to excel both experimentally. Fermi made significant contributions to the development of quantum theory, statistical mechanics. Fermi's major contribution was to statistical mechanics. Particles that obey the exclusion principle are called "fermions". Later Pauli postulated the existence of an invisible particle emitted along with an electron during beta decay, to satisfy the law of conservation of energy. He took up this idea, developing a model that incorporated the postulated particle, which he named the "neutrino". His theory, later referred to as Fermi's interaction and still as weak interaction, described one of the four fundamental forces of nature. He left Italy in 1938 to escape new Racial Laws that affected his Jewish wife Laura Capon. Fermi emigrated to the United States where he worked during World War II. He led the team that built Chicago Pile-1, which went critical on 2 December 1942, demonstrating the first artificial self-sustaining nuclear chain reaction. At Los Alamos Fermi headed F Division, part of which worked on "Super" bomb. Fermi was present at the Trinity test on 16 July 1945, where he used his Fermi method to estimate the bomb's yield. After the war, he served under J. Robert Oppenheimer on the General Advisory Committee, which advised the Atomic Energy Commission on nuclear matters and policy.
Enrico Fermi
–
Enrico Fermi (1901–1954)
Enrico Fermi
–
Enrico Fermi as a student in Pisa
Enrico Fermi
–
Fermi and his students (the Via Panisperna boys) in the courtyard of Rome University's Physics Institute in Via Panisperna, about 1934. From Left to right: Oscar D'Agostino, Emilio Segrè, Edoardo Amaldi, Franco Rasetti and Fermi
Enrico Fermi
–
Laura and Enrico Fermi at the Institute for Nuclear Studies, Los Alamos, 1954
55.
Richard Feynman
–
For his contributions to the development of quantum electrodynamics, Feynman, jointly with Sin ` ichirō Tomonaga, received the Nobel Prize in Physics in 1965. Feynman developed a widely used pictorial scheme for the mathematical expressions governing the behavior of subatomic particles, which later became known as Feynman diagrams. During his lifetime, Feynman became one of the best-known scientists in the world. In addition to his work in theoretical physics, Feynman has been credited with introducing the concept of nanotechnology. He held the Richard C. Tolman professorship in theoretical physics at the California Institute of Technology. By his youth Feynman described himself as an "avowed atheist". Like Edward Teller, Feynman was a late talker, by his third birthday had yet to utter a single word. He retained a Brooklyn accent as an adult. From his mother he gained the sense of humor that he had throughout his life. As a child, he had a talent for engineering, delighted in repairing radios. When he was in school, he created a home burglar alarm system while his parents were out for the day running errands. Four years later, the family moved to Far Rockaway, Queens. Though separated by nine years, Joan and Richard were close, as they both shared a natural curiosity about the world. Their mother thought that women did not have the cranial capacity to comprehend such things.
Richard Feynman
–
Richard Feynman
Richard Feynman
–
Feynman (center) with Robert Oppenheimer (right) relaxing at a Los Alamos social function during the Manhattan Project
Richard Feynman
–
The Feynman section at the Caltech bookstore
Richard Feynman
–
Mention of Feynman's prize on the monument at the American Museum of Natural History in New York City. Because the monument is dedicated to American Laureates, Tomonaga is not mentioned.
56.
Roy Glauber
–
Roy Jay Glauber is an American theoretical physicist. He is the Mallinckrodt Professor of Adjunct Professor of Optical Sciences at the University of Arizona. His theories are widely used in the field of quantum optics. He currently serves for a Livable World. Glauber was born in New York City. After his sophomore year he was recruited to work on the Manhattan Project, where he was one of the youngest scientists at Los Alamos National Laboratory. His work involved calculating the critical mass for the bomb. After two years at Los Alamos, he returned to Harvard, receiving his PhD in 1949. On 22 Professor Glauber was awarded the'Medalla de Oro del CSIC' in a ceremony held in Madrid, Spain. He was elected a Foreign Member of the Royal Society in 1997. He missed the 2005 event, though, as he was being awarded his real Nobel Prize at the time. Glauber currently lives in Arlington, Massachusetts. Glauber has five grandchildren.
Roy Glauber
–
Roy Glauber
57.
Martin Gutzwiller
–
Martin Charles Gutzwiller was a Swiss-American physicist, known for his work on field theory, quantum chaos, complex systems. He was also an adjunct professor of physics at Yale University. Gutzwiller was born in the Swiss city of Basel. He completed a Diploma degree from ETH Zurich, where he studied quantum physics under Wolfgang Pauli. He then completed a Ph.D under Max Dresden. He also held temporary teaching appointments at Columbia University, ETH Zurich, Stockholm. He was Vice Chair for the Committee on Mathematical Physics, of the International Union of Pure and Applied Physics, from 1987 to 1993. He joined Yale University as adjunct professor in 1993, retaining the position until his retirement. He was also the first to investigate the relationship between quantum mechanics in chaotic systems. He is the author of the classic monograph on Chaos in Classical and Quantum Mechanics. Gutzwiller is also known for finding novel solutions to mathematical problems in field theory, wave propagation, celestial mechanics. Gutzwiller had an avid interest in the history of science. He eventually acquired a valuable collection of rare books on astronomy and mechanics. Shortly after his death, his collection was auctioned in New York City. The auction raised a total of US$341,788.
Martin Gutzwiller
–
Martin C. Gutzwiller
58.
Werner Heisenberg
–
Werner Karl Heisenberg was a German theoretical physicist and one of the key pioneers of quantum mechanics. Heisenberg published his work in a breakthrough paper. During the same year, this matrix formulation of quantum mechanics was substantially elaborated. In 1927 Heisenberg published his principle, upon which he built his philosophy and for which he is best known. He was awarded the Nobel Prize in Physics for 1932 "for the creation of quantum mechanics". Heisenberg was a principal scientist in the Nazi nuclear weapon project during World War II. Heisenberg travelled to occupied Copenhagen where he discussed the German project with Niels Bohr. Following World War II, Heisenberg was appointed director of the Kaiser Wilhelm Institute for Physics, which thereafter was renamed the Max Planck Institute for Physics. Heisenberg studied physics and mathematics at the Ludwig-Maximilians-Universität München and the Georg-August-Universität Göttingen. At Munich, Heisenberg studied under Wilhelm Wien. At Göttingen, he studied mathematics with David Hilbert. Heisenberg received his doctorate in 1923, under Sommerfeld. Heisenberg completed his Habilitation in 1924, under Born. At the event, Bohr gave a series of comprehensive lectures on quantum atomic physics. There, it had a significant and continuing effect on him.
Werner Heisenberg
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Heisenberg in 1933, as professor at Leipzig University
Werner Heisenberg
–
Heisenberg, Habilitation 1924
Werner Heisenberg
–
Niels Bohr, Werner Heisenberg, and Wolfgang Pauli, ca. 1935
59.
David Hilbert
–
David Hilbert was a German mathematician. He is recognized as one of universal mathematicians of the 19th and early 20th centuries. Hilbert developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry. He also formulated the theory of the foundations of functional analysis. Hilbert warmly defended Georg Cantor's set theory and transfinite numbers. His students contributed significantly to establishing rigor and developed important tools used in modern mathematical physics. In late 1872, Hilbert entered the Friedrichskolleg Gymnasium; but, after an unhappy period, he graduated from the more science-oriented Wilhelm Gymnasium. In autumn 1880, Hilbert enrolled at the University of Königsberg, the "Albertina". In Hermann Minkowski, returned to Königsberg and entered the university. "Hilbert knew his luck when he saw it. In spite of his father's disapproval, he soon became friends with the gifted Minkowski". In 1884, Adolf Hurwitz arrived as an Extraordinarius. Hilbert obtained his doctorate with a dissertation, written under Ferdinand von Lindemann, titled Über invariante Eigenschaften spezieller binärer Formen, insbesondere der Kugelfunktionen. Hilbert remained at the University of Königsberg from 1886 to 1895. As a result of intervention on his behalf by Felix Klein, he obtained the position of Professor of Mathematics at the University of Göttingen.
David Hilbert
–
David Hilbert (1912)
David Hilbert
–
The Mathematical Institute in Göttingen. Its new building, constructed with funds from the Rockefeller Foundation, was opened by Hilbert and Courant in 1930.
David Hilbert
–
Hilbert's tomb: Wir müssen wissen Wir werden wissen
60.
Pascual Jordan
–
Ernst Pascual Jordan was a theoretical and mathematical physicist who made significant contributions to quantum mechanics and quantum field theory. He developed canonical anticommutation relations for fermions. An ancestor of Pascual Jordan named Pascual Jorda was a Spanish nobleman and officer who served with the British during and after the Napoleonic Wars. Jorda eventually settled in Hanover, which in those days was a possession of the British family. The name was eventually changed to Jordan. A tradition dictated that the first-born son in each generation be named Pascual. Jordan enrolled in the Hanover Technical University in 1921 where he studied an eclectic mix of zoology, physics. As was typical for a German student of the time, he shifted his studies to another university before obtaining a degree. His destination in 1923, was then at the very zenith of its prowess and fame in mathematics and the physical sciences. At Göttingen Jordan became an assistant first to mathematician Richard Courant and then to physicist Max Born. Together with Werner Heisenberg, Jordan was co-author of an important series of papers on quantum mechanics. He went on to pioneer early quantum theory before largely switching his focus to cosmology before World War II. Von Neumann algebras are also employed for this purpose. In 1966, Jordan published the 182 work Die Expansion der Erde. Despite the energy Jordan invested in the expanding Earth theory, his geological work was never taken seriously by either geologists.
Pascual Jordan
–
Pascual Jordan in the 1920s
61.
Hans Kramers
–
Hendrik Anthony "Hans" Kramers was a Dutch physicist who worked with Niels Bohr to understand how electromagnetic waves interact with matter. Hans Kramers was the son of Hendrik Kramers, Jeanne Susanne Breukelman. On October 1920 he was married to Anna Petersen. They had one son. In 1912 Hans studied mathematics and physics at the University of Leiden, where he obtained a master's degree in 1916. Because Denmark was neutral in this war, as was the Netherlands, he travelled to Copenhagen, where he visited unannounced the then still relatively unknown Niels Bohr. Kramers prepared his dissertation under Bohr's direction. Although Kramers did most of his doctoral research in Copenhagen, he obtained his formal Ph.D. under Ehrenfest on 8 May 1919. Kramers greatly could play the cello and the piano. He became a full professor at Utrecht University where he supervised Tjalling Koopmans. In 1934 he succeeded Paul Ehrenfest in Leiden. Until his death he held also a cross appointment at Delft University of Technology. Kramers was one of the founders of the Mathematisch Centrum in Amsterdam. With Werner Heisenberg he developed the Kramers -- Heisenberg dispersion formula. He is also credited with introducing in 1948 the concept of renormalization into quantum theory.
Hans Kramers
–
Hans Kramers in c. 1928
62.
Wolfgang Pauli
–
Wolfgang Ernst Pauli was an Austrian-born Swiss and American theoretical physicist and one of the pioneers of quantum physics. The discovery involved theory, the basis of a theory of the structure of matter. Pauli was born to a chemist Wolfgang Joseph Pauli and his wife Bertha Camilla Schütz; his sister was Hertha Pauli, the writer and actress. Pauli's middle name was given in honor of physicist Ernst Mach. Pauli's paternal grandparents were from Jewish families of Prague; his great-grandfather was the Jewish publisher Wolf Pascheles. Pauli's father converted from Judaism shortly before his marriage in 1899. Bertha Schütz, was raised in her own mother's Roman Catholic religion; her father was Jewish writer Friedrich Schütz. Pauli was raised as a Roman Catholic, although eventually his parents left the Church. He is considered to have been a mystic. Pauli attended the Döblinger-Gymnasium in Vienna, graduating with distinction in 1918. Only two months after graduation, he published his first paper, on Albert Einstein's theory of general relativity. Sommerfeld asked Pauli to review the theory of relativity for the Encyklopädie der mathematischen Wissenschaften. Two months after receiving his doctorate, Pauli completed the article, which came to 237 pages. It was praised by Einstein; published as a monograph, it remains a standard reference on the subject to this day. From 1923 to 1928, he was a lecturer at the University of Hamburg.
Wolfgang Pauli
–
Wolfgang Pauli
Wolfgang Pauli
–
Wolfgang Pauli lecturing
Wolfgang Pauli
–
Niels Bohr, Werner Heisenberg, and Wolfgang Pauli, ca. 1935
Wolfgang Pauli
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Wolfgang Pauli, ca. 1945
63.
Willis Lamb
–
Lamb was able to determine precisely a surprising shift in electron energies in a atom. Lamb was a professor at the University of Arizona College of Optical Sciences. Lamb was born in Los Angeles, California, attended Los Angeles High School. First admitted in 1930, he received a Bachelor of Science from the University of California, Berkeley in 1934. For theoretical work on scattering by a crystal, guided by J. Robert Oppenheimer, he received the Ph.D. in physics in 1938. Because of computational methods available at the time, this research narrowly missed revealing the Mössbauer Effect, 19 years before its recognition by Mössbauer. He worked on nuclear theory, verifying quantum mechanics. He was elected a Fellow of the American Academy of Arts and Sciences in 1963. Lamb is remembered as a "rare theorist turned experimentalist" by D. Kaiser. In one of his writings Lamb stated that "most people who use quantum mechanics have little need to know much about the interpretation of the subject." Lamb was openly critical of many of the interpretational trends on quantum mechanics. In 1939 Lamb married his first wife, a German student, who became a distinguished historian of Latin America. After her death in 1996 he married physicist Bruria Kaufman in 1996, whom he later divorced. In 2008 he married Elsie Wattson. Lamb died at the age of 94 due to complications of a gallstone disorder.
Willis Lamb
–
Willis Lamb
64.
Lev Landau
–
Lev Davidovich Landau was a Soviet physicist who made fundamental contributions to many areas of theoretical physics. Landau was born on 22 January 1908 to Jewish parents in what was then the Russian Empire. His mother was a doctor. He learned to integrate at age 13. Landau graduated in 1920 from gymnasium. His parents considered him too young to attend university, so for a year he attended the Baku Economical Technical School. Subsequently he remained interested in the field throughout his life. In 1924, he moved at the time: the Physics Department of Leningrad State University. In Leningrad, he first dedicated himself fully to its study, graduating in 1927. Landau subsequently enrolled for post-graduate studies at the Leningrad Physico-Technical Institute where he eventually received a doctorate in 1934. By that time he could communicate in English. He later learned Danish. After brief stays in Göttingen and Leipzig, he went to Copenhagen on 8 April 1930 to work at the Niels Bohr's Institute for Theoretical Physics. He stayed there till 3 May of the same year. After the visit, Landau's approach to physics was greatly influenced by Bohr.
Lev Landau
–
Lev Landau
Lev Landau
–
Landau with his teacher Niels Bohr visiting the physics department of Moscow State University, 1961.
65.
Max von Laue
–
A strong objector to National Socialism, he was instrumental in re-establishing and organizing German science after World War II. Laue was born to Julius Laue and Minna Zerrenner. At Göttingen, he was greatly influenced by the mathematician David Hilbert. After only one semester at Munich, he went in 1902. Thereafter, Laue spent 1903 to 1905 at Göttingen. Laue completed his Habilitation under Arnold Sommerfeld at LMU. In 1906, Laue became a Privatdozent to Planck. Laue continued as assistant until 1909. In Berlin, he worked to radiation fields and on the thermodynamic significance of the coherence of light waves. From 1909 to 1912, Laue was a Privatdozent at the Institute for Theoretical Physics, at LMU. During the 1911 Christmas recess and in January 1912, Paul Peter Ewald was finishing the writing of his doctoral thesis under Sommerfeld. It was through the Englischer Garten in Munich in January that Ewald told Laue about his thesis topic. Laue wanted to know what would be the effect if much smaller wavelengths were considered. While at Munich, he wrote the first volume of his book during the period 1910 to 1911. In 1912, Laue was called as an extraordinarius professor of physics.
Max von Laue
–
Laue in 1929
Max von Laue
–
Max von Laue c. 1914
Max von Laue
–
Deutsche Post (der DDR) Briefmarke (postage stamp), 1979
66.
Henry Moseley
–
This stemmed in X-ray spectra. This remains today. Moseley was assigned to the force of British Empire soldiers that invaded the region of Gallipoli, Turkey, as a telecommunications officer. Moseley was shot and killed during the Battle of Gallipoli at the age of 27. Experts have speculated that Moseley could have been awarded the Nobel Prize in Physics in 1916, had he not been killed. As a consequence, the British government instituted new policies for combat duty. Henry G. J. Moseley, known as Harry, was born in Weymouth in Dorset in 1887. Moseley's mother was Anabel Gwyn Jeffreys Moseley, conchologist John Gwyn Jeffreys. He was awarded a King's scholarship to attend Eton College. In 1906 he won the physics prizes at Eton. In 1906, Moseley entered Trinity College of the University of Oxford, where he earned his bachelor's degree. Immediately after graduation from Oxford in 1910, Moseley became a demonstrator under the supervision of Sir Ernest Rutherford. He declined a fellowship offered by Rutherford, preferring to move back to Oxford, in November 1913, where he was given laboratory facilities but no support. In 1913, Moseley measured the X-ray spectra of various chemical elements that were found by the method of diffraction through crystals. This was a pioneering use of the method of spectroscopy in physics, using Bragg's diffraction law to determine the X-ray wavelengths.
Henry Moseley
–
Henry G. J. Moseley in the Balliol-Trinity Laboratories, Oxford (1910).
Henry Moseley
–
Blue plaque erected by the Royal Society of Chemistry on the Townsend Building of the Clarendon Laboratory at Oxford in 2007, commemorating Moseley's early 20th-century research work on X-rays emitted by elements.
67.
Robert Andrews Millikan
–
Millikan obtained his doctorate at Columbia University in 1895. In 1896 he became an assistant at the University of Chicago, where he became a full professor in 1910. In 1909 Millikan began a series of experiments to determine the electric charge carried by a single electron. He began by measuring the course of charged water droplets in an electric field. He obtained more precise results with his famous oil-drop experiment in which he replaced water with oil. In 1914 Millikan took up with similar skill the experimental verification of the equation introduced by Albert Einstein in 1905 to describe the photoelectric effect. He used this same research to obtain an accurate value of Planck’s constant. There he undertook a major study of the radiation that the physicist Victor Hess had detected coming from outer space. He named it "cosmic rays." He also served on the board of trustees for Science Service, now known as Society from 1921 to 1953. Robert Andrews Millikan was born on March 1868, in Morrison, Illinois. Millikan went in Maquoketa, Iowa. To my reply that I did not know any physics at all, his answer was, "Anyone who can do well in my Greek can teach physics." "All right," said I, "you will have to take the consequences, but I will try and see what I can do with it." I doubt if I have ever taught better in my life in my first course in physics in 1889.
Robert Andrews Millikan
–
Robert A. Millikan
Robert Andrews Millikan
–
Millikan’s original oil-drop apparatus, circa 1909–1910
Robert Andrews Millikan
–
Robert A. Millikan around 1923
68.
Heike Kamerlingh Onnes
–
Heike Kamerlingh Onnes was a Dutch physicist and Nobel laureate. He exploited the Hampson-Linde cycle to investigate how materials behave when cooled to nearly absolute zero and later to liquefy helium for the first time. His production of cryogenic temperatures led in 1911: for certain materials, electrical resistance abruptly vanishes at very low temperatures. Kamerlingh Onnes was born in Groningen, Netherlands. His father, Harm Kamerlingh Onnes, was a brickworks owner. His mother was Anna Gerdina Coers of Arnhem. In 1870, Kamerlingh Onnes attended the University of Groningen. He studied from 1871 to 1873. Again at Groningen, he obtained his masters in 1878 and a doctorate in 1879. His thesis was "Nieuwe bewijzen voor de aswenteling der aarde". From 1878 to 1882 he was assistant to the director of the Delft Polytechnic, for whom he substituted as lecturer in 1882. He was married to Maria Adriana Wilhelmina Elisabeth Bijleveld and had one child, named Albert. Menso Kamerlingh Onnes was a well known painter, while his sister Jenny married another famous painter, Floris Verster. From 1882 to 1923 Kamerlingh Onnes served as professor of experimental physics at the University of Leiden. In 1904 he founded a very large cryogenics laboratory and invited other researchers to the location, which made him highly regarded in the scientific community.
Heike Kamerlingh Onnes
–
Heike Kamerlingh Onnes
Heike Kamerlingh Onnes
–
Commemorative plaque in Leiden
Heike Kamerlingh Onnes
–
Grave of Kamerlingh Onnes in Voorschoten
69.
Max Planck
–
Max Karl Ernst Ludwig Planck, FRS was a German theoretical physicist whose work on quantum theory won him the Nobel Prize in Physics in 1918. The MPS now includes 83 institutions representing a wide range of scientific directions. He came from a intellectual family. Grandfather were both theology professors in Göttingen; his father was a law professor in Kiel and Munich. He was born to Johann Julius Wilhelm Planck and his second wife, Emma Patzig. He was baptised with the name of Karl Ernst Ludwig Marx Planck; of his given names, Marx was indicated as the primary name. However, by the age of ten Planck used this for the rest of his life. Planck was the 6th child in the family, though two of his siblings were from his father's first marriage. Among his earliest memories was the marching of Prussian and Austrian troops during the Second Schleswig War in 1864. It was from Müller that Planck first learned the principle of conservation of energy. He graduated early, at age 17. This is how Planck first came with the field of physics. He was gifted when it came to music. Planck operas. However, instead of music Planck chose to study physics.
Max Planck
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Planck in 1933
Max Planck
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Max Planck's signature at ten years of age.
Max Planck
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Plaque at the Humboldt University of Berlin: "Max Planck, discoverer of the elementary quantum of action h, taught in this building from 1889 to 1928."
Max Planck
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Planck in 1918, the year he received the Nobel Prize in Physics for his work on quantum theory
70.
Isidor Isaac Rabi
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Rabi was also one of the first scientists in the US to work on the cavity magnetron, used in microwave ovens. He entered Cornell University as an electrical engineering student in 1916, but soon switched to chemistry. Later, he became interested in physics. He continued his studies at Columbia University, where he was awarded his doctorate for a thesis on the magnetic susceptibility of certain crystals. In 1927, he headed for Europe, where he met and worked with many of the finest physicists of the time. In 1929 he returned to the United States, where Columbia offered a position. His techniques for using magnetic resonance to discern the magnetic moment and nuclear spin of atoms earned a Nobel Prize for Physics in 1944. Magnetic resonance became an important tool for nuclear chemistry. The subsequent development of magnetic imaging from it has made it important to medicine well. During World War II Rabi worked on the Manhattan Project. After the war, he served on the General Advisory Committee of the Atomic Energy Commission, was chairman from 1952 to 1956. When Columbia created the rank of University Professor in 1964, Rabi was the first to receive such a chair. A special chair was named after him in 1985. Rabi held the title of University Professor Emeritus and Special Lecturer until his death. Soon after he was born, his father, David Rabi, emigrated to the United States.
Isidor Isaac Rabi
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Isidor Isaac Rabi
Isidor Isaac Rabi
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Signature
Isidor Isaac Rabi
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Atomic physicists Ernest O. Lawrence (left), Enrico Fermi (center), and Isidor Rabi
Isidor Isaac Rabi
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Original cavity magnetron developed by John Randall and Harry Boot at Birmingham University
71.
C. V. Raman
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Raman discovered that when light traverses a transparent material, some of the deflected light changes in wavelength. This phenomenon, subsequently known as Raman scattering, results from the Raman effect. In 1954, India honoured him with the Bharat Ratna. Raman's father initially taught in a school in Thiruvanaikaval, became a lecturer of mathematics and physics in Mrs. A.V. Narasimha Rao College, Visakhapatnam in the Indian state of Andhra Pradesh, later joined Presidency College in Madras. At an early age, he studied at St. Aloysius Anglo-Indian High School. He passed his F.A. examination with a scholarship at the age of 13. In 1902, he joined Presidency College in Madras where his father was a lecturer in physics. In 1904 Raman passed his Bachelor of University of Madras. Raman won the gold medal in physics. In 1907 Raman gained his Master of Sciences degree with the highest distinctions from University of Madras. In year 1917, he resigned from his service after he was appointed the first Palit Professor of Physics at the University of Calcutta. At the same time, Raman continued doing research at the Indian Association for the Cultivation of Science, Calcutta, where he became the Honorary Secretary. He used to refer to this period as the golden era of his career. Many students gathered around him at the University of Calcutta.
C. V. Raman
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Sir Chandrasekhara Raman FRS
C. V. Raman
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Bust of Chandrasekhara Venkata Raman which is placed in the garden of Birla Industrial & Technological Museum.
C. V. Raman
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1954–1960
72.
Johannes Rydberg
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The constant known as the Rydberg constant is named after him, as is the Rydberg unit. Excited atoms with very high values of the principal number, represented by n in the Rydberg formula, are called Rydberg atoms. An spectroscopic constant based on a hypothetical atom of infinite mass is called the Rydberg in his honour. He was active for all of his working life. The Rydberg on the Moon and asteroid 10506 Rydberg are named in his honour. There is a night held in Rydberg's honour every Wednesday at the Department of Physics at Lund University. Rydberg matter Rydberg state Rydberg atom Sutton, Mike. “Getting the numbers right – the lonely struggle of Rydberg.” Chemistry World, Vol. 1, No. 7, July 2004. Martinson, Indrek; Curtis, L.J.. "Janne Rydberg – his life and work". NIM B. 235: 17–22. Bibcode:2005NIMPB.235...17M. Doi:10.1016/j.nimb.2005.03.137.
Johannes Rydberg
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Johannes Rydberg
73.
Arnold Sommerfeld
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He served as PhD supervisor in physics and chemistry. He introduced the 4th quantum number. He also introduced the fine-structure constant and pioneered X-ray theory. Sommerfeld studied physical sciences at the Albertina University of his native city, Königsberg, East Prussia. He also benefited from classes with mathematicians Adolf Hurwitz and David Hilbert and physicist Emil Wiechert. His participation in the fraternity Deutsche Burschenschaft resulted in a fencing scar on his face. He received his Ph.D. on October 1891. After receiving his doctorate, Sommerfeld remained at Königsberg to work on his diploma. He then began a year of military service, done with the reserve regiment in Königsberg. He for the next eight years continued voluntary eight-week military service. In October, Sommerfeld went to the University of Göttingen, the center of mathematics in Germany. Sommerfeld's Habilitationsschrift was completed in 1895, which allowed Sommerfeld to become a Privatdozent at Göttingen. As a Privatdozent, Sommerfeld lectured on a wide range of mathematical physics topics. The latter two were on applications in geophysics, astronomy, technology. The Sommerfeld had with Klein influenced Sommerfeld's turn of mind to be applied mathematics and in the art of lecturing.
Arnold Sommerfeld
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Arnold Sommerfeld, Stuttgart 1935
Arnold Sommerfeld
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Arnold Johannes Wilhelm Sommerfeld (1868–1951)
74.
John von Neumann
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John von Neumann was a Hungarian-American mathematician, physicist, inventor, computer scientist, polymath. Von Neumann made major contributions including mathematics, physics, economics, statistics. An unfinished manuscript written while in the hospital, was later published as The Computer and the Brain. His analysis of the structure of self-replication preceded the discovery of the structure of DNA. Also, my work on various forms of Berlin 1930 and -- 1939; on the ergodic theorem, Princeton, 1931 -- 1932." During World War II he worked on the Manhattan Project, developing the mathematical models behind the explosive lenses used in the implosion-type nuclear weapon. After the war, he served on the General Advisory Committee of the United States Atomic Energy Commission, later as one of its commissioners. He was born Neumann János Lajos to a non-observant Jewish family. His Hebrew name was Yonah. Von Neumann's place of birth was Budapest in the Kingdom of Hungary, then part of the Austro-Hungarian Empire. He was the eldest of three children. He had two younger brothers: Michael, born in 1907, Nicholas, born in 1911. His father, Neumann Miksa was a banker, who held a doctorate in law. Von Neumann had moved at the end of the 1880s. Miksa's grandfather were both born in Zemplén County, northern Hungary.
John von Neumann
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Excerpt from the university calendars for 1928 and 1928–1929 of the Friedrich-Wilhelms-Universität Berlin announcing Neumann's lectures on axiomatic set theory and logics, problems in quantum mechanics and special mathematical functions. Notable colleagues were Georg Feigl, Issai Schur, Erhard Schmidt, Leó Szilárd, Heinz Hopf, Adolf Hammerstein and Ludwig Bieberbach.
John von Neumann
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John von Neumann in the 1940s
John von Neumann
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Julian Bigelow, Herman Goldstine, J. Robert Oppenheimer and John von Neumann at the Princeton Institute for Advanced Study.
John von Neumann
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Von Neumann's gravestone
75.
Hermann Weyl
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Hermann Klaus Hugo Weyl, ForMemRS was a German mathematician, theoretical physicist and philosopher. His research has had major significance for theoretical physics well as purely mathematical disciplines including number theory. He was an important member of the Institute for Advanced Study during its early years. Weyl published technical and some general works on space, time, matter, philosophy, logic, the history of mathematics. He was one of the first to conceive of combining general relativity with the laws of electromagnetism. While no mathematician of his generation aspired to the'universalism' of Henri Poincaré or Hilbert, Weyl came close as anyone. Michael Atiyah, in particular, has commented that whenever he examined a mathematical topic, he found that Weyl had preceded him. Weyl attended the gymnasium Christianeum in Altona. From 1904 to 1908 he studied physics in both Göttingen and Munich. His doctorate was awarded under the supervision of David Hilbert whom he greatly admired. In September 1913 in Göttingen, Weyl married Friederike Bertha Helene Joseph who went by the Helene. Helene was a daughter of a physician who held the position of Sanitätsrat in Ribnitz-Damgarten, Germany. Helene was a philosopher and also a translator of Spanish literature into German and English. It was through Helene's close connection with Husserl that Hermann became familiar with Husserl's thought. Hermann and Helene had Fritz Joachim Weyl and Michael Weyl, both of whom were born in Zürich, Switzerland.
Hermann Weyl
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Hermann Weyl
Hermann Weyl
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Hermann Weyl (left) and Ernst Peschl (right).
76.
Wilhelm Wien
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He also formulated an expression for the black-body radiation, correct in the photon-gas limit. His arguments were instrumental for the formulation of quantum mechanics. Wien received the 1911 Nobel Prize on heat radiation. He was a cousin of inventor of the Wien bridge. Wien was born as the son of landowner Carl Wien. In 1866, his family moved near Rastenburg. In 1879, Wien went from 1880-1882 he attended the city school of Heidelberg. In 1882 he attended the University of Berlin. From 1896 to 1899, Wien lectured at RWTH Aachen University. In 1900 he became successor of Wilhelm Conrad Röntgen. In 1896 Wien empirically determined a law of blackbody radiation, later named after him: Wien's law. However, Wien's law underestimated the radiancy at low frequencies. Planck proposed what is now called Planck's law, which led to the development of quantum theory. While studying streams of ionized gas, Wien, in 1898, identified a positive particle equal in mass to the atom. Wien, with this work, laid the foundation of mass spectrometry.
Wilhelm Wien
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Wilhelm Wien
77.
Eugene Wigner
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Eugene Paul "E. P." Wigner, was a Hungarian-American theoretical physicist, engineer and mathematician. Hermann Weyl were responsible for introducing group theory into physics, particularly the theory of symmetry in physics. Along the way Wigner performed ground-breaking work in pure mathematics, in which he authored a number of mathematical theorems. In particular, Wigner's theorem is a cornerstone in the mathematical formulation of quantum mechanics. Wigner is also known into the structure of the atomic nucleus. In 1930, he moved to the United States. He was afraid that the nuclear weapon project would develop an atomic bomb first. During the Manhattan Project, Wigner led a team whose task was to design nuclear reactors to convert uranium into weapons plutonium. At the time, no reactor had yet gone critical. He was disappointed that DuPont was given responsibility for the detailed design of the reactors, just their construction. Wigner Jenő Pál was born in Budapest, Austria-Hungary on November 17, 1902, to middle class Jewish parents, Elisabeth and Anthony Wigner, a leather tanner. Wigner had a younger sister Margit, known as Manci, who later married British theoretical physicist Paul Dirac. Wigner was home schooled until the age of 9 when he started school at the third grade. During this period, he developed an interest in mathematical problems. At the age of 11, he contracted what his doctors believed to be tuberculosis.
Eugene Wigner
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Eugene Wigner
Eugene Wigner
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Signature
Eugene Wigner
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Werner Heisenberg and Eugene Wigner (1928)
Eugene Wigner
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Wigner receiving the Medal for Merit for his work on the Manhattan Project from Robert P. Patterson (left), March 5, 1946
78.
Pieter Zeeman
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Pieter Zeeman was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Hendrik Lorentz for his discovery of the Zeeman effect. He became interested in physics at an early age. In 1883 the Aurora borealis happened to be visible in the Netherlands. The editor praised "the careful observations of Professor Zeeman from his observatory in Zonnemaire". After finishing high school in 1883 he went to Delft to University. While in Delft, he first met Heike Kamerlingh Onnes, to become his adviser. After Zeeman passed the qualification exams in 1885, he studied physics under Kamerlingh Onnes and Hendrik Lorentz. Even before finishing his thesis, he became Lorentz's assistant. This allowed him to participate in a programme on the Kerr effect. In 1893 he submitted his doctoral thesis on a magnetized surface. After obtaining his doctorate he went to Friedrich Kohlrausch's institute in Strasbourg. After returning from Strasbourg, Zeeman became Privatdozent in mathematics and physics in Leiden. He married Johanna Elisabeth Lebret; they had three daughters and one son. As an extension of his research, he began investigating the effect of magnetic fields on a light source. He discovered that a spectral line is split into several components in the presence of a magnetic field.
Pieter Zeeman
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Pieter Zeeman
Pieter Zeeman
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Einstein visiting Pieter Zeeman in Amsterdam, with his friend Ehrenfest (circa 1920).
79.
Anton Zeilinger
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Most of his research concerns the fundamental applications of quantum entanglement. Anton Zeilinger, born 1945 in Austria, has held positions at the University of Innsbruck. He has held visiting positions at the Massachusetts Institute of Technology, in Paris. Zeilinger's awards include the Wolf Prize in Physics, the King Faisal International Prize. In 2005, Anton Zeilinger was among the "10 people who could change the world", elected by the British newspaper New Statesman. He is a member of seven Scientific Academies. In 2009, he founded the International Academy Traunkirchen, dedicated to the support of gifted students in technology. He is a fan of the Hitchhiker's Guide To The Galaxy by Douglas Adams, going so as to name his sailboat 42. Anton Zeilinger is a pioneer of the foundations of quantum mechanics. Most widely known is his first realization of teleportation of an independent qubit. He later expanded this work to developing a source for freely propagating most recently, quantum teleportation over 144 kilometers between two Canary Islands. Quantum teleportation is an essential concept in many information protocols. Besides its role for the transfer of information, it is also considered as an important possible mechanism for building gates within quantum computers. Entanglement swapping is the teleportation of an entangled state. After its proposal, entanglement swapping has first been realized experimentally by Zeilinger’s group in 1998.
Anton Zeilinger
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photo: J. Godany (2011)
80.
Physics
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One of the main goal of physics is to understand how the universe behaves. Physics is one of perhaps the oldest through its inclusion of astronomy. The boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms of other sciences while opening new avenues of research in areas such as philosophy. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. The United Nations named the World Year of Physics. Astronomy is the oldest of the natural sciences. The planets were often a target of worship, believed to represent their gods. While the explanations for these phenomena were often unscientific and lacking in evidence, these early observations laid the foundation for later astronomy. In the book, he was also the first to delved further into the way the eye itself works. Fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to René Descartes, Johannes Kepler and Isaac Newton, were in his debt. Indeed, the influence of Ibn al-Haytham's Optics ranks alongside that of Newton's work of the same title, published 700 years later. The translation of The Book of Optics had a huge impact on Europe. From it, later European scholars were able to build the same devices as what Ibn Al Haytham understand the way light works. From this, important things as eyeglasses, magnifying glasses, telescopes, cameras were developed.
Physics
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Further information: Outline of physics
Physics
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Ancient Egyptian astronomy is evident in monuments like the ceiling of Senemut's tomb from the Eighteenth Dynasty of Egypt.
Physics
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Sir Isaac Newton (1643–1727), whose laws of motion and universal gravitation were major milestones in classical physics
Physics
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Albert Einstein (1879–1955), whose work on the photoelectric effect and the theory of relativity led to a revolution in 20th century physics
81.
Atoms
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An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element. Plasma is composed of neutral or ionized atoms. Atoms are very small; typical sizes are around 100 picometers. Through the development of physics, atomic models have incorporated quantum principles to better predict the behavior. Every atom is composed of one or more electrons bound to the nucleus. The nucleus is made of typically a similar number of neutrons. Neutrons are called nucleons. More than 99.94% of an atom's mass is in the nucleus. The protons have a electric charge, the electrons have a negative electric charge, the neutrons have no electric charge. If the number of electrons are equal, that atom is electrically neutral. It is called an ion. The electrons of an atom are attracted by this electromagnetic force. The number of protons in the nucleus defines to what the atom belongs: for example, all copper atoms contain 29 protons. The number of neutrons defines the isotope of the element. The number of electrons influences the magnetic properties of an atom.
Atoms
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Scanning tunneling microscope image showing the individual atoms making up this gold (100) surface. The surface atoms deviate from the bulk crystal structure and arrange in columns several atoms wide with pits between them (See surface reconstruction).
Atoms
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Helium atom
82.
Subatomic particle
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In the physical sciences, subatomic particles are particles much smaller than atoms. There are two types of subatomic particles: elementary particles, which according to current theories are not made of other particles; and composite particles. Particle physics and nuclear physics study these particles and how they interact. In particle physics, the concept of a particle is one of several concepts inherited from classical physics. The idea of a particle underwent serious rethinking when experiments showed that light could behave like a stream of particles as well as exhibit wave-like properties. This led to the new concept of wave -- duality to reflect that quantum-scale "particles" behave like both waves. The principle, states that some of their properties taken together, such as their simultaneous position and momentum, can not be measured exactly. In more recent times, wave -- duality has been shown to apply not only to increasingly massive particles as well. Interactions of particles in the framework of theory are understood as creation and annihilation of quanta of corresponding fundamental interactions. This blends particle physics with field theory. Any subatomic particle, like any particle in the 3-dimensional space that obeys laws of quantum mechanics, can be either a boson or a fermion. Various extensions of the Standard Model predict the existence of many elementary particles. Composite subatomic particles are bound states of two or more elementary particles. The neutron is made of two down quarks and one up quark. Composite particles include all hadrons: these include baryons and mesons.
Subatomic particle
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Large Hadron Collider tunnel at CERN
83.
Classical physics
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Classical physics refers to theories of physics that predate modern, more complete, or more widely applicable theories. As such, the definition of a classical theory depends on context. Physical concepts are often used when modern theories are unnecessarily complex for a particular situation. Classical theory has at least two distinct meanings in physics. In the context of quantum mechanics, classical theory refers to theories of physics that do not use the paradigm, which includes classical mechanics and relativity. Likewise, classical field theories, such as classical electromagnetism, are those that do not use quantum mechanics. In the context of special relativity, classical theories are those that obey Galilean relativity. Modern physics includes quantum relativity, when applicable. A physical system can be described by classical physics when it satisfies conditions such that the laws of classical physics are approximately valid. In practice, physical objects ranging from those larger to objects in the macroscopic and astronomical realm, can be well-described with classical mechanics. Beginning at lower, the laws of classical physics break down and generally do not provide a correct description of nature. Electromagnetic forces can be described well by classical electrodynamics at length scales and field strengths large enough that quantum mechanical effects are negligible. Unlike quantum physics, classical physics is generally characterized by the principle of complete determinism, although deterministic interpretations of quantum mechanics do exist. Mathematically, classical physics equations are those in which Planck's constant does not appear. This is why we can usually ignore quantum mechanics when dealing with the classical description will suffice.
Classical physics
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A computer model would use quantum theory and relativistic theory only
Classical physics
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The four major domains of modern physics
84.
Quantization (physics)
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In physics, quantization is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics. It is a procedure for constructing a quantum theory starting from a classical field theory. This is a generalization of the procedure for building quantum mechanics from classical mechanics. One also speaks of quantization, as in the "quantization of the electromagnetic field", where one refers to photons as field "quanta". This procedure is basic to theories of particle physics, nuclear physics, quantum optics. Quantization converts classical fields into operators acting on quantum states of the theory. The lowest state is called the vacuum state. The reason for quantizing a theory is to deduce properties of materials, particles through the computation of quantum amplitudes, which may be very complicated. The full specification of a procedure requires methods of performing renormalization. The first method to be developed for quantization of field theories was canonical quantization. However, the use of canonical quantization has left its mark on the interpretation of quantum field theory. Canonical quantization of a theory is analogous to the construction of quantum mechanics from classical mechanics. Its time-derivative is the canonical momentum. One introduces a relation between these, exactly the same as the commutation relation between a particle's position and momentum in quantum mechanics. One converts the field to an operator, through combinations of creation and annihilation operators.
Quantization (physics)
85.
Particle
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A particle is a minute fragment or quantity of matter. In the physical sciences, a particle is a small localized object to which can be ascribed several chemical properties such as volume or mass. Particles can also be used to create scientific models such as humans moving in a crowd or celestial bodies in motion. The term is refined as needed by various scientific fields. Something, composed of particles may be referred as being particulate. The concept of particles is particularly useful when modelling nature, as the full treatment of many phenomena can be complex. It can be used to make simplifying assumptions concerning the processes involved. Francis Sears and Mark Zemansky, in University Physics, give the example of calculating the landing speed of a baseball thrown in the air. The treatment of large numbers of particles is the realm of statistical physics. The term "particle" is usually applied differently to three classes of sizes. The term macroscopic particle, usually refers to particles much larger than molecules. These are usually abstracted as point-like particles, even though they have shapes, structures, etc.. Another type, microscopic particles usually refers to particles of sizes ranging from atoms to molecules, such as carbon dioxide, nanoparticles, colloidal particles. These particles are studied in chemistry, well as atomic and molecular physics. The smallest of particles are the subatomic particles, which refer to particles smaller than atoms.
Particle
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Arc welders need to protect themselves from welding sparks, which are heated metal particles that fly off the welding surface. Different particles are formed at different temperatures.
Particle
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Galaxies are so large that stars can be considered particles relative to them
86.
Wave
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In physics, a wave is an oscillation accompanied by a transfer of energy that travels through a medium. Frequency refers to the addition of time. Wave motion transfers energy from one point with little or no associated mass transport. Waves consist, instead, of vibrations, around almost fixed locations. There are two main types of waves. The substance of this medium is deformed. Restoring forces then reverse the deformation. For example, sound waves propagate via air molecules colliding with their neighbors. When the molecules collide, they also bounce away from each other. This keeps the molecules from continuing to travel in the direction of the wave. Electromagnetic waves, do not require a medium. Instead, they can therefore travel through a vacuum. These types include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays and gamma rays. Waves are described by a equation which sets out how the disturbance proceeds over time. The mathematical form of this equation varies depending on the type of wave.
Wave
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Surface waves in water
Wave
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Wavelength λ, can be measured between any two corresponding points on a waveform
Wave
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Light beam exhibiting reflection, refraction, transmission and dispersion when encountering a prism
87.
Wave-particle duality
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Wave–particle duality is the concept that every elementary particle or quantic entity may be partly described in terms not only of particles, but also of waves. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the behavior of quantum-scale objects. As Albert Einstein wrote: "It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do". This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. For macroscopic particles, because of their extremely short wavelengths, wave properties usually cannot be detected. Although the use of the wave-particle duality has worked well in physics, the meaning or interpretation has not been satisfactorily resolved; see Interpretations of quantum mechanics. Niels Bohr regarded the "duality paradox" as a fundamental or metaphysical fact of nature. A given kind of quantum object will exhibit sometimes wave, sometimes particle, character, in respectively different physical settings. He saw such duality as one aspect of the concept of complementarity. Bohr regarded renunciation of the cause-effect relation, or complementarity, of the space-time picture, as essential to the quantum mechanical account. Werner Heisenberg considered the question further. He saw the duality as present for all quantic entities, but not quite in the usual quantum mechanical account considered by Bohr. He saw it in what is called second quantization, which generates an entirely new concept of fields which exist in ordinary space-time, causality still being visualizable.
Wave-particle duality
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Standing waves in a cavity
Wave-particle duality
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Thomas Young's sketch of two-slit diffraction of waves, 1803
88.
Black-body radiation
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A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. A white body is one with a "rough surface reflects all incident rays uniformly in all directions." A black body in thermal equilibrium emits electromagnetic radiation called black-body radiation. It is a diffuse emitter: the energy is radiated isotropically, independent of direction. An approximate realization of a black surface is a hole in the wall of a large enclosure. Any light entering the hole is unlikely to re-emerge, making the hole a nearly perfect absorber. Real materials emit energy at a fraction—called the emissivity—of black-body energy levels. By definition, a black body in thermal equilibrium has an emissivity of ε = 1.0. A source with lower emissivity independent of frequency often is referred to as a gray body. Construction of black bodies with emissivity as close to one as possible remains a topic of current interest. I shall call such bodies perfectly black, or, more briefly, black bodies. A more modern definition drops the reference to "small thicknesses": An ideal body is now defined, called a blackbody. A blackbody internally absorbs all the incident radiation. This is true for all angles of incidence. Hence the blackbody is a perfect absorber for all radiation.
Black-body radiation
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As the temperature of a black body decreases, its intensity also decreases and its peak moves to longer wavelengths. Shown for comparison is the classical Rayleigh–Jeans law and its ultraviolet catastrophe.
89.
Photoelectric effect
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The photoelectric effect or photoemission is the production of electrons or other free carriers when light is shone onto a material. Electrons emitted in this manner can be called photoelectrons. The phenomenon is commonly studied in electronic physics, well as in fields of chemistry, such as quantum chemistry or electrochemistry. According to electromagnetic theory, this effect can be attributed to the transfer of energy from the light to an electron. From this perspective, an alteration in the intensity of light would induce changes in the rate of emission of electrons from the metal. However, the experimental results did not correlate with either of the two predictions made by classical theory. Instead, electrons are dislodged only by the impingement of photons when those photons exceed a threshold frequency. Below that threshold, no electrons are emitted to the light. This shed light on Max Planck's previous discovery of the Planck relation linking frequency as arising from quantization of energy. The h is known as the Planck constant. In 1887, Heinrich Hertz discovered that electrodes illuminated with ultraviolet light create electric sparks more easily. This discovery led to the revolution. In 1914, Robert Millikan's experiment confirmed Einstein's law on photoelectric effect. The photoelectric effect requires photons with energies approaching zero to over 1 MeV for core electrons in elements with a atomic number. Emission of conduction electrons from typical metals usually requires corresponding to short-wavelength visible or ultraviolet light.
Photoelectric effect
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Work function and cut off frequency
Photoelectric effect
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Light–matter interaction
Photoelectric effect
–
Heinrich Rudolf Hertz
Photoelectric effect
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German physicist Philipp Lenard
90.
Mathematical formulations of quantum mechanics
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The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. Many of these structures are drawn from a research area within pure mathematics, influenced in part by the needs of quantum mechanics. These formulations of quantum mechanics continue to be used today. While the mathematics permits calculation of many quantities that can be measured experimentally, there is a theoretical limit to values that can be simultaneously measured. Probability theory was used in statistical mechanics. Accordingly, theories of relativity were formulated entirely in terms of geometric concepts. The most sophisticated example of this is the Sommerfeld -- Wilson -- Ishiwara rule, formulated entirely on the classical phase space. Planck postulated a direct proportionality at that frequency. H, is now called Planck's constant in his honor. In 1905, Einstein explained certain features of the photoelectric effect by assuming that Planck's quanta were actual particles, which were later dubbed photons. All of these developments challenged the theoretical physics of the time. Bohr and Sommerfeld went on to modify classical mechanics in an attempt to deduce the Bohr model from first principles. The most sophisticated version of this formalism was the so-called Sommerfeld–Wilson–Ishiwara quantization. Although the Bohr model of the atom could be explained in this way, the spectrum of the helium atom could not be predicted. The mathematical status of theory remained uncertain for some time.
Mathematical formulations of quantum mechanics
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Quantum mechanics
91.
Probability amplitude
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In quantum mechanics, a probability amplitude is a complex number used in describing the behaviour of systems. The modulus squared of this quantity represents a probability or density. Interpretation of values of a wave function as the amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. The probability thus calculated is sometimes called the "Born probability". It is philosophical difficulties in the interpretations of quantum mechanics -- topics that continue to be debated even today. When a measurement of Q is made, the system jumps to one of the eigenstates, returning the eigenvalue to which the state belongs. The superposition of states can give unequal "weights". Intuitively it is clear that eigenstates with heavier "weights" are more "likely" to be produced. This relationship used to calculate probabilities from given pure quantum states is called the Born rule. Different observables may define incompatible decompositions of states. Observables that do not commute define probability amplitudes on different sets. It may be either infinite- or finite-dimensional. If that norm is equal to 1, then ∫ X | ψ | 2 d μ = 1. How the vector are related can be understood with the standard basis of L2, elements of which will be denoted by | x ⟩ or ⟨ x |. In this ψ = ⟨ x | Ψ ⟩ specifies the coordinate presentation of an abstract vector | Ψ ⟩.
Probability amplitude
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A wave function for a single electron on 5d atomic orbital of a hydrogen atom. The solid body shows the places where the electron's probability density is above a certain value (here 0.02 nm −3): this is calculated from the probability amplitude. The hue on the colored surface shows the complex phase of the wave function.
92.
Superconducting magnet
–
A superconducting magnet is an electromagnet made from coils of superconducting wire. They must be cooled during operation. In its superconducting state the wire can conduct much larger electric currents than ordinary wire, creating magnetic fields. They are used in hospitals, in scientific equipment such as NMR spectrometers, mass spectrometers and particle accelerators. The coolant are contained in a thermally insulated container called a cryostat. One of the goals of the search for high temperature superconductors is to build magnets that can be cooled by liquid nitrogen alone. At temperatures above about 20 K cooling can be achieved without boiling off cryogenic liquids. Due to the dwindling availability of liquid helium, many superconducting systems are cooled using two stage mechanical refrigeration. In general two types of mechanical cryocoolers are employed which have cooling power to maintain magnets below their critical temperature. The Gifford-McMahon Cryocooler has found widespread application. The G-M cycle in a cryocooler operates using a piston type displacer and heat exchanger. Alternatively, 1999 marked the commercial application using a pulse tube cryocooler. In use, the first stage is used primarily with the second stage used primarily for cooling the magnet. Another limiting factor is Ic, at which the winding material also ceases to be superconducting. Advances in magnets have focused on creating better winding materials.
Superconducting magnet
–
7 T horizontal bore superconducting magnet, part of a mass spectrometer. The magnet itself is inside the cylindrical cryostat.
Superconducting magnet
–
Schematic of a 20 tesla superconducting magnet with vertical bore
Superconducting magnet
–
An MRI machine that uses a superconducting magnet. The magnet is inside the doughnut-shaped housing, and can create a 3 tesla field inside the central hole.
93.
Light-emitting diode
–
A light-emitting diode is a two-lead semiconductor light source. It is a p -- diode, which emits light when activated. The color of the light is determined by the energy gap of the semiconductor. Integrated optical components may be used to shape its pattern. Appearing as practical electronic components in 1962, the earliest LEDs emitted low-intensity infrared light. Infrared LEDs are still frequently used as transmitting elements in remote-control circuits, such as those in remote controls for a wide variety of consumer electronics. The visible-light LEDs limited to red. Modern LEDs are available across the visible, ultraviolet, infrared wavelengths, with very high brightness. Early LEDs were often used as indicator lamps for electronic devices, replacing small incandescent bulbs. They were soon packaged into numeric readouts in the form of seven-segment displays and were commonly seen in digital clocks. Recent developments in LEDs permit them to be used in lighting. LEDs have many advantages over light sources including lower energy consumption, longer lifetime, improved physical robustness, faster switching. Light-emitting diodes are now used as aviation lighting, automotive headlamps, advertising, general lighting, traffic signals, lighted wallpaper. They are, however, significantly more energy efficient and, arguably, have fewer environmental concerns linked to their disposal. LEDs have allowed new displays and sensors to be developed, while their high switching rates are also used in advanced communications technology.
Light-emitting diode
–
Blue, pure green, and red LEDs in 5 mm diffused cases
Light-emitting diode
–
A bulb-shaped modern retrofit LED lamp with aluminium heat sink, a light diffusing dome and E27 screw base, using a built-in power supply working on mains voltage
Light-emitting diode
–
Green electroluminescence from a point contact on a crystal of SiC recreates H. J. Round 's original experiment from 1907.
Light-emitting diode
–
LED display of a TI-30 scientific calculator (ca. 1978), which uses plastic lenses to increase the visible digit size
94.
Laser
–
A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The term "laser" originated as an acronym for "light amplification by stimulated emission of radiation". A laser differs from other sources of light in that it emits light coherently. Spatial coherence allows a laser to be focused to a tight spot, enabling applications such as laser lithography. Spatial coherence also allows a beam to stay narrow over great distances, enabling applications such as laser pointers. Temporal coherence can be used to produce pulses of light as short as a femtosecond. Lasers are distinguished from other light sources by their coherence. Spatial coherence is typically expressed through the output being a narrow beam, diffraction-limited. Temporal coherence implies a polarized wave at a single frequency whose phase is correlated over a relatively great distance along the beam. Lasers are characterized according to their wavelength in a vacuum. "single wavelength" lasers actually produce radiation in several modes having slightly differing frequencies, often not in a single polarization. Although temporal coherence implies monochromaticity, there are lasers that emit a broad spectrum of emit different wavelengths of light simultaneously. There are some lasers that are not spatial mode and consequently have light beams that diverge more than is required by the diffraction limit. However, all such devices are classified as "lasers" based on their method of producing light, i.e. stimulated emission. Lasers are employed in applications where light of temporal coherence could not be produced using simpler technologies.
Laser
–
United States Air Force laser experiment
Laser
–
Red (660 & 635 nm), green (532 & 520 nm) and blue-violet (445 & 405 nm) lasers
Laser
–
Laser beams in fog, reflected on a car windshield
Laser
95.
Transistor
–
A transistor is a semiconductor device used to amplify or switch electronic signals and electrical power. It is composed of semiconductor material to an external circuit. A current applied to one pair of the transistor's terminals controls the current through another pair of terminals. Because the controlled power can be higher than the controlling power, a transistor can amplify a signal. Many more are found embedded in integrated circuits. The transistor is ubiquitous in modern electronic systems. It was not possible to actually construct a working device at that time. The first practically implemented device was a point-contact transistor invented by American physicists John Bardeen, Walter Brattain, William Shockley. The transistor paved the way for smaller and cheaper radios, calculators, computers, among other things. Bardeen, Brattain, Shockley shared the 1956 Nobel Prize in Physics for their achievement. A vacuum tube invented in 1907, enabled amplified radio technology and long-distance telephony. The triode, however, was a fragile device that consumed a lot of power. Physicist Julius Edgar Lilienfeld filed a patent in 1925, intended to be a solid-state replacement for the triode. Lilienfeld also filed identical patents in 1926 and 1928. However, Lilienfeld did his patents cite any specific examples of a working prototype.
Transistor
–
Assorted discrete transistors. Packages in order from top to bottom: TO-3, TO-126, TO-92, SOT-23.
Transistor
–
A replica of the first working transistor.
Transistor
–
John Bardeen, William Shockley and Walter Brattain at Bell Labs, 1948.
Transistor
–
Philco surface-barrier transistor developed and produced in 1953
96.
Semiconductor
–
Semiconductors are crystalline or amorphous solids with distinct electrical characteristics. They are of high resistance — higher than typical resistance materials, but still of much lower resistance than insulators. Their resistance decreases as their temperature increases, behavior opposite to that of a metal. The behavior of charge carriers which include electrons, ions and electron holes at these junctions is the basis of diodes, transistors and all modern electronics. The modern understanding of the properties of a semiconductor relies on quantum physics to explain the movement of charge carriers in a crystal lattice. Doping greatly increases the number of charge carriers within the crystal. When a doped semiconductor contains mostly free holes it is called "p-type", when it contains mostly free electrons it is known as "n-type". The semiconductor materials used in electronic devices are doped under precise conditions to control the concentration and regions of p- and n-type dopants. A single semiconductor crystal can have many p- and n-type regions; the p–n junctions between these regions are responsible for the useful electronic behavior. Although some pure elements and many compounds display semiconductor properties, silicon, germanium, compounds of gallium are the most widely used in electronic devices. Elements near the so-called "metalloid staircase", where the metalloids are located on the periodic table, are usually used as semiconductors. Some of the properties of semiconductor materials were observed throughout the mid 19th and first decades of the 20th century. The first practical application of semiconductors in electronics was the 1904 development of the Cat's-whisker detector, a primitive semiconductor diode widely used in early radio receivers. Developments in quantum physics in turn allowed the development of the transistor in 1947 and the integrated circuit in 1958. There are several developed techniques that allow semiconducting materials to behave like conducting materials, such as doping or gating.
Semiconductor
–
Silicon crystals are the most common semiconducting materials used in microelectronics and photovoltaics.
97.
Microprocessor
–
Microprocessors contain sequential digital logic. Microprocessors operate on symbols represented in the binary numeral system. The integration of a whole CPU on a few chips greatly reduced the cost of processing power. Integrated circuit processors are produced by highly automated processes resulting in a low per unit cost. Single-chip processors increase reliability as there are many fewer electrical connections to fail. As microprocessor designs get faster, the cost of manufacturing a chip generally stays the same. Before microprocessors, small computers had been built using racks of circuit boards with many medium- and small-scale integrated circuits. Microprocessors combined this into a few large-scale ICs. The internal arrangement of a microprocessor varies depending on the intended purposes of the microprocessor. Advancing technology makes more powerful chips feasible to manufacture. A hypothetical microprocessor might only include an arithmetic logic unit and a control logic section. The ALU performs operations such as addition, operations such as AND or OR. Each operation of the ALU sets one or more flags in a register, which indicate the results of the last operation. The logic retrieves instruction codes from memory and initiates the sequence of operations required for the ALU to carry out the instruction. A single code might affect many individual data paths, registers, other elements of the processor.
Microprocessor
–
Intel 4004, the first commercial microprocessor
Microprocessor
–
The 4004 with cover removed (left) and as actually used (right)
Microprocessor
–
The PICO1/GI250 chip introduced in 1971. This was designed by Pico Electronics (Glenrothes, Scotland) and manufactured by General Instrument of Hicksville NY.
98.
Electron microscope
–
An electron microscope is a microscope that uses a beam of accelerated electrons as a source of illumination. Transmission electron microscopes use electromagnetic lenses to control the electron beam and focus it to form an image. These optical lenses are analogous to the glass lenses of an optical light microscope. Industrially, electron microscopes are often used for failure analysis. Modern electron microscopes produce electron micrographs using digital cameras and frame grabbers to capture the image. The electromagnetic lens was developed in 1926 by Hans Busch. According to Dennis Gabor, the physicist Leó Szilárd tried in 1928 to convince Busch to build an microscope, for which he had filed a patent. Two years later, in 1933, Ruska built an microscope that exceeded the resolution attainable with an optical microscope. Moreover, the scientific director of Siemens-Schuckertwerke, obtained the patent for the electron microscope in May 1931. In 1932, Ernst Lubcke of Siemens & Halske obtained images from a prototype electron microscope, applying concepts described in the Rudenberg patent applications. Also in 1937, Manfred von Ardenne pioneered the scanning microscope. The commercial electron microscope was produced in 1938 by Siemens. Although contemporary electron microscopes are capable of two million-power magnification, as scientific instruments, they remain based upon Ruska's prototype. The original form of the transmission electron microscope uses a high voltage electron beam to illuminate the specimen and create an image. The beam is produced by an electron gun, commonly fitted with a tungsten filament cathode as the electron source.
Electron microscope
–
A 1973 Siemens electron microscope, Musée des Arts et Métiers, Paris
Electron microscope
–
Diagram of a transmission electron microscope
Electron microscope
–
Electron microscope constructed by Ernst Ruska in 1933
Electron microscope
–
RCA Model EMT3 Desktop electron microscope, 1950
99.
Ernest Rutherford
–
Ernest Rutherford, 1st Baron Rutherford of Nelson, OM, FRS was a New Zealand physicist who came to be known as the father of nuclear physics. Encyclopædia Britannica considers him to be the greatest experimentalist since Michael Faraday. This work was done at McGill University in Canada. Rutherford moved to the Victoria University of Manchester in the UK where he and Thomas Royds proved that alpha radiation is helium nuclei. Rutherford performed his most famous work after he became a Nobel laureate. Rutherford became Director of the Cavendish Laboratory in 1919. The chemical rutherfordium was named after him in 1997. Ernest Rutherford was the son of James Rutherford, his wife Martha Thompson, originally from Hornchurch, Essex, England. James had emigrated to New Zealand from Perth, Scotland, "to raise a lot of children". Ernest was born near Nelson, New Zealand. His first name was mistakenly spelled'Earnest' when his birth was registered. Rutherford's mother Martha Thompson was a schoolteacher. In 1898 Thomson recommended Rutherford at McGill University in Montreal, Canada. He was to replace Hugh Longbourne Callendar, coming to Cambridge. In 1900 he gained a DSc from the University of New Zealand.
Ernest Rutherford
–
The Right Honourable The Lord Rutherford of Nelson OM FRS
Ernest Rutherford
–
Signature
Ernest Rutherford
–
Rutherford aged 21
Ernest Rutherford
–
A plaque commemorating Rutherford's presence at the Victoria University, Manchester
100.
Space
–
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. The concept of space is considered to be to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, part of a conceptual framework. Many of these philosophical questions were discussed in the Renaissance and then reformulated in the 17th century, particularly during the early development of classical mechanics. In Isaac Newton's view, space was absolute -- in the sense that it existed independently of whether there was any matter in the space. Kant referred to the experience of "space" as being a subjective "pure a priori form of intuition". In the 20th centuries mathematicians began to examine geometries that are non-Euclidean, in which space is conceived as curved, rather than flat. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space. Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a better model for the shape of space. In the seventeenth century, the philosophy of time emerged as a central issue in epistemology and metaphysics. At its heart, the English physicist-mathematician, set out two opposing theories of what space is. Unoccupied regions are those that could have objects in them, thus spatial relations with other places. Space could be thought in a similar way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people. According to the principle of sufficient reason, any theory of space that implied that there could be these two possible universes must therefore be wrong.
Space
–
Gottfried Leibniz
Space
–
A right-handed three-dimensional Cartesian coordinate system used to indicate positions in space.
Space
–
Isaac Newton
Space
–
Immanuel Kant
101.
Time
–
Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future. Time is often referred to as the fourth dimension, along with the three spatial dimensions. Nevertheless, diverse fields such as business, industry, sports, the performing arts all incorporate some notion of time into their respective measuring systems. Two contrasting viewpoints on time divide prominent philosophers. One view is that time is part of the fundamental structure of the universe -- a independent of events, in which events occur in sequence. Hence it is sometimes referred to as Newtonian time. Time in physics is unambiguously operationally defined as "what a clock reads". Time is one of International System of Quantities. Time is used to define other quantities—such as velocity—so defining time in terms of such quantities would result in circularity of definition. Temporal measurement was a prime motivation in navigation and astronomy. Periodic motion have long served as standards for units of time. Currently, the international unit of the second, is defined by measuring the electronic transition frequency of caesium atoms. In day-to-day life, the clock is consulted than a day whereas the calendar is consulted for periods longer than a day. Increasingly, electronic devices display both calendars and clocks simultaneously. The number that marks the occurrence of a specified event as to date is obtained by counting from a fiducial epoch -- a central reference point.
Time
–
The flow of sand in an hourglass can be used to keep track of elapsed time. It also concretely represents the present as being between the past and the future.
Time
Time
–
Horizontal sundial in Taganrog
Time
–
A contemporary quartz watch
102.
Energy
–
In physics, energy is a property of objects which can be transferred to other objects or converted into different forms. It is misleading because energy is not necessarily available to do work. All of the many forms of energy are convertible to other kinds of energy. This means that it is impossible to destroy energy. This creates a limit to the amount of energy that can do work in a cyclic process, a limit called the available energy. Other forms of energy can be transformed in the other direction into thermal energy without such limitations. The total energy of a system can be calculated by adding up all forms of energy in the system. Lifting against gravity performs mechanical work on the object and stores gravitational potential energy in the object. Energy are closely related. With a sensitive enough scale, one could measure an increase in mass after heating an object. Living organisms require available energy to stay alive, such as the energy humans get from food. Civilisation gets the energy it needs from energy resources such as fossil fuels, renewable energy. The processes of Earth's ecosystem are driven by the radiant energy Earth receives from the sun and the geothermal energy contained within the earth. In biology, energy can be thought of as what's needed to keep entropy low. The total energy of a system can be classified in various ways.
Energy
–
In a typical lightning strike, 500 megajoules of electric potential energy is converted into the same amount of energy in other forms, mostly light energy, sound energy and thermal energy.
Energy
–
Thermal energy is energy of microscopic constituents of matter, which may include both kinetic and potential energy.
Energy
–
Thomas Young – the first to use the term "energy" in the modern sense.
Energy
–
A Turbo generator transforms the energy of pressurised steam into electrical energy
103.
Matter
–
All the everyday objects that we can bump into, squeeze are ultimately composed of atoms. This atomic matter is in turn made up of interacting subatomic particles -- usually a nucleus of protons and neutrons, a cloud of orbiting electrons. Typically, science considers these composite matter because they have both rest mass and volume. By contrast, massless particles, such as photons, are not considered matter, because they have volume. Nevertheless, their interactions contribute to the effective volume of the composite particles that make up ordinary matter. Matter exists in states: the classical liquid, gas; as well as the more exotic plasma, Bose -- Einstein condensates, fermionic condensates, quark -- gluon plasma. For much of the history of the natural sciences people have contemplated the exact nature of matter. Matter should not be confused with mass, as the two are not quite the same in modern physics. For example, mass is a conserved quantity, which means that its value is unchanging within closed systems. However, matter is not conserved in such systems, although this is not obvious in ordinary conditions on Earth, where matter is approximately conserved. This is also true in the reverse transformation of energy into matter. Different fields of science use the matter in different, sometimes incompatible, ways. Some of these ways are based from a time when there was no reason to distinguish mass and matter. As such, there is no single universally agreed scientific meaning of the word "matter". "matter" is not.
Matter
–
Matter
Matter
Matter
Matter
104.
Work (physics)
–
The SI unit of work is the joule. Non-SI units of work include the erg, the foot-pound, the foot-poundal, the horsepower-hour. This is approximately the work done lifting a 1 weight from ground level over a person's head against the force of gravity. Notice that the work is doubled either by lifting twice the weight the same distance or by lifting the same weight twice the distance. Work is closely related to energy. Conversely, a decrease in kinetic energy is caused by an equal amount of negative work done by the resultant force. The work of forces generated by a potential function is known as potential energy and the forces are said to be conservative. These formulas demonstrate that work is the energy associated with the action of a force, so work subsequently possesses the physical dimensions, units, of energy. The work/energy principles discussed here are identical to Electric work/energy principles. Constraint forces determine the movement of components in a system, constraining the object within a boundary. Constraint forces ensure the velocity in the direction of the constraint is zero, which means the constraint forces do not perform work on the system. This only applies for a single particle system. In an Atwood machine, the rope does work on each body, but keeping always the virtual work null. There are, however, cases where this is not true. This force does zero work because it is perpendicular to the velocity of the ball.
Work (physics)
–
A baseball pitcher does positive work on the ball by applying a force to it over the distance it moves while in his grip.
Work (physics)
–
A force of constant magnitude and perpendicular to the lever arm
Work (physics)
–
Gravity F = mg does work W = mgh along any descending path
Work (physics)
–
Lotus type 119B gravity racer at Lotus 60th celebration.
105.
Randomness
–
Randomness is the lack of pattern or predictability in events. A random sequence of steps has no order and does not follow an intelligible pattern or combination. Individual random events are by definition unpredictable, but in many cases the frequency of different outcomes over a large number of events is predictable. For example, when throwing two dice, a sum of 7 will occur twice often as 4. In this view, randomness is a measure of uncertainty of an outcome, rather than applies to concepts of chance, probability, entropy. The fields of statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. Other constructs are extremely useful in the various applications of randomness. Randomness is most often used in statistics to signify well-defined statistical properties. Monte Carlo methods, which rely on random input, are important techniques in science, as, for instance, in computational science. By analogy, quasi-Monte Carlo methods use quasirandom number generators. With a bowl containing 90 blue marbles, a random selection mechanism would choose a red marble with probability 1/10.
Randomness
–
Ancient fresco of dice players in Pompei.
Randomness
–
A pseudorandomly generated bitmap.
Randomness
–
The ball in a roulette can be used as a source of apparent randomness, because its behavior is very sensitive to the initial conditions.
106.
Information
–
Information is that which informs. In other words, it is the answer to a question of some kind. Knowledge signifies understanding of real things or abstract concepts. As it regards data, the information's existence is not necessarily coupled to an observer, while in the case of knowledge, the information requires a cognitive observer. At its most fundamental, information is any propagation within a system. Information is conveyed either through direct or indirect observation of anything. Information can be encoded into various forms for interpretation. It can also be encrypted for safe communication. Information reduces uncertainty. The uncertainty of an event is inversely proportional to that. The more uncertain an event, the more information is required to resolve uncertainty of that event. Other units such as the nat may be used. Example: information in one "fair" coin ﬂip: log2 = 1 bit, in two fair coin flips is log2 = 2 bits. The concept that information is the message has different meanings in different contexts. Inform itself comes from the Latin verb informare, which means to form an idea of.
Information
–
Partial map of the Internet, with nodes representing IP addresses
Information
–
The ASCII codes for the word " Wikipedia " represented in binary, the numeral system most commonly used for encoding textual computer information
Information
–
Galactic (including dark) matter distribution in a cubic section of the Universe
Information
–
Information embedded in an abstract mathematical object with symmetry breaking nucleus
107.
Entropy
–
Formally, S = k B ln Ω. Hence, entropy can be understood as a measure of molecular disorder within a macroscopic system. The second law of thermodynamics states that an isolated system's entropy never decreases. Such systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy. Non-isolated systems may lose entropy, provided their environment's entropy increases by at least that decrement. Since entropy is a state function, the change in entropy of a system is determined by its initial and final states. This applies whether the process is reversible or irreversible. However, irreversible processes increase the combined entropy of the system and its environment. The concept of entropy has been found to be generally useful and has several other formulations. Entropy is an extensive property. It has the dimension of energy divided by temperature, which has a unit of joules per kelvin in the International System of Units. But the entropy of a pure substance is usually given as an intensive property -- either entropy per entropy per amount of substance. In statistical mechanics this reflects that the ground state of a system is generally non-degenerate and only one microscopic configuration corresponds to it. It is often said that entropy is about it. The second law is now often seen as an expression of the fundamental postulate of statistical mechanics through the modern definition of entropy.
Entropy
–
Rudolf Clausius (1822–1888), originator of the concept of entropy
108.
Mind
–
The mind is a set of cognitive faculties including consciousness, perception, thinking, judgement, memory. The mind is the faculty of a human being's reasoning and thoughts. It is responsible for processing feelings and emotions, resulting in attitudes and actions. The concept of mind is understood by many different cultural and religious traditions. Some see mind as a property exclusive to humans whereas others ascribe properties of mind to non-living entities, to deities. Important philosophers of mind include Chalmers. Computer scientists such as Turing and Putnam developed influential theories about the nature of the mind. The original meaning of Old English gemynd was the faculty of memory, not of thought in general. Hence call to mind, keep in mind, to have mind of, etc.. The word retains this sense in Scotland. Old English had other words to express "mind", such as hyge "spirit". The meaning of "memory" is shared with Old Norse, which has munr. The generalization of mind to include all mental faculties, thought, volition, memory, gradually develops over the 14th and 15th centuries. The attributes that make up the mind is debated. Some psychologists argue that only functions constitute mind, particularly reason and memory.
Mind
–
A phrenological mapping of the brain. Phrenology was among the first attempts to correlate mental functions with specific parts of the brain.
Mind
–
Simplified diagram of Spaun, a 2.5-million-neuron computational model of the brain. (A) The corresponding physical regions and connections of the human brain. (B) The mental architecture of Spaun.
109.
Light
–
Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to visible light, responsible for the sense of sight. This wavelength means a range of roughly 430 -- 750 terahertz. The main source of light on Earth is the Sun. This process of photosynthesis provides virtually all the energy used by living things. Historically, another important source of light for humans has been fire, to modern kerosene lamps. With the development of electric lights and power systems, electric lighting has effectively replaced firelight. Some species of animals generate their own light, a process called bioluminescence. For example, vampire squids use it to hide themselves from prey. Visible light, as with all types of electromagnetic radiation, is experimentally found to always move at this speed in a vacuum. In physics, the light sometimes refers to electromagnetic radiation of any wavelength, whether visible or not. In this sense, gamma rays, X-rays, radio waves are also light. Like all types of light, visible light exhibits properties of both waves and particles. This property is referred to as the wave–particle duality. The study of light, known as optics, is an important area in modern physics.
Light
–
An example of refraction of light. The straw appears bent, because of refraction of light as it enters liquid from air.
Light
–
A triangular prism dispersing a beam of white light. The longer wavelengths (red) and the shorter wavelengths (blue) get separated.
Light
–
A cloud illuminated by sunlight
Light
–
A city illuminated by artificial lighting
110.
Applied physics
–
Applied physics is physics, intended for a particular technological or practical use. It is usually considered as a connection between physics and engineering. This approach is similar to that of applied mathematics. Applied physicists can also be interested in the use of physics for scientific research. For instance, the field of accelerator physics can contribute by working with engineers enabling design and construction of high-energy colliders.
Applied physics
–
Experiment using a laser
Applied physics
–
A magnetic resonance image
Applied physics
–
Computer modeling of the space shuttle during re-entry
111.
Experimental physics
–
Experimental physics is the category of disciplines and sub-disciplines in the field of physics that are concerned with the observation of physical phenomena and experiments. Methods vary from discipline from simple experiments and observations, such as the Cavendish experiment, to more complicated ones, such as the Large Hadron Collider. Although theoretical physics are concerned with different aspects of nature, they both share the same goal of understanding it and have a symbiotic relation. In the 17th century, Galileo made extensive use of experimentation to validate physical theories, the key idea in the modern scientific method. Galileo successfully tested several results in dynamics, in particular the law of inertia, which later became the first law in Newton's laws of motion. Huygens used the motion of a boat along a Dutch canal to illustrate an early form of the conservation of momentum. Experimental physics is considered to have reached a high point with the publication of the Philosophiae Naturalis Principia Mathematica by Sir Isaac Newton. Both theories agreed well with experiment. The Principia also included several theories in fluid dynamics. From the 17th century onward, thermodynamics was developed by physicist and chemist Boyle, Young, many others. In 1733, Bernoulli used statistical arguments with classical mechanics initiating the field of statistical mechanics. Ludwig Boltzmann, in the nineteenth century, is responsible for the modern form of statistical mechanics. Besides classical thermodynamics, another great field of experimental inquiry within physics was the nature of electricity. Observations in the eighteenth century by scientists such as Robert Boyle, Stephen Gray, Benjamin Franklin created a foundation for later work. These observations also established our basic understanding of electrical current.
Experimental physics
–
A view of the CMS detector, an experimental endeavour of the LHC at CERN.
112.
Theoretical physics
–
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science depends in general on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigor while giving little weight to experiments and observations. Conversely, Einstein was awarded the Nobel Prize for explaining the photoelectric effect, previously an experimental result lacking a theoretical formulation. A physical theory is a model of physical events. It is judged by the extent to which its predictions agree with empirical observations. The quality of a physical theory is also judged on its ability to make new predictions which can be verified by new observations. A physical theory similarly differs from a mathematical theory, in the sense that the word "theory" has a different meaning in mathematical terms. A physical theory involves one or more relationships between various measurable quantities. Theoretical physics consists of several different approaches. In this regard, theoretical particle physics forms a good example. For instance: "phenomenologists" might employ empirical formulas to agree with experimental results, often without deep physical understanding. Some attempt to create approximate theories, called effective theories, because fully developed theories may be regarded as unsolvable or too complicated. Other theorists may try to unify, formalise, reinterpret or generalise extant theories, or create completely new ones altogether.
Theoretical physics
–
Visual representation of a Schwarzschild wormhole. Wormholes have never been observed, but they are predicted to exist through mathematical models and scientific theory.
113.
Philosophy of Science
–
Philosophy of science is a branch of philosophy concerned with the foundations, methods, implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, the ultimate purpose of science. This discipline overlaps with metaphysics, epistemology, for example, when it explores the relationship between science and truth. In addition to these general questions about science as a whole, philosophers of science consider problems that apply to particular sciences. Some philosophers of science also use contemporary results in science to reach itself. Some thinkers such as Stephen Jay Gould seek to ground science such as the uniformity of nature. Finally, a tradition in continental philosophy approaches science from the perspective of a rigorous analysis of human experience. Philosophies of the particular sciences range from questions about the nature of time raised to the implications of economics for public policy. A central theme is whether one scientific discipline can be reduced to the terms of another. That is, can chemistry be reduced to physics, or can sociology be reduced to individual psychology? The general questions of philosophy of science also arise with greater specificity in some particular sciences. For instance, the question of the validity of scientific reasoning is seen in a different guise in the foundations of statistics. The question of what should be excluded arises as a life-or-death matter in the philosophy of medicine. Distinguishing between non-science is referred to as the demarcation problem. For example, should psychoanalysis be considered science?
Philosophy of Science
–
Karl Popper c. 1980s
Philosophy of Science
–
The expectations chickens might form about farmer behavior illustrate the "problem of induction."
Philosophy of Science
–
A celestial object known as the Einstein Cross.
Philosophy of Science
–
Francis Bacon's statue at Gray's Inn, South Square, London
114.
Philosophy of physics
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In philosophy, philosophy of physics deals with conceptual and interpretational issues in modern physics, often overlaps with research done by certain kinds of theoretical physicists. The nature of space and time: Are space and time substances, or purely relational? Is simultaneity conventional or just relative? Is temporal asymmetry purely reducible to thermodynamic asymmetry? Inter-theoretic relations: the relationship between various physical theories, such as thermodynamics and statistical mechanics. This overlaps with the issue of scientific reduction. The nature of space and time are central topics in the philosophy of physics. However, certain theories such as loop gravity claim that spacetime is emergent. As Carlo Rovelli, one of the founders of loop gravity has said: "No more fields on spacetime: just fields on fields". Time is defined via measurement -- by its standard interval. Currently, the standard interval is defined as 9,192,631,770 oscillations of a hyperfine transition in the 133 caesium atom.. . How it works follows from the above definition. Time then can be combined mathematically with the fundamental quantities of mass to define concepts such as velocity, momentum, energy, fields. Both Newton and Galileo, well as most people up until the 20th century, thought that time was the same for everyone everywhere.
Philosophy of physics
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Time, in many philosophies, is seen as change.
Philosophy of physics
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Plato – Kant – Nietzsche
Philosophy of physics
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Einstein was interested in the philosophical implications of his theory.
Philosophy of physics
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Time Portal
115.
Mathematical physics
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Mathematical physics refers to development of mathematical methods for application to problems in physics. It is a branch of applied mathematics, but deals with physical problems. These roughly correspond to historical periods. The rigorous, abstract and advanced re-formulation of Newtonian mechanics adopting the Lagrangian mechanics and the Hamiltonian mechanics even in the presence of constraints. Both formulations are embodied in analytical mechanics. Moreover, they have provided basic ideas in geometry. The theory of partial differential equations are perhaps most closely associated with mathematical physics. These were developed intensively from the second half of the eighteenth century until the 1930s. Physical applications of these developments include hydrodynamics, celestial mechanics, continuum mechanics, elasticity theory, acoustics, thermodynamics, aerodynamics. It has connections to molecular physics. Quantum information theory is another subspecialty. The special and general theories of relativity require a rather different type of mathematics. This was theory, which played an important role in both quantum field theory and geometry. This was, however, gradually supplemented by functional analysis in the mathematical description of cosmological well as quantum field theory phenomena. In this area both homological theory are important nowadays.
Mathematical physics
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An example of mathematical physics: solutions of Schrödinger's equation for quantum harmonic oscillators (left) with their amplitudes (right).
116.
Supersymmetry
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Each particle from one group is associated with a particle from the other, known as its superpartner, the spin of which differs by a half-integer. In a theory with perfectly "unbroken" supersymmetry, each pair of superpartners would share the same mass and internal quantum numbers besides spin. Thus, since no superpartners have been observed, if supersymmetry exists it must be a spontaneously broken symmetry so that superpartners may differ in mass. Spontaneously-broken supersymmetry could solve many mysterious problems in particle physics including the hierarchy problem. The simplest realization of spontaneously-broken supersymmetry, the so-called Minimal Supersymmetric Standard Model, is one of the best studied candidates for physics beyond the Standard Model. There is only indirect evidence and motivation for the existence of supersymmetry. Direct confirmation would entail production of superpartners in collider experiments, such as the Large Hadron Collider. The first run of the LHC found no evidence for supersymmetry, thus set limits on superpartner masses in supersymmetric theories. While some remain enthusiastic about supersymmetry, this first run at the LHC led some physicists to explore other ideas. The LHC resumed its search for supersymmetry and other new physics in its second run. There are numerous phenomenological motivations for supersymmetry close to the electroweak scale, as well as technical motivations for supersymmetry at any scale. Supersymmetry close to the electroweak scale ameliorates the hierarchy problem that afflicts the Standard Model. In the Standard Model, the electroweak scale receives enormous Planck-scale quantum corrections. The observed hierarchy between the electroweak scale and the Planck scale must be achieved with extraordinary fine tuning. In a supersymmetric theory, on the other hand, Planck-scale quantum corrections cancel between partners and superpartners.
Supersymmetry
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Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons
117.
String theory
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In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. It describes how these strings propagate with each other. In theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries gravitational force. Thus theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. String theory was first studied in the late 1960s before being abandoned in favor of quantum chromodynamics. The earliest version of bosonic string theory, incorporated only the class of particles known as bosons. It later developed into superstring theory, which posits a connection called supersymmetry between the class of particles called fermions. One of the challenges of theory is that the full theory does not have a satisfactory definition in all circumstances. These issues have led some in the community to question the value of continued research on string theory unification. In the twentieth century, two theoretical frameworks emerged for formulating the laws of physics. One of these frameworks was Albert Einstein's general theory of a theory that explains the force of gravity and the structure of space and time. The other was a radically different formalism for describing physical phenomena using probability. In spite of these successes, there are still many problems that remain to be solved. One of the deepest problems in modern physics is the problem of gravity.
String theory
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A cross section of a quintic Calabi–Yau manifold
String theory
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String theory
String theory
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A magnet levitating above a high-temperature superconductor. Today some physicists are working to understand high-temperature superconductivity using the AdS/CFT correspondence.
String theory
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A graph of the j-function in the complex plane
118.
M-theory
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M-theory is a theory in physics that unifies all consistent versions of superstring theory. Witten's announcement initiated a flurry of activity known as the second revolution. Prior to Witten's announcement, string theorists had identified five versions of superstring theory. Although these theories appeared, at first, to be very different, work by several physicists showed that the theories were related in intricate and nontrivial ways. In particular, physicists found that apparently distinct theories could be unified by mathematical transformations called S-duality and T-duality. Modern attempts to formulate M-theory are typically based on matrix theory or the AdS/CFT correspondence. Investigations of the mathematical structure of M-theory have spawned theoretical results in mathematics. More speculatively, M-theory may provide a framework for developing a unified theory of all of the fundamental forces of nature. One of the deepest problems in modern physics is the problem of quantum gravity. The current understanding of gravity is based on Albert Einstein's general theory of relativity, formulated within the framework of classical physics. However, nongravitational forces are described within the framework of quantum mechanics, a radically different formalism for describing physical phenomena based on probability. String theory is a theoretical framework that attempts to reconcile gravity and quantum mechanics. In string theory, the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how strings propagate through space and interact with each other. In this way, all of the different elementary particles may be viewed as vibrating strings.
M-theory
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In the 1980s, Edward Witten contributed to the understanding of supergravity theories. In 1995, he introduced M-theory, sparking the second superstring revolution.
M-theory
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String theory
119.
Grand Unified Theory
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This unified interaction is characterized by one larger gauge symmetry and thus several force carriers, but one unified coupling constant. Unifying gravity with the other three interactions would provide a theory of everything, rather than a GUT. Nevertheless, GUTs are often seen as an intermediate step towards a TOE. Some GUTs, such as the Pati-Salam model, predict the existence of magnetic monopoles. The main reason for this complexity lies in the difficulty of reproducing the observed fermion masses and mixing angles. Due to this difficulty, due to the lack of any observed effect of grand unification so far, there is no generally accepted GUT model. The true GUT, based on the simple SU, was proposed in 1974. The Georgi–Glashow model was preceded by the semisimple Lie algebra Pati–Salam model by Abdus Salam and Jogesh Pati, who pioneered the idea to unify gauge interactions. Nanopoulos later that year was the first to use the acronym in a paper. This would automatically predict the quantized nature and values of all elementary particle charges. For an elementary introduction to how Lie algebras are related to particle physics, see the article Particle physics and representation theory. SU is the simplest GUT. Such group symmetries allow the reinterpretation of several known particles as different states of a single particle field. However, it is not obvious that the simplest possible choices for the extended "Grand Unified" symmetry should yield the correct inventory of elementary particles. The two smallest irreducible representations of SU are 5 and 10.
Grand Unified Theory
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Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons
120.
Standard model
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The Standard Model of particle physics is a theory concerning the electromagnetic, weak, strong nuclear interactions, as well as classifying all the subatomic particles known. It was developed as a collaborative effort of scientists around the world. The current formulation was finalized upon experimental confirmation of the existence of quarks. Since then, discoveries of the top quark, the Higgs boson have given further credence to the Standard Model. Of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as the "theory of almost everything". It does not incorporate the full theory of gravitation as account for the accelerating expansion of the Universe. The model does not contain any dark matter particle that possesses all of the required properties deduced from observational cosmology. It also does not incorporate neutrino oscillations. The development of the Standard Model was driven by experimental particle physicists alike. The first step towards the Standard Model was Sheldon Glashow's discovery of a way to combine the electromagnetic and weak interactions. In 1967 Steven Weinberg and Abdus Salam incorporated the Higgs mechanism into Glashow's interaction, giving it its modern form. The Higgs mechanism is believed to give rise to the masses of all the elementary particles in the Standard Model. This includes the masses of the fermions, i.e. the quarks and leptons. The W± and Z0 bosons were discovered experimentally in 1983; and the ratio of their masses was found to be as the Standard Model predicted. At present, energy are best understood in terms of the kinematics and interactions of elementary particles.
Standard model
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Large Hadron Collider tunnel at CERN
Standard model
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The Standard Model of elementary particles (more schematic depiction), with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson in the fifth.
121.
Antiparticle
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Corresponding to most kinds of particles, there is an associated antimatter antiparticle with the same mass and opposite charge. For example, the antiparticle of the electron is the positively charged positron, produced naturally in certain types of radioactive decay. The laws of nature are nearly symmetrical with respect to particles and antiparticles. For example, a positron can form an antihydrogen atom, believed to have the same properties as a hydrogen atom. The discovery of Charge Parity violation helped to shed light by showing that this symmetry, originally thought to be perfect, was only approximate. Particle-antiparticle pairs can annihilate each producing photons; since the charges of the particle and antiparticle are opposite, total charge is conserved. For example, the positrons produced in natural decay quickly annihilate themselves with electrons, producing pairs of gamma rays, a process exploited in positron emission tomography. Antiparticles are produced naturally in the interaction of cosmic rays in the Earth's atmosphere. The latter is seen in many processes in which both its antiparticle are created simultaneously, as in particle accelerators. This is the inverse of the particle-antiparticle process. Although their antiparticles have opposite charges, electrically neutral particles need not be identical to their antiparticles. However, neutral particles are their own antiparticles, such as photons, hypothetical gravitons, some WIMPs. The charge-to-mass ratio of a particle can be measured by observing the radius of curling of its cloud-chamber track in a magnetic field. Positrons, because of the direction that their paths curled, were at first mistaken for electrons travelling in the opposite direction. The antineutron were found by Emilio Segrè and Owen Chamberlain in 1955 at the University of California, Berkeley.
Antiparticle
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Illustration of electric charge of particles (left) and antiparticles (right). From top to bottom; electron / positron, proton / antiproton, neutron / antineutron.
122.
Antimatter
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Collisions between antiparticles lead to the annihilation of both, giving rise to variable proportions of intense photons, neutrinos, less massive particle -- antiparticle pairs. Antiparticles bind with each other to form antimatter, just as particles bind to form normal matter. For example, an antiproton can form an antihydrogen atom. Physical principles indicate that complex atomic nuclei are possible, as well as anti-atoms corresponding to the known chemical elements. Studies of cosmic rays have identified both antiprotons, presumably produced by collisions between particles of ordinary matter. Satellite-based searches of cosmic rays for antihelium particles have yielded nothing. This asymmetry of antimatter in the visible universe is one of the great unsolved problems in physics. The process by which this inequality between antiparticles developed is called baryogenesis. Antimatter in the form of anti-atoms is one of the most difficult materials to produce. Antimatter in the form of individual anti-particles, however, is commonly produced in some types of radioactive decay. The nuclei of antihelium have been artificially produced with difficulty. These are the most complex anti-nuclei far observed. The idea of negative matter appears in past theories of matter that have now been abandoned. Using the once popular theory of gravity, the possibility of matter with negative gravity was discussed by William Hicks in the 1880s. Between the 1890s, Karl Pearson proposed the existence of "squirts" and sinks of the flow of aether.
Antimatter
123.
Electromagnetism
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Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually is one of the four fundamental interactions in nature. The other three fundamental interactions are the strong interaction, gravitation. The electromagnetic force plays a major role in determining the internal properties of most objects encountered in daily life. Ordinary matter is a manifestation of the electromagnetic force. The electromagnetic force governs the processes involved in chemistry, which arise from interactions between the electrons of neighboring atoms. There are mathematical descriptions of the electromagnetic field. In classical electrodynamics, electric fields are described as electric current. Although electromagnetism is considered one of the four fundamental forces, at high energy electromagnetic force are unified as a single electroweak force. During the quark epoch the unified force broke into the two separate forces as the universe cooled. Originally, magnetism were considered to be two separate forces. An electric current inside a wire creates a corresponding magnetic field outside the wire. Its direction depends on the direction of the current in the wire. While preparing for an lecture on 21 April 1820, Hans Christian Ørsted made a surprising observation. However, he began more intensive investigations.
Electromagnetism
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Lightning is an electrostatic discharge that travels between two charged regions.
Electromagnetism
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Hans Christian Ørsted.
Electromagnetism
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André-Marie Ampère
Electromagnetism
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Michael Faraday
124.
Quantum electrodynamics
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In particle physics, quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how matter is the first theory where full agreement between special relativity is achieved. In technical terms, QED can be described as a perturbation theory of the electromagnetic quantum vacuum. At higher orders in the series infinities emerged, making such computations meaningless and casting serious doubts on the internal consistency of the theory itself. With no solution for this problem known at the time, it appeared that a fundamental incompatibility existed between special relativity and quantum mechanics. Difficulties with the theory increased through the end of 1940. These experiments unequivocally exposed discrepancies which the theory was unable to explain. A first indication of a possible way out was given by Hans Bethe. Despite the limitations of the computation, agreement was excellent. The idea was simply to attach infinities to corrections of mass and charge that were actually fixed to a finite value by experiments. In this way, the infinities get absorbed in those constants and yield a finite result in good agreement with experiments. This procedure was named renormalization. Richard Feynman were jointly awarded with a Nobel prize for their work in this area. QED has served as the model and template for all subsequent quantum field theories. Near the end of his life, Richard P. Feynman gave a series of lectures on QED intended for the lay public.
Quantum electrodynamics
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Paul Dirac
Quantum electrodynamics
Quantum electrodynamics
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Hans Bethe
Quantum electrodynamics
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Feynman (center) and Oppenheimer (right) at Los Alamos.
125.
Weak interaction
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In particle physics, the weak interaction is one of the four known fundamental interactions of nature, alongside the strong interaction, electromagnetism, gravitation. The weak interaction is responsible for radioactive decay, which plays an essential role in nuclear fission. However the term QFD is rarely used because the weak force is best understood in terms of electro-weak theory. The Standard Model of particle physics, which does not address gravity, provides a uniform framework for understanding how strong interactions work. An interaction occurs when two particles, typically but not necessarily force-carrying bosons. The fermions involved in such exchanges can be either elementary or composite, although at the deepest levels, all weak interactions ultimately are between elementary particles. In the case of the weak interaction, fermions can exchange three distinct types of force carriers known as Z bosons. During the epoch of the early universe, the force separated into the electromagnetic and weak forces. Important examples of the weak interaction include the fusion of hydrogen into deuterium that powers the Sun's process. Most fermions will decay by a weak interaction over time. Such decay makes radiocarbon dating possible, as carbon-14 decays through the weak interaction to nitrogen-14. It can also create commonly used in illumination, in the related field of betavoltaics. The weak interaction is unique in that it allows for quarks to swap their flavour for another. The swapping of those properties is mediated by the bosons. Also, similarly, the only one to break charge symmetry.
Weak interaction
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Large Hadron Collider tunnel at CERN
Weak interaction
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The radioactive beta decay is possible due to the weak interaction, which transforms a neutron into: a proton, an electron, and an electron antineutrino.
126.
Electroweak interaction
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In particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at low energies, the theory models them as two different aspects of the same force. On the order of 100 GeV, they would merge into a single electroweak force. Thus, if the universe is hot enough, weak force merge into a combined electroweak force. During the epoch, the electroweak force separated from the strong force. During the epoch, the electroweak force split into the electromagnetic and weak force. In 1999, Gerardus' t Hooft and Martinus Veltman were awarded the Nobel prize for showing that the theory is renormalizable. Mathematically, the unification is accomplished under an SU × U group. The axes representing the particles have just been rotated, in the plane, by the angle θW. The L term describes the interaction between the three W particles and the B particle. L f is the kinetic term for the Standard Model fermions. The interaction of the fermions are through the gauge covariant derivative. C. The Lagrangian reorganizes itself after the Higgs boson acquires a vacuum value. Due to its complexity, this Lagrangian is best described by breaking it up into several parts as follows.
Electroweak interaction
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Large Hadron Collider tunnel at CERN
127.
Strong interaction
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The nuclear force holds most ordinary matter together because it confines quarks into hadron particles such as proton and neutron. In addition, the strong force binds protons to create atomic nuclei. On the smaller scale, it is the force that holds quarks together to form protons, other hadron particles. In the latter context, it is often known as the force. The strong force inherently has such a high strength that hadrons bound by the strong force can produce massive particles. Thus, if hadrons are struck by high-energy particles, they give rise to new hadrons instead of emitting freely moving radiation. In the context of neutrons together to form atomic nuclei, the strong interaction is called the nuclear force. In this case, it is the residuum of the strong interaction between the quarks that make up the neutrons. As such, the strong interaction obeys a quite different distance-dependent behavior between nucleons, from when it is acting to bind quarks within nucleons. The strong interaction is mediated by the exchange of massless particles called gluons that act between quarks, other gluons. Gluons are thought to interact by way of a type of charge called color charge. These rules are detailed in the theory of quantum chromodynamics, the theory of quark-gluon interactions. After the Big Bang and during the electroweak epoch of the universe, the force separated from the strong force. Before the 1970s, physicists were uncertain as to how the atomic nucleus was bound together. It was known that protons possessed positive electric charge, while neutrons were electrically neutral.
Strong interaction
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Large Hadron Collider tunnel at CERN
Strong interaction
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The nucleus of a helium atom. The two protons have the same charge, but still stay together due to the residual nuclear force
128.
Quantum chromodynamics
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QCD is a type of theory called a non-abelian gauge theory with symmetry group SU. The QCD analog of electric charge is a property called color. Gluons are the force carrier of the theory, like photons are for the electromagnetic force in quantum electrodynamics. The theory is an important part of the Standard Model of particle physics. A large body of experimental evidence for QCD has been gathered over the years. QCD enjoys two peculiar properties: Confinement, which means that the force between quarks does not diminish as they are separated. Asymptotic freedom, which means that in very high-energy reactions, quarks and gluons interact very weakly creating a quark–gluon plasma. This prediction of QCD was first discovered by David Politzer, David Gross. For this work they were awarded the 2004 Nobel Prize in Physics. The temperature between these two properties has been measured by the ALICE experiment to be well above 160 MeV. Below this temperature, confinement is dominant, while above it, asymptotic freedom becomes dominant. American physicist Murray Gell-Mann coined the word quark in its present sense. It originally comes from the phrase "Three quarks for Muster Mark" in Finnegans Wake by James Joyce. Gell-Mann got around that "by supposing that one ingredient of the line'Three quarks for Muster Mark' was a cry of'Three quarts for Mister...' Heard in H.C.
Quantum chromodynamics
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Large Hadron Collider tunnel at CERN
129.
Atomic physics
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Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and the processes by which these arrangements change. Unless otherwise stated, it can be assumed that the atom includes ions. The term atomic physics can be associated with nuclear power and nuclear weapons, due to the synonymous use of atomic and nuclear in standard English. Physics research groups are usually so classified. Atomic physics primarily considers atoms in isolation. Atomic models will consist of a single nucleus that may be surrounded by one or more bound electrons. It is not concerned with the formation of molecules, nor does it examine atoms in a solid state as condensed matter. Atomic is concerned with atomic particles. This means that the individual atoms can be treated as if each were in isolation, as the vast majority of the time they are. By this consideration atomic physics provides the underlying theory in plasma physics and atmospheric physics, even though both deal with very large numbers of atoms. Electrons form notional shells around the nucleus. These can be interaction with a colliding particle. Electrons that populate a shell are said to be in a bound state. The energy necessary to remove an electron from its shell is called the binding energy.
Atomic physics
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In the Bohr model, the transition of an electron with n=3 to the shell n=2 is shown, where a photon is emitted. An electron from shell (n=2) must have been removed beforehand by ionization
130.
Particle physics
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Particle physics is the branch of physics that studies the nature of the particles that constitute matter and radiation. By our current understanding, these elementary particles are excitations of the quantum fields that also govern their interactions. The currently dominant theory explaining these fundamental particles and fields, along with their dynamics, is called the Standard Model. In more technical terms, they are described in a Hilbert space, also treated in theory. Their interactions observed to date can be described entirely by a quantum theory called the Standard Model. The Standard Model, as currently formulated, has 61 elementary particles. Those elementary particles can combine to form composite particles, accounting for the hundreds of other species of particles that have been discovered since the 1960s. The Standard Model has been found to agree with almost all the experimental tests conducted to date. However, most particle physicists believe that it is an incomplete description of nature and that a more fundamental theory awaits discovery. In recent years, measurements of neutrino mass have provided the first experimental deviations from the Standard Model. The idea that all matter is composed of elementary particles dates from at least the 6th century BC. In the 19th century, John Dalton, through his work on stoichiometry, concluded that each element of nature was composed of a single, unique type of particle. Throughout the 1950s and 1960s, a bewildering variety of particles were found in scattering experiments. It was referred to informally as the "particle zoo". The current state of the classification of all elementary particles is explained by the Standard Model.
Particle physics
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Large Hadron Collider tunnel at CERN
131.
Nuclear physics
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Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions. The field of particle physics evolved out of nuclear physics and is typically taught in close association with nuclear physics. The discovery of the electron by J. J. Thomson a year later was an indication that the atom had internal structure. By the turn of the century physicists had also discovered three types of radiation emanating from atoms, which they named alpha, beta, gamma radiation. Experiments by Otto Hahn in 1911 and by James Chadwick in 1914 discovered that the beta decay spectrum was continuous rather than discrete. This was a problem for nuclear physics at the time, because it seemed to indicate that energy was not conserved in these decays. Rutherford was awarded the Nobel Prize in Chemistry in 1908 for his "investigations into the disintegration of the elements and the chemistry of radioactive substances". In 1905 Albert Einstein formulated the idea of mass–energy equivalence. In 1906 Ernest Rutherford published "Retardation of the α Particle from Radium in passing through matter." Greatly expanded work was published by Geiger. In 1911–1912 Rutherford went before the Royal Society to explain the experiments and propound the new theory of the atomic nucleus as we now understand it. The plum pudding model had predicted that the alpha particles should come out of the foil with their trajectories being at most slightly bent. He likened it to firing a bullet at tissue paper and having it bounce off. The Rutherford model worked quite well until studies of nuclear spin were carried out by Franco Rasetti at the California Institute of Technology in 1929. By 1925 it was known that protons and electrons each had a spin of 1⁄2.
Nuclear physics
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Nuclear physics
132.
Higgs boson
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The Higgs boson is an elementary particle in the Standard Model of particle physics. It is the excitation of the Higgs field, a fundamental field of crucial importance to particle physics theory first suspected to exist in the 1960s. Unlike known fields such as the electromagnetic field, it has a non-zero constant value in vacuum. The existence of the Higgs field would also resolve several long-standing puzzles, such as the reason for the weak force's extremely short range. Although it is hypothesised that the Higgs field permeates the entire Universe, evidence for its existence has been very difficult to obtain. These are extremely difficult to produce and detect. Since then, the particle has been shown to interact, decay in many of the ways predicted by the Standard Model. It was also tentatively confirmed to have two fundamental attributes of a Higgs boson. This appears to be the elementary scalar particle discovered in nature. The Higgs boson is named after one of six physicists who, in 1964, proposed the mechanism that suggested the existence of such a particle. On December 2013, two of them, Peter Higgs and François Englert, were awarded the Nobel Prize in Physics for their work and prediction. Although Higgs's name has come to be associated with this theory, several researchers between about 1972 independently developed different parts of it. In the Standard Model, the Higgs particle is a boson with no spin, colour charge. It is also decaying into other particles almost immediately. It is a quantum excitation of the four components of the Higgs field.
Higgs boson
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Large Hadron Collider tunnel at CERN
Higgs boson
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Candidate Higgs boson events from collisions between protons in the LHC. The top event in the CMS experiment shows a decay into two photons (dashed yellow lines and green towers). The lower event in the ATLAS experiment shows a decay into 4 muons (red tracks).
Higgs boson
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The six authors of the 1964 PRL papers, who received the 2010 J. J. Sakurai Prize for their work. From left to right: Kibble, Guralnik, Hagen, Englert, Brout. Right: Higgs.
Higgs boson
133.
Atomic, molecular, and optical physics
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The three areas are closely interrelated. AMO theory includes classical, semi-classical and quantum treatments. The term atomic physics is often associated with nuclear power and nuclear bombs, due to the synonymous use of atomic and nuclear in standard English. The important experimental techniques are the various types of spectroscopy. Molecular physics, while closely related to atomic physics, also overlaps greatly with chemical physics. Both subfields are primarily concerned with electronic structure and the dynamical processes by which these arrangements change. Generally this work involves using quantum mechanics. For molecular physics this approach is known as quantum chemistry. One important aspect of molecular physics is that the atomic theory in the field of atomic physics expands to the molecular orbital theory. Molecular physics is concerned with atomic processes in molecules, but it is additionally concerned with effects due to the molecular structure. Additionally to the electronic excitation states which are known from atoms, molecules are able to rotate and to vibrate. These rotations and vibrations are quantized; there are discrete energy levels. The smallest energy differences exist between rotational states, therefore rotational spectra are in the far infrared region of the electromagnetic spectrum. Spectra resulting from electronic transitions are mostly in the ultraviolet regions. From measuring rotational and vibrational spectra properties of molecules like the distance between the nuclei can be calculated.
Atomic, molecular, and optical physics
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An optical lattice formed by laser interference. Optical lattices are used to simulate interacting condensed matter systems.
134.
Condensed matter physics
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Condensed matter physics is a branch of physics that deals with the physical properties of condensed phases of matter, where particles adhere to each other. Condensed matter physicists seek to understand the behavior of these phases by using physical laws. In particular, they include the laws of quantum mechanics, electromagnetism and statistical mechanics. The field overlaps with chemistry, materials science, nanotechnology, relates closely to atomic physics and biophysics. Theoretical condensed matter physics shares important concepts and techniques with theoretical particle and nuclear physics. The Bell Telephone Laboratories was one of the first institutes to conduct a research program in condensed matter physics. References to "condensed" state can be traced to earlier sources. As a matter of fact, it would be more correct to unify them under the title of'condensed bodies'". One of the first studies of condensed states of matter was by English chemist Humphry Davy, in the first decades of the nineteenth century. Davy observed that of the forty chemical elements known at the time, twenty-six had metallic properties such as lustre, ductility and high electrical and thermal conductivity. This indicated that the atoms in Dalton's atomic theory were not indivisible as Dalton claimed, but had inner structure. By 1908, James Dewar and H. Kamerlingh Onnes were successfully able to liquefy hydrogen and then newly discovered helium, respectively. Paul Drude in 1900 proposed the first theoretical model for a classical electron moving through a metallic solid. The phenomenon completely surprised the best theoretical physicists of the time, it remained unexplained for several decades. Drude's classical model was augmented by Wolfgang Pauli, Arnold Sommerfeld, Felix Bloch and other physicists.
Condensed matter physics
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Heike Kamerlingh Onnes and Johannes van der Waals with the helium "liquefactor" in Leiden (1908)
Condensed matter physics
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Condensed matter physics
Condensed matter physics
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A replica of the first point-contact transistor in Bell labs
Condensed matter physics
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Computer simulation of "nanogears" made of fullerene molecules. It is hoped that advances in nanoscience will lead to machines working on the molecular scale.
135.
Quantum information
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In physics and computer science, quantum information is information, held in the state of a quantum system. Quantum information can be manipulated using engineering techniques known as quantum information processing. Quantum information differs strongly from classical information, epitomized by the bit, in many unfamiliar ways. Among these are the following: A unit of information is the qubit. Unlike digital states, a qubit is continuous-valued, describable by a direction on the Bloch sphere. Despite being continuously valued in this way, a qubit is the smallest possible unit of information. The reason for this indivisibility is due to the Heisenberg principle: despite the qubit state being continuously-valued, it is impossible to measure the value precisely. A qubit cannot be converted into classical bits;, it cannot be "read". This is the no-teleportation theorem. Despite the no-teleportation theorem, qubits can be moved from one physical particle to another, by means of quantum teleportation. That is, qubits can be transported, independently of the underlying physical particle. An arbitrary qubit destroyed. This is the content of the the no-deleting theorem. Qubits can be changed, by applying linear transformations or quantum gates to them, to alter their state. Classical bits may be extracted from configurations of multiple qubits, through the use of quantum gates.
Quantum information
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General
136.
Quantum computation
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Quantum computing studies theoretical computation systems that make direct use of quantum-mechanical phenomena, such as superposition and entanglement, to perform operations on data. Quantum computers are different from binary electronic computers based on transistors. A quantum Turing machine is also known as the universal quantum computer. Quantum computers share theoretical similarities with probabilistic computers. A quantum computer with spins as quantum bits was also formulated for use as a quantum space–time in 1968. There exist quantum algorithms, such as Simon's algorithm, that run faster than any possible classical algorithm. Given computational resources, a classical computer could in theory simulate any quantum algorithm, as quantum computation does not violate the Church -- Turing thesis. On the other hand, quantum computers may be able to efficiently solve problems which are not practically feasible on classical computers. A classical computer has a memory made up of bits, where each bit is represented by either a zero. A computer maintains a sequence of qubits. In general, a computer with n qubits can be in an arbitrary superposition of up to 2 n different states simultaneously. The sequence of gates to be applied is called a algorithm. The outcome can therefore be at most n classical bits of information. Quantum algorithms are often probabilistic, in that they provide the correct solution only with a known probability. An example of an implementation of qubits of a computer could start with the use of particles with two spin states: "down" and "up".
Quantum computation
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Photograph of a chip constructed by D-Wave Systems Inc., mounted and wire-bonded in a sample holder. The D-Wave processor is designed to use 128 superconducting logic elements that exhibit controllable and tunable coupling to perform operations.
Quantum computation
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The Bloch sphere is a representation of a qubit, the fundamental building block of quantum computers.
137.
Spintronics
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Spintronics differs from the older magnetoelectronics, in that spins are manipulated by both magnetic and electrical fields. Spintronics emerged in the 1980s concerning spin-dependent transport phenomena in solid-state devices. The spin of the electron is an intrinsic momentum, separate from the momentum due to its orbital motion. Like orbital momentum, the spin has an associated magnetic moment, the magnitude of, expressed as μ = 2 q m e ℏ. In many materials, electron spins are equally present in both the up and the down state, no transport properties are dependent on spin. A spintronic device requires manipulation of a spin-polarized population of electrons, resulting in an excess of spin down electrons. The polarization of any spin dependent property X can be written as P X = X ↑ − X ↓ X ↑ + X ↓. A net polarization can spin down. Methods include putting a material in a large magnetic field, the exchange energy present in a ferromagnet or forcing the system out of equilibrium. The period of time that such a non-equilibrium population can be maintained is known as the spin lifetime, τ. In a diffusive conductor, a spin λ can be defined as the distance over which a non-equilibrium spin population can propagate. Spin lifetimes of conduction electrons in metals are relatively short. An important research area is devoted to extending this lifetime to technologically relevant timescales. The mechanisms of decay for a population can be broadly classified as spin-flip scattering and spin dephasing. In confined structures, dephasing can be suppressed, leading to spin lifetimes of milliseconds at low temperatures.
Spintronics
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A plot showing a spin up, spin down, and the resulting spin polarized population of electrons. Inside a spin injector, the polarization is constant, while outside the injector, the polarization decays exponentially to zero as the spin up and down populations go to equilibrium.
138.
Superconductivity
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Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic flux fields occurring in certain materials when cooled below a characteristic critical temperature. It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 8, 1911 in Leiden. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon. The occurrence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of perfect conductivity in classical physics. The electrical resistance of a metallic conductor decreases gradually as temperature is lowered. Such as silver, this decrease is limited by other defects. Even near absolute zero, a real sample of a normal conductor shows some resistance. In a superconductor, the resistance drops abruptly to zero when the material is cooled below its critical temperature. An electric current flowing through a loop of superconducting wire can persist indefinitely with no power source. In 1986, it was discovered that some cuprate-perovskite ceramic materials have a critical temperature above 90 K. Such a high transition temperature is theoretically impossible for a conventional superconductor, leading the materials to be termed high-temperature superconductors. Nitrogen boils at superconduction at higher temperatures than this facilitates many applications that are less practical at lower temperatures. There are many criteria by which superconductors are classified. By theory of operation: It is conventional if it can be explained by the BCS theory or its derivatives, or unconventional, otherwise. By material: Superconductor material classes include chemical elements, organic superconductors.
Superconductivity
–
A magnet levitating above a high-temperature superconductor, cooled with liquid nitrogen. Persistent electric current flows on the surface of the superconductor, acting to exclude the magnetic field of the magnet (Faraday's law of induction). This current effectively forms an electromagnet that repels the magnet.
Superconductivity
–
A high-temperature superconductor levitating above a magnet
Superconductivity
–
Electric cables for accelerators at CERN. Both the massive and slim cables are rated for 12,500 A. Top: conventional cables for LEP; bottom: superconductor-based cables for the LHC
Superconductivity
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Heike Kamerlingh Onnes (right), the discoverer of superconductivity. Paul Ehrenfest, Hendrik Lorentz, Niels Bohr stand to his left.
139.
Non-linear dynamics
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In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space. The evolution rule of the dynamical system is a function that describes what future states follow from the current state. The concept of a dynamical system has its origins in Newtonian mechanics. To determine the state for all future times requires iterating many times -- a small step. The procedure is referred as solving the system or integrating the system. Before the advent of computers, finding an orbit required sophisticated mathematical techniques and could be accomplished only for a small class of dynamical systems. Numerical methods implemented on electronic computing machines have simplified the task of determining the orbits of a dynamical system. For dynamical systems, most dynamical systems are too complicated to be understood in terms of individual trajectories. The approximations used bring into question the validity or relevance of numerical solutions. To address several notions of stability have been introduced in the study such as Lyapunov stability or structural stability. The stability of the dynamical system implies that there is a class of models or initial conditions for which the trajectories would be equivalent. The operation for comparing orbits to establish their equivalence changes with the different notions of stability. The type of trajectory may be more important than one particular trajectory. Some trajectories may be periodic, whereas others may wander through many different states of the system. Applications often require enumerating these classes or maintaining the system within one class.
Non-linear dynamics
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The Lorenz attractor arises in the study of the Lorenz Oscillator, a dynamical system.
140.
Photonics
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Photonics is the science of light generation, detection, manipulation through emission, transmission, modulation, signal processing, switching, amplification, detection/sensing. Though covering all light's technical applications over the whole spectrum, most photonic applications are in the range of visible and near-infrared light. The term photonics developed as an outgrowth of the practical light emitters invented in the early 1960s and optical fibers developed in the 1970s. Photonics as a field began with the invention of the laser in 1960. Other developments followed: the erbium-doped fiber amplifier. These inventions formed the basis for the telecommunications revolution of the late 20th century and provided the infrastructure for the Internet. Though coined earlier, the term photonics came into common use in the 1980s as fiber-optic transmission was adopted by network operators. At that time, the term was used widely at Bell Laboratories. Its use was confirmed when the IEEE Lasers and Electro-Optics Society established an archival journal named Photonics Technology Letters at the end of the 1980s. During the period leading up to the dot-com crash circa 2001, photonics as a field focused largely on optical telecommunications. Further growth of photonics is likely if current silicon photonics developments are successful. Photonics is closely related to optics. Classical optics long preceded the discovery that light is quantized, when Albert Einstein famously explained the photoelectric effect in 1905. Optics tools include various optical components and instruments developed throughout the 15th to 19th centuries. Photonics is related to quantum optics, optomechanics, quantum electronics.
Photonics
–
Dispersion of light (photons) by a prism.
Photonics
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A sea mouse (Aphrodita aculeata), showing colorful spines, a remarkable example of photonic engineering by a living organism
141.
Neurophysics
Neurophysics
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Basic science
142.
Plasma physics
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Plasma is one of the four fundamental states of matter. Plasma has properties unlike those of the other states. The presence of a significant number of charge carriers makes plasma electrically conductive so that it responds strongly to electromagnetic fields. Like gas, plasma does not have a definite shape or a definite volume unless enclosed in a container. Under the influence of a magnetic field, it may form structures such as filaments, double layers. A common form of plasma on Earth is produced in neon signs. Much of the understanding of plasma has come from the pursuit of nuclear fusion and power, for which plasma physics provides the scientific foundation. Plasma is an electrically neutral medium of unbound positive and negative particles. It is important to note that although the particles are unbound, they are not ‘free’ in the sense of not experiencing forces. This governs collective behavior with many degrees of variation. The average number of particles in the Debye sphere is given by the plasma parameter, "Λ". Bulk interactions: The Debye screening length is short compared to the physical size of the plasma. This criterion means that interactions in the bulk of the plasma are more important than those at its edges, where boundary effects may take place. When this criterion is satisfied, the plasma is quasineutral. Plasma frequency: The electron plasma frequency is large compared to the electron-neutral collision frequency.
Plasma physics
–
Plasma
Plasma physics
Plasma physics
Plasma physics
143.
Special relativity
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In physics, special relativity is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time. In Albert Einstein's original pedagogical treatment, it is based on two postulates: The laws of physics are invariant in all inertial systems. The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source. It was originally proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies". As of today, special relativity is the most accurate model of motion at any speed. Even so, the Newtonian mechanics model is still useful as an approximation at small velocities relative to the speed of light. It has replaced the conventional notion of an universal time with the notion of a time, dependent on spatial position. Rather than an invariant interval between two events, there is an invariant interval. A defining feature of special relativity is the replacement of the Galilean transformations of Newtonian mechanics with the Lorentz transformations. Time and space cannot be defined separately from each other. Rather space and time are interwoven into a single continuum known as spacetime. Events that occur at the same time for one observer can occur at different times for another. The theory is "special" in that it only applies in the special case where the curvature of spacetime due to gravity is negligible. In order to include gravity, Einstein formulated general relativity in 1915. Special relativity, contrary to some outdated descriptions, is capable of handling accelerated frames of reference.
Special relativity
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Albert Einstein around 1905, the year his " Annus Mirabilis papers " – which included Zur Elektrodynamik bewegter Körper, the paper founding special relativity – were published.
144.
General relativity
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General relativity is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. In particular, the curvature of spacetime is directly related to the momentum of whatever matter and radiation are present. The relation is specified by a system of partial differential equations. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational time delay. The predictions of general relativity have been confirmed to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory, consistent with experimental data. Einstein's theory has astrophysical implications. General relativity also predicts the existence of gravitational waves, which have since been observed directly by physics LIGO. In addition, general relativity is the basis of cosmological models of a consistently expanding universe. Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his relativistic framework. The Einstein field equations are very difficult to solve. Einstein used approximation methods in working out initial predictions of the theory. But early as 1916, the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the Schwarzschild metric. The objects known today as black holes. In 1917, Einstein applied his theory as a whole initiating the field of relativistic cosmology.
General relativity
–
A simulated black hole of 10 solar masses within the Milky Way, seen from a distance of 600 kilometers.
General relativity
–
Albert Einstein developed the theories of special and general relativity. Picture from 1921.
General relativity
–
Einstein cross: four images of the same astronomical object, produced by a gravitational lens
General relativity
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Artist's impression of the space-borne gravitational wave detector LISA
145.
Dark matter
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Dark matter is an unidentified type of matter distinct from dark energy, baryonic matter, neutrinos. It comprises approximately 27 % of the energy in the observable universe. The standard model of cosmology indicates that the total mass -- energy of the universe contains 4.9 % ordinary matter, 68.3 % dark energy. Thus, dark matter constitutes 84.5 % of total mass, while dark energy plus dark matter constitute 95.1 % of mass -- energy content. Many experiments to detect dark matter particles through non-gravitational means are under way. The first to suggest the existence of dark matter was Dutch astronomer Jacobus Kapteyn in 1922. Fellow Dutchman and radio pioneer Jan Oort also hypothesized the existence of dark matter in 1932. In 1933, Swiss astrophysicist Fritz Zwicky, who studied galactic clusters while working at the California Institute of Technology, made a similar inference. Zwicky obtained evidence of unseen mass that he called dunkle Materie ` dark matter'. He estimated that the cluster had about 400 times more mass than was visually observable. The effect of the visible galaxies was far too small for such fast orbits, thus mass must be hidden from view. Based on these conclusions, Zwicky associated gravitation attraction to hold the cluster together. This was the formal inference about the existence of dark matter. However, Zwicky did correctly infer that the bulk of the matter was dark. The robust indications that the mass to light ratio was anything other than unity came from measurements of galaxy rotation curves.
Dark matter
–
Dark matter is invisible. Based on the effect of gravitational lensing, a ring of dark matter has been inferred in this image of a galaxy cluster (CL0024+17) and has been represented in blue.
Dark matter
–
Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons
Dark matter
–
Estimated distribution of matter and energy in the universe, today (top) and when the CMB was released (bottom)
Dark matter
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Observations have provided hints that the dark matter around one of the central four merging galaxies is not moving with the galaxy itself.
146.
Dark energy
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Dark energy is the most accepted hypothesis to explain the observations since the 1990s indicating that the universe is expanding at an accelerating rate. The mass–energy of dark matter and ordinary matter contribute 26.8% and 4.9%, respectively, other components such as neutrinos and photons contribute a very small amount. However, it comes to dominate the mass–energy of the universe because it is uniform across space. Contributions from scalar fields that are constant in space are usually also included in the constant. The cosmological constant can be formulated to be equivalent to the zero-point radiation of space i.e. the energy. Scalar fields that do change in space can be difficult to distinguish from a constant because the change may be extremely slow. High-precision measurements of the expansion of the universe are required to understand how the rate changes over time and space. In general relativity, the evolution of the rate is parameterized by the cosmological equation of state. Measuring the equation of state for dark energy is one of the biggest efforts in observational today. Dark energy has been used as a crucial ingredient in a recent attempt to formulate a cyclic model for the universe. Many things about the nature of dark energy remain matters of speculation. The theoretical need for a type of additional energy, not dark matter to form the observationally flat universe. It can be inferred from measures of large scale wave-patterns of mass density in the universe. Dark energy is not known to interact through any of the fundamental forces other than gravity. Since it is quite rarefied — roughly 10−27 kg/m3 — it is unlikely to be detectable in laboratory experiments.
Dark energy
–
Diagram representing the accelerated expansion of the universe due to dark energy.
Dark energy
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A Type Ia supernova (bright spot on the bottom-left) near a galaxy
Dark energy
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The equation of state of Dark Energy for 4 common models by Redshift. A: CPL Model, B: Jassal Model, C: Barboza & Alcaniz Model, D: Wetterich Model
147.
Emergence
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Emergence is central of complex systems. In philosophy, theories that emphasize emergent properties have been called emergentism. Almost all accounts of emergentism include a form of ontological irreducibility to the lower levels. In philosophy, emergence is often understood to be a claim about the etiology of a system's properties. One of the first modern philosophers to write on emergence, termed this categorial novum. This idea of emergence has been around since at least the time of Aristotle. John Stuart Mill and Julian Huxley are two of many philosophers who have written on the concept. Further, every resultant is clearly traceable in its components, because these are commensurable. It can not be reduced to their sum or their difference." Economist Jeffrey Goldstein provided a current definition of emergence in the Emergence. Goldstein initially defined emergence as: "coherent structures, patterns and properties during the process of self-organization in complex systems". For good measure, Goldstein throws in supervenience. They serve merely to describe consistent relationships in nature. The underlying causal agencies must be separately specified. But that aside, the game of chess illustrates... why any rules of emergence and evolution are insufficient.
Emergence
–
The formation of complex symmetrical and fractal patterns by Snowflakes is an example of emergence in a physical system.
Emergence
–
A termite "cathedral" mound produced by a termite colony is a classic example of emergence in nature.
Emergence
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Ripple patterns in a sand dune created by wind or water is an example of an emergent structure in nature.
Emergence
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Giant's Causeway in Northern Ireland is an example of a complex emergent structure created by natural processes.
148.
Complex systems
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Complex systems present problems both in mathematical modelling and philosophical foundations. One of a variety of journals using this approach to complexity is Complex Systems. Such systems are used in computer science, biology, economics, physics, chemistry, architecture and many other fields. It is also called complex systems theory, complexity science, study of complex systems, complex networks, network science, sciences of complexity, historical physics. A variety of abstract complex systems is studied as a field of mathematics. The key problems of complex systems are difficulties with their formal simulation. In different research contexts complex systems are defined on the basis of their different attributes. Since all complex systems have many interconnected components, the science of networks and theory are important and useful tools for the study of complex systems. A theory for the resilience of system of systems represented by a network of interdependent networks was developed by Buldyrev et al. A consensus regarding a universal definition of complex system does not yet exist. The study of complex system models is used for many scientific questions poorly suited to the traditional mechanistic conception provided by science. Linear systems represent the main class of systems for which general techniques for stability analysis exist. However, engineering practice must now include elements of complex systems research. This debate would notably lead economists, other parties to explore the question of computational complexity. The first institute focused on the Santa Fe Institute, was founded in 1984.
Complex systems
–
Complex systems
Complex systems
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A Braitenberg simulation, programmed in breve, an artificial life simulator
Complex systems
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A complex adaptive system model
Complex systems
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This is a schematic representation of three types of mathematical models of complex systems with the level of their mechanistic understanding.
149.
Black Holes
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The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of the region from which no escape is possible is called the event horizon. Although the event horizon has an enormous effect on the fate and circumstances of an object crossing it, no locally detectable features appear to be observed. In many ways a black hole acts like an ideal black body, as it reflects no light. This temperature is on the order of billionths of a kelvin for black holes of stellar mass, making it essentially impossible to observe. Objects whose gravitational fields are too strong for light to escape were first considered in the 18th century by John Michell and Pierre-Simon Laplace. Black holes were long considered a mathematical curiosity; it was during the 1960s that theoretical work showed they were a generic prediction of general relativity. The discovery of neutron stars sparked interest in gravitationally collapsed compact objects as a possible astrophysical reality. Black holes of stellar mass are expected to form when very massive stars collapse at the end of their life cycle. After a black hole has formed, it can continue to grow by absorbing mass from its surroundings. By merging with black holes, black holes of millions of solar masses may form. There is general consensus that supermassive black holes exist in the centers of most galaxies. Matter that falls onto a black hole can form an external accretion disk heated by friction, forming some of the brightest objects in the universe. If there are other stars orbiting a black hole, their orbits can be used to determine the black hole's mass and location. Such observations can be used to exclude possible alternatives such as neutron stars.
Black Holes
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Predicted appearance of non-rotating black hole with toroidal ring of ionised matter, such as has been proposed as a model for Sagittarius A*. The asymmetry is due to the Doppler effect resulting from the enormous orbital speed needed for centrifugal balance of the very strong gravitational attraction of the hole.
Black Holes
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Simulation of gravitational lensing by a black hole, which distorts the image of a galaxy in the background
Black Holes
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A simple illustration of a non-spinning black hole
Black Holes
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A simulated event in the CMS detector, a collision in which a micro black hole may be created.
150.
Holographic principle
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Cosmological holography has not been made mathematically precise, partly because the horizon grows with time. The holographic principle resolves the black paradox within the framework of string theory. These are the so-called "Wheeler's bags of gold". An object with relatively high entropy is microscopically random, like a hot gas. A known configuration of classical fields has zero entropy: there is nothing random about electric and magnetic fields, or gravitational waves. Since black holes are exact solutions of Einstein's equations, they were thought not to have any entropy either. But Jacob Bekenstein noted that this leads to a violation of the second law of thermodynamics. If one throws a hot gas into a black hole once it crosses the horizon, the entropy would disappear. The random properties of the gas would longer be seen once the black hole had settled down. Bekenstein assumed that black holes are maximum entropy objects—that they have more entropy than anything else in the same volume. In a sphere of radius R, the entropy in a relativistic gas increases as the energy increases. The only known limit is gravitational; when there is too much energy the gas collapses into a black hole. He concluded that the black entropy is directly proportional to the area of the horizon. Stephen Hawking had shown earlier that the total horizon area of a collection of black holes always increases with time. The horizon is a boundary defined by light-like geodesics; it is those light rays that are just barely unable to escape.
Holographic principle
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String theory
151.
Astrophysics
–
Among the objects studied are the Sun, other stars, galaxies, extrasolar planets, the interstellar medium and the cosmic microwave background. The properties examined include luminosity, density, temperature, chemical composition. In practice, astronomical research often involves a substantial amount of work in the realms of theoretical and observational physics. Although astronomy is as ancient as recorded history itself, it was long separated from the study of terrestrial physics. Their challenge was that the tools had not yet been invented with which to prove these assertions. For much of the nineteenth century, astronomical research was focused on the routine work of computing the motions of astronomical objects. Kirchhoff deduced that the dark lines in the solar spectrum are caused by chemical elements in the Solar atmosphere. Stars were also found on Earth. He thus claimed the line represented a new element, called helium, after the Greek Helios, the Sun personified. In 1885, Edward C. By 1890, a catalog of over 10,000 stars had been prepared that grouped them into thirteen spectral types. Most significantly, she discovered that helium were the principal components of stars. This discovery was so unexpected that her dissertation readers convinced her to modify the conclusion before publication. However, later research confirmed her discovery. By the end of the 20th century, further study of experimental spectra advanced, particularly as a result of the advent of quantum physics.
Astrophysics
–
Early 20th-century comparison of elemental, solar, and stellar spectra
Astrophysics
–
Supernova remnant LMC N 63A imaged in x-ray (blue), optical (green) and radio (red) wavelengths. The X-ray glow is from material heated to about ten million degrees Celsius by a shock wave generated by the supernova explosion.
Astrophysics
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The stream lines on this simulation of a supernova show the flow of matter behind the shock wave giving clues as to the origin of pulsars
152.
Observable universe
–
There are at least two trillion galaxies in the observable universe. Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction. That is, the observable universe is a spherical volume centered on the observer. Every location in the Universe has its observable universe, which may not overlap with the one centered on Earth. The word observable used in this sense does not depend on whether modern technology actually permits detection of radiation from an object in this region. It simply indicates that it is possible in principle for light or other signals from the object to reach an observer on Earth. In practice, we can see light only from back as the time of photon decoupling in the recombination epoch. That is when particles were first able to emit photons that were not quickly re-absorbed by other particles. Before then, the Universe was filled with a plasma, opaque to photons. The detection of gravitational waves indicates there is now a possibility of detecting non-light signals from before the recombination epoch. These are the photons we detect today as cosmic radiation. However, with future technology, it may be possible to observe the still older relic neutrino background, or even more distant events via gravitational waves. In the future, light from distant galaxies will have had more time to travel, so additional regions will become observable. . This fact can be used to define a type of cosmic event horizon whose distance from the Earth changes over time.
Observable universe
–
Hubble Ultra-Deep Field image of a region of the observable universe (equivalent sky area size shown in bottom left corner), near the constellation Fornax. Each spot is a galaxy, consisting of billions of stars. The light from the smallest, most red-shifted galaxies originated nearly 14 billion years ago.
Observable universe
–
Visualization of the whole observable universe. The scale is such that the fine grains represent collections of large numbers of superclusters. The Virgo Supercluster – home of Milky Way – is marked at the center, but is too small to be seen.
Observable universe
–
An example of one of the most common misconceptions about the size of the observable universe. Despite the fact that the universe is 13.8 billion years old, the distance to the edge of the observable universe is not 13.8 billion light-years, because the universe is expanding. This plaque appears at the Rose Center for Earth and Space in New York City.
Observable universe
–
Image (computer simulated) of an area of space more than 50 million light years across, presenting a possible large-scale distribution of light sources in the universe - precise relative contributions of galaxies and quasars are unclear.
153.
Big Bang
–
The Big Bang theory is the prevailing cosmological model for the universe from the earliest known periods through its subsequent large-scale evolution. If the known laws of physics are extrapolated to the highest regime, the result is a singularity, typically associated with the Big Bang. After the initial expansion, the universe cooled sufficiently to allow the formation of subatomic particles, later simple atoms. Giant clouds of these primordial elements later coalesced in halos of dark matter eventually forming the stars and galaxies visible today. More recently, measurements of the redshifts of supernovae indicate that the expansion of the universe is accelerating, an observation attributed to dark energy's existence. American astronomer Edwin Hubble observed that the distances to faraway galaxies were strongly correlated with their redshifts. Assuming the Copernican principle, the only remaining interpretation is that all observable regions of the universe are receding from all others. Since we know that the distance between galaxies increases today, it must mean that in the past galaxies were closer together. The continuous expansion of the universe implies that the universe was hotter in the past. However, these accelerators can only probe far into high energy regimes. The first subatomic particles to be formed included protons, electrons. Though atomic nuclei formed within the first three minutes after the Big Bang, thousands of years passed before the first electrically neutral atoms formed. The majority of atoms produced by the Big Bang were traces of lithium. The framework for the Big Bang model relies on simplifying assumptions such as homogeneity and isotropy of space. Similar solutions were worked on by Willem de Sitter.
Big Bang
–
Panoramic view of the entire near-infrared sky reveals the distribution of galaxies beyond the Milky Way. Galaxies are color-coded by redshift.
Big Bang
–
According to the Big Bang model, the universe expanded from an extremely dense and hot state and continues to expand.
Big Bang
–
Abell 2744 galaxy cluster - Hubble Frontier Fields view.
Big Bang
–
Lambda-CDM, accelerated expansion of the universe. The time-line in this schematic diagram extends from the big bang/inflation era 13.7 Gyr ago to the present cosmological time.
154.
Cosmology
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Cosmology is the study of the origin, evolution, eventual fate of the universe. Mythological cosmology is a body of beliefs based on mythological, religious, esoteric literature and traditions of creation and eschatology. Cosmology differs from astronomy in that the former is concerned with the Universe as a whole while the latter deals with celestial objects. Astrophysics have played a central role in shaping the understanding of the universe through scientific observation and experiment. Physical cosmology was shaped through both observation in an analysis of the whole universe. Cosmogony studies the origin of the Universe, cosmography maps the features of the Universe. In Diderot's Encyclopédie, cosmology is broken down into aerology, geology, hydrology. Metaphysical cosmology has also been described as the placing of man to all other entities. Physical cosmology is the branch of astrophysics that deals with the study of the physical origins and evolution of the Universe. It also includes the study of the nature of the Universe on a large scale. In its earliest form, it was what is now known as "celestial mechanics", the study of the heavens. Greek Aristarchus of Samos, Aristotle, Ptolemy proposed different cosmological theories. The geocentric Ptolemaic system was the prevailing theory until the 16th century when Nicolaus Copernicus, subsequently Galileo Galilei, proposed a heliocentric system. This is one of the most famous examples of epistemological rupture in physical cosmology. When Isaac Newton published the Principia Mathematica in 1687, he finally figured out how the heavens moved.
Cosmology
–
The Hubble eXtreme Deep Field (XDF) was completed in September 2012 and shows the farthest galaxies ever photographed. Except for the few stars in the foreground (which are bright and easily recognizable because only they have diffraction spikes), every speck of light in the photo is an individual galaxy, some of them as old as 13.2 billion years; the observable universe is estimated to contain more than 200 billion galaxies.
Cosmology
–
Evidence of gravitational waves in the infant universe may have been uncovered by the microscopic examination of the focal plane of the BICEP2 radio telescope.
Cosmology
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Art
155.
Theories of gravitation
–
Gravity, or gravitation, is a natural phenomenon by which all things with mass are brought toward one another, including planets, stars and galaxies. Since mass are equivalent, all forms of energy, including light, also cause gravitation and are under the influence of it. On Earth, gravity causes the ocean tides. Gravity has an infinite range, although its effects become increasingly weaker on farther objects. The most extreme example of this curvature of spacetime is a black hole, from which nothing can escape once past its horizon, not even light. More gravity results in gravitational time dilation, where time lapses more slowly at a lower gravitational potential. Gravity is the weakest of the four fundamental interactions of nature. As a consequence, gravity plays no role in determining the internal properties of everyday matter. On the other hand, gravity is the cause of the formation, shape and trajectory of astronomical bodies. While the European thinkers are rightly credited with development of gravitational theory, there were pre-existing ideas which had identified the force of gravity. Later, the works of Brahmagupta referred to the presence of this force. Modern work on gravitational theory began in the late 16th and early 17th centuries. This was a major departure from Aristotle's belief that heavier objects have a higher gravitational acceleration. Galileo postulated resistance as the reason that objects with less mass may fall slower in an atmosphere. Galileo's work set the stage for the formulation of Newton's theory of gravity.
Theories of gravitation
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Sir Isaac Newton, an English physicist who lived from 1642 to 1727
Theories of gravitation
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Two-dimensional analogy of spacetime distortion generated by the mass of an object. Matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. White lines do not represent the curvature of space but instead represent the coordinate system imposed on the curved spacetime, which would be rectilinear in a flat spacetime.
Theories of gravitation
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Ball falling freely under gravity. See text for description.
Theories of gravitation
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Gravity acts on stars that conform our Milky Way.
156.
Loop quantum gravity
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Loop quantum gravity is a theory that attempts to describe the quantum properties of the universe and gravity. It is also a theory of quantum spacetime because, according to general relativity, gravity is a manifestation of the geometry of spacetime. LQG is an attempt to merge quantum mechanics and general relativity. According to Einstein, gravity is not a force – it is a property of space-time itself. Loop gravity is an attempt to develop a theory of gravity based directly on Einstein's geometrical formulation. The main output of the theory is a physical picture of space where space is granular. The granularity is a direct consequence of the quantization. It has the same nature as the granularity of the photons in the quantum theory of electromagnetism and the discrete energy levels of atoms. Here, it is space itself, discrete. In other words, there is a minimum distance possible to travel through it. More precisely, space can be viewed as an extremely fine fabric or network "woven" of finite loops. These networks of loops are called spin networks. The evolution of a network over time is called a foam. The predicted size of this structure is the Planck length, approximately 10−35 meters. According to the theory, there is no meaning to distance at scales smaller than the Planck scale.
Loop quantum gravity
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Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons
Loop quantum gravity
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Graphical representation of the simplest non-trivial Mandestam identity relating different Wilson loops.
Loop quantum gravity
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The action of the Hamiltonian constraint translated to the path integral or so-called spin foam description. A single node splits into three nodes, creating a spin foam vertex. is the value of at the vertex and are the matrix elements of the Hamiltonian constraint.
Loop quantum gravity
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An artist depiction of two black holes merging, a process in which the laws of thermodynamics are upheld.
157.
Quantum gravity
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The current understanding of gravity is based on Albert Einstein's general theory of relativity, formulated within the framework of classical physics. The necessity of a mechanical description of gravity follows from the fact that one can not consistently couple a classical system to a one. The problem is that the one gets in this way therefore can not be used to make meaningful physical predictions. A recent development is the theory of causal fermion systems which gives mechanics, quantum field theory as limiting cases. A theory of quantum gravity, also a grand unification of all known interactions is sometimes referred to as The Theory of Everything. As a result, gravity is a mainly theoretical enterprise, although there are speculations about how gravitational effects might be observed in existing experiments. Much of the difficulty in meshing these theories at all energy scales comes from the different assumptions that these theories make on how the universe works. Quantum field theory depends on particle fields embedded in the flat space-time of special relativity. General relativity models gravity as a curvature within space-time that changes as a gravitational mass moves. Historically, the most obvious way of combining the two ran quickly into what is known as the renormalization problem. Quantum gravity can be treated as an effective field theory. Effective quantum field theories come with some high-energy cutoff, beyond which we do not expect that the theory provides a good description of nature. This same logic works just well for the highly successful theory of low-energy pions as for gravity. Indeed, the first quantum-mechanical corrections to graviton-scattering and Newton's law of gravitation have been explicitly computed. This problem must be put in the proper context, however.
Quantum gravity
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Gravity Probe B (GP-B) has measured spacetime curvature near Earth to test related models in application of Einstein's general theory of relativity.
Quantum gravity
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Interaction in the subatomic world: world lines of point-like particles in the Standard Model or a world sheet swept up by closed strings in string theory
158.
Theory of Everything
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Finding a ToE is one of the unsolved problems in physics. Over the few centuries, two theoretical frameworks have been developed that, as a whole, most closely resemble a ToE. These two theories upon which all modern physics rests are general relativity and quantum theory. QFT successfully implemented unified the interactions between the three non-gravitational forces: weak, strong, electromagnetic force. Through years of research, physicists have experimentally confirmed with tremendous accuracy virtually every prediction made in their appropriate domains of applicability. In accordance with their findings, scientists also learned that GR and QFT, as they are currently formulated, are mutually incompatible – they cannot both be right. Since the usual domains of applicability of GR and QFT are so different, most situations require that only one of the two theories be used. In pursuit of this goal, gravity has become an area of active research. Eventually a explanatory framework, called "string theory", has emerged that intends to be the ultimate theory of the universe. String theory posits that at the beginning of the universe, the four fundamental forces were once a fundamental force. According to theory, every particle in the universe, at its most microscopic level, consists of varying combinations of vibrating strings with preferred patterns of vibration. String theory further claims that it is through these oscillatory patterns of strings that a particle of unique mass and force charge is created. Initially, the theory of everything was used with an ironic connotation to refer to various overgeneralized theories. Physicist John Ellis claims to have introduced the term in 1986. Over time, the term stuck in popularizations of theoretical research.
Theory of Everything
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Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons
159.
Henri Becquerel
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Antoine Henri Becquerel was a French physicist, Nobel laureate, the first person to discover evidence of radioactivity. For work in this field he, along with Pierre Curie, received the 1903 Nobel Prize in Physics. The becquerel, is named after him. Becquerel was born into a rich family which produced four generations of scientists: Becquerel's grandfather, father, son. He studied engineering at the École des Ponts et Chaussées. In 1890 he married Louise Désirée Lorieux. In 1892, he became the third in his family to occupy the chair at the Muséum National d'Histoire Naturelle. In 1894, he became chief engineer in the Department of Bridges and Highways. Becquerel's discovery of spontaneous radioactivity is a famous example of how chance favors the prepared mind. Becquerel had long been interested in the emission of light of one color following a body's exposure to light of another color. His first experiments appeared to show this. When one then develops the photographic plate, one recognizes that the silhouette of the phosphorescent substance appears in black on the negative. One must reduce silver salts. But further experiments led him to doubt and then abandon this hypothesis. Instead the silhouettes appeared with great intensity...
Henri Becquerel
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Henri Becquerel, French physicist
Henri Becquerel
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Becquerel in the lab
Henri Becquerel
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Image of Becquerel's photographic plate which has been fogged by exposure to radiation from a uranium salt. The shadow of a metal Maltese Cross placed between the plate and the uranium salt is clearly visible.
160.
Hendrik Lorentz
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He also derived the transformation equations which formed the basis of the special theory of Albert Einstein. Hendrik Lorentz was born in the son of Gerrit Frederik Lorentz, a well-off nurseryman, Geertruida van Ginkel. After his mother's death, his father married Luberta Hupkes. Despite being raised as a Protestant, he was a freethinker in religious matters. From 1866 to 1869 he attended the a new type of public high school recently established by Johan Rudolph Thorbecke. His results in school were exemplary; not only did he excel in the physical sciences and math, but also in English, French, German. In 1870 he passed the exams in classical languages which were then required to University. He opted for a position at the Universiteit van Amsterdam at the last moment. On 25 January 1878 Lorentz delivered his inaugural lecture on "De theoriën in de natuurkunde". In 1881 he became member of the Royal Netherlands Academy of Arts and Sciences. During the first twenty years in Leiden, Lorentz was primarily interested in the theory of electromagnetism to explain the relationship of electricity, light. After that, he extended his research to a much wider area while still focusing on theoretical physics. Lorentz made significant contributions to fields ranging to general relativity. His most important contributions were in the area of the electron theory, relativity. Lorentz suggested that the oscillations of these charged particles were the source of light.
Hendrik Lorentz
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Hendrik Antoon Lorentz
Hendrik Lorentz
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Portrait by Jan Veth
Hendrik Lorentz
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Albert Einstein and Hendrik Antoon Lorentz, photographed by Ehrenfest in front of his home in Leiden in 1921.
161.
Pierre Curie
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Pierre Curie was a French physicist, a pioneer in crystallography, magnetism, piezoelectricity and radioactivity. Born in Paris on 15 May 1859, he was the son of Sophie-Claire Depouilly Curie. Pierre was educated by a doctor, in his early teens showed a strong aptitude for mathematics and geometry. When he was 16, Pierre earned his degree. Instead Pierre worked as a instructor. In 1880, his older brother Jacques demonstrated that an electric potential was generated when crystals were compressed, i.e. piezoelectricity. To provide accurate measurements needed for their work, he created a highly sensitive instrument called the Curie Scale. Pierre used weights, pneumatic dampeners to create the scale. Also, to aid their work, they invented the Piezoelectric Quartz Electrometer. Afterwards in 1881, they demonstrated the reverse effect: that crystals could be made to deform when subject to an electric field. Almost all electronic circuits now rely on this in the form of crystal oscillators. Pierre Curie was introduced by their friend, physicist Józef Wierusz-Kowalski. He took Maria as his student. His admiration for her grew when he realized that she would not inhibit his research. Pierre began to regard her as his muse.
Pierre Curie
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Pierre Curie
Pierre Curie
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Propriétés magnétiques des corps à diverses temperatures (Curie's dissertation, 1895)
Pierre Curie
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The crypt at the Panthéon in Paris
162.
Marie Curie
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Marie Skłodowska Curie, born Maria Salomea Skłodowska, was a Polish and naturalized-French physicist and chemist who conducted pioneering research on radioactivity. She was born in what was then the Kingdom of Poland, part of the Russian Empire. She began her practical scientific training in Warsaw. In 1891, aged 24, she followed her older Bronisława to study in Paris, where she earned her higher degrees and conducted her subsequent scientific work. She shared the 1903 Nobel Prize with her husband Pierre Curie and with physicist Henri Becquerel. She won the 1911 Nobel Prize in Chemistry. Her achievements included the development of the theory of radioactivity, the discovery of two elements, polonium and radium. Under her direction, the world's first studies were conducted into the treatment of neoplasms, using radioactive isotopes. She founded the Curie Institutes in Warsaw, which remain major centres of medical research today. During World War I, she established the military field radiological centres. While a French citizen, Marie Skłodowska Curie never lost her sense of Polish identity. She took them on visits to Poland. She named the first element that she discovered -- polonium, which she isolated in 1898 -- after her native country. The elder siblings of Maria were Zofia, Józef, Bronisława and Helena. This condemned the subsequent generation, including Maria, her brother, to a difficult struggle to get ahead in life.
Marie Curie
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Marie Skłodowska Curie, c. 1920
Marie Curie
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Birthplace on ulica Freta in Warsaw's " New Town " – now home to the Maria Skłodowska-Curie Museum
Marie Curie
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Władysław Skłodowski with daughters (from left) Maria, Bronisława, Helena, 1890
Marie Curie
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At a Warsaw laboratory, in 1890–91, Maria Skłodowska did her first scientific work
163.
Frederick Soddy
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Soddy also proved the existence of isotopes of certain radioactive elements. Soddy was born at 5 Bolton Road, Eastbourne, England. Soddy was a researcher at Oxford from 1898 to 1900. In 1900 Soddy became a demonstrator at McGill University in Montreal, Quebec where he worked with Ernest Rutherford on radioactivity. He and Rutherford realized that the anomalous behaviour of radioactive elements was because they decayed into other elements. This decay also produced alpha, gamma radiation. When radioactivity was first discovered, no one was sure what the cause was. It needed careful work by Soddy and Rutherford to prove that atomic transmutation was in fact occurring. With Sir William Ramsay at University College London, he showed that the decay of radium produced helium gas. In the experiment a sample of radium was enclosed in a thin-walled envelope sited within an evacuated glass bulb. From 1904 to 1914, he was a lecturer at the University of Glasgow. In May 1910 he was elected a Fellow of the Royal Society. In 1914 Soddy was appointed at the University of Aberdeen where he worked on research related to World War I. The work that his research assistant Ada Hitchins did at Glasgow and Aberdeen showed that uranium decays to radium. It also showed that a radioactive element may have more than one atomic mass though the chemical properties are identical.
Frederick Soddy
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Frederick Soddy
164.
Frank Wilczek
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Frank Anthony Wilczek is an American theoretical physicist, mathematician and a Nobel laureate. Wilczek is currently the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology, well as full Professor at Stockholm University. Wilczek is on the Scientific Advisory Board for the Future of Life Institute. Born in New York, of Polish and Italian origin, he was educated in the public schools of Queens, attending Martin Van Buren High School. It was as a result of Frank Wilczek having been administered an IQ test. Wilczek was raised Catholic. He holds the Herman Feshbach Professorship of Physics at MIT Center for Theoretical Physics. He became a foreign member of the Royal Netherlands Academy of Arts and Sciences in 2000. Wilczek was awarded the Lorentz Medal in 2002. He won the Lilienfeld Prize of the American Physical Society in 2003. In the same year Wilczek was awarded the Faculty of Mathematics and Physics Commemorative Medal from Charles University in Prague. Wilczek was Particle Physics Prize of the European Physical Society. He was also the co-recipient for Science. On January 2013 he received an honorary doctorate from the Faculty of Science and Technology at Uppsala University, Sweden. Wilczek currently serves for Science & the Public.
Frank Wilczek
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Frank Wilczek
165.
Ernest Walton
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Ernest Walton was born to a Methodist minister father, Rev John Walton and Anna Sinton. In 1922 Walton won scholarships for the study of mathematics and science. He was awarded master's degrees from Trinity in 1926 and 1927, respectively. During these years at college, Walton received numerous prizes for excellence including the Foundation Scholarship in 1924. Walton remained at Cambridge as a researcher until 1934. The splitting of the nuclei produced helium nuclei. This was experimental verification of theories about atomic structure, proposed earlier by Rutherford, others. The successful apparatus -- a type of accelerator now called the Cockcroft-Walton generator -- helped to usher in an era of particle-accelerator-based experimental nuclear physics. It was this research at Cambridge in the early 1930s that won the Nobel Prize in physics in 1951. Walton's lecturing was considered outstanding as he had the ability to present complicated matters in easy-to-understand terms. Although he retired from Trinity College Dublin in 1974, he retained his association at Trinity up to his final illness. His was a familiar face in the tea-room. Shortly before his death he marked his lifelong devotion by presenting his Nobel medal and citation to the college. Ernest Walton died on 25 June 1995, aged 91. He is buried in Dún Laoghaire -- Rathdown.
Ernest Walton
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Ernest Walton
Ernest Walton
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Earnest Walton's Grave in Deansgrange Cemetery, south County Dublin
166.
Johannes Diderik van der Waals
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Johannes Diderik van der Waals was a Dutch theoretical physicist and thermodynamicist famous for his work on an equation of state for gases and liquids. His name is primarily associated with the van der Waals equation of state that describes the behavior of their condensation to the liquid phase. His name is also associated with van der Waals forces, with van der Waals radii. Spearheaded by Wilhelm Ostwald, a strong philosophical current that denied the existence of molecules arose towards the end of the 19th century. The molecular existence was considered the molecular hypothesis unnecessary. But Van der Waals's work allowed an assessment of their size and attractive strength. The effect of Van der Waals's work on molecular physics in the 20th century was fundamental. By introducing parameters characterizing molecular attraction in constructing his equation of state, Van der Waals set the tone for modern molecular science. Heike Kamerlingh Onnes was significantly influenced by the work of van der Waals. A largely self-taught man in van der Waals originally worked as a school teacher. Van became the first professor of the University of Amsterdam when in 1877 the old Athenaeum was upgraded to Municipal University. Van der Waals won the 1910 Nobel Prize on the equation of state for gases and liquids. Johannes Diderik van der Waals was born on 23 November 1837 in Leiden in the Netherlands. Van was the eldest of ten children born to Elisabeth van den Berg. His father was a carpenter in Leiden.
Johannes Diderik van der Waals
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Johannes van der Waals
167.
Freeman Dyson
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Freeman John Dyson FRS is an English-born American theoretical physicist and mathematician, known for his work in quantum electrodynamics, solid-state physics, astronomy and nuclear engineering. Born on December 1923 at Crowthorne in Berkshire, he is the son of the English composer George Dyson, later knighted. After Dyson was born she worked as a social worker. At the age of five Dyson calculated the number of atoms in the sun. Politically, he says he was "brought up as a socialist". From 1936 to 1941, he was a Scholar at Winchester College, where his father was Director of Music. After the war, he was admitted to Cambridge, where he obtained a Bachelor of Arts degree in mathematics. In 1947, Dyson published two papers in theory. In 1947, he moved as a Commonwealth Fellow to earn a physics doctorate with Hans Bethe at Cornell University. Within a week, however, Dyson had made the acquaintance of Richard Feynman. The budding English physicist attached himself as quickly as possible. Dyson then moved to the Institute before returning to England, where he was a teaching fellow at the University of Birmingham. He never got his PhD. Robert Oppenheimer, in particular, was persuaded by Dyson that Feynman's new theory was as valid as Tomonaga's. Oppenheimer rewarded Dyson with a lifetime appointment in Oppenheimer's words.
Freeman Dyson
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At the Long Now Seminar in San Francisco, 2005
Freeman Dyson
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External video
168.
Stephen Hawking
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Hawking was the first to set forth a theory of cosmology explained by a union of the general theory of relativity and quantum mechanics. He is a vigorous supporter of the many-worlds interpretation of quantum mechanics. In 2002, Hawking was ranked number 25 in the BBC's poll of the 100 Greatest Britons. He has a slow-progressing form of amyotrophic lateral sclerosis that has gradually paralysed him over the decades. He now communicates using a single cheek muscle attached to a speech-generating device. Hawking was born on 8 January 1942 in Oxford, England, to Frank and Isobel Hawking. His mother was Scottish. Despite their families' financial constraints, both parents attended the University of Oxford, where Frank studied medicine and Isobel, Philosophy, Politics and Economics. They lived in Highgate, but as London was being bombed in those years, Isobel went to Oxford to give birth in greater safety. He has an adopted brother, Edward. In St Albans, the family were considered highly intelligent and somewhat eccentric; meals were often spent with each person silently reading a book. They lived a frugal existence in a large, cluttered, poorly maintained house, travelled in a converted London taxicab. Hawking began his schooling at the Byron House School; he later blamed its "progressive methods" for his failure to learn to read while at the school. The family placed a high value on education. The 13-year-old Hawking was ill on the day of the examination.
Stephen Hawking
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Hawking at NASA, 1980s
Stephen Hawking
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Hawking with string theorists David Gross and Edward Witten at the 2001 Strings Conference, TIFR, India
Stephen Hawking
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Stephen Hawking holding a public lecture at the Stockholm Waterfront congress center, 24 August 2015.
Stephen Hawking
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Stephen Hawking at the Bibliothèque nationale de France to inaugurate the Laboratory of Astronomy and Particles in Paris, and the French release of his work God Created the Integers, 5 May 2006.
169.
Philip Warren Anderson
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Philip Warren Anderson is an American physicist and Nobel laureate. Anderson was born in Indianapolis, Indiana and grew up in Urbana, Illinois. He graduated from University Laboratory High School in Urbana in 1940. Afterwards, he went to Harvard University for undergraduate and graduate work, with a wartime stint at the U.S. Naval Research Laboratory in-between. In graduate school he studied under John Hasbrouck van Vleck. From 1949 to 1984 he was employed in New Jersey, where he worked in condensed matter physics. He was elected a Fellow of the American Academy of Arts and Sciences in 1963. From 1967 to 1975, Anderson was a professor of theoretical physics at Cambridge University. Co-researchers Sir Nevill Francis Mott and John van Vleck shared the award with him. In 1982, he was awarded the National Medal of Science. He retired from Bell Labs in 1984 and is currently Joseph Henry Professor of Physics, Emeritus at Princeton University. Anderson's writings include Concepts of Solids, Basic Notions of Condensed Matter Physics and The Theory of Superconductivity in the High-Tc Cuprates. Anderson currently serves on the board of advisors of Scientists and Engineers for America, an organization focused on promoting sound science in American government. He is a first degree-master of the Chinese board Go. Anderson has also made conceptual contributions through his explication of emergent phenomena.
Philip Warren Anderson
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Philip Warren Anderson
170.
Sir George Paget Thomson
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Thomson was born in Cambridge, England, the son of physicist and Nobel laureate J. J. Thomson and Rose Elisabeth Paget, daughter of George Edward Paget. After brief service in France, he worked at Farnborough and elsewhere. He resigned his commission in 1920. After briefly serving in the First World War Thomson then moved to the University of Aberdeen. George Thomson was jointly awarded the Nobel Prize for Physics in 1937 in discovering the wave-like properties of the electron. The prize was shared with Clinton Joseph Davisson who had made the same discovery independently. Between 1929–1930 Thomson was a Non–Resident Lecturer at Cornell University, Ithaca, New York. In 1930 he was appointed Professor at Imperial College London in the chair of the late Hugh Longbourne Callendar. In the late 1930s and during the Second World War Thomson specialised in nuclear physics, concentrating on military applications. In particular Thomson was the chairman of the crucial MAUD Committee in 1940–1941 that concluded that an atomic bomb was feasible. In later life he also wrote works on aerodynamics and the value of science in society. Thomson stayed until 1952 when he became Master of Corpus Christi College, Cambridge. In 1964, the college honoured his tenure on the college's Leckhampton campus. In addition to winning the Nobel Prize in Physics, Thomson was knighted in 1943. He gave "Two aspects of science" as president of the British Association for 1959 -- 1960.
Sir George Paget Thomson
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Sir George Paget Thomson
171.
John Archibald Wheeler
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John Archibald Wheeler was an American theoretical physicist. He was largely responsible for reviving interest after World War II. Wheeler also worked in explaining the basic principles behind nuclear fission. Together with Gregory Breit, Wheeler developed the concept of Breit–Wheeler process. Wheeler studied under Breit and Bohr on a National Research Council fellowship. In 1939 he teamed up with Bohr to write a series of papers using the liquid model to explain the mechanism of fission. He returned to Princeton after the war returned to government service to help design and build the hydrogen bomb in the early 1950s. For most of his career, Wheeler was a professor at Princeton University, which he joined in 1938, remaining until his retirement in 1976. At Princeton he supervised 46 PhDs, more than any other professor in the Princeton department. Wheeler was born in Jacksonville, Florida on July 1911 to librarians Joseph Lewis Wheeler and Mabel Archibald Wheeler. He was the oldest of four children, having two younger brothers, a younger sister, Mary. Joseph earned a Ph.D. from Columbia University. Robert worked as a geologist for oil companies and at colleges. Mary became a librarian. They spent a year in 1921 to 1922 on a farm in Benson, Vermont, where Wheeler attended a one-room school.
John Archibald Wheeler
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John Archibald Wheeler (right) together with Eckehard W. Mielke (de) in front of lake in Holstein before the Hermann Weyl-Conference 1985 in Kiel, Germany
John Archibald Wheeler
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Loading tubes of the Hanford B Reactor
John Archibald Wheeler
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The "Sausage" device of Ivy Mike nuclear test on Enewetak Atoll. The Sausage was the first true hydrogen bomb ever tested.
John Archibald Wheeler
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Illustration of a black hole and its surrounding disk
172.
Roger Penrose
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Sir Roger Penrose OM FRS is an English mathematical physicist, mathematician and philosopher of science. He is known to general cosmology. His uncle was artist Roland Penrose, whose son with photographer Lee Miller is Antony Penrose. Penrose is the brother of mathematician Oliver Penrose and of chess Grandmaster Jonathan Penrose. He attended London, where he graduated in mathematics. He devised and popularised the Penrose triangle in the 1950s, describing it as "impossibility in its purest form" and exchanged material with the artist M. C. Escher, whose earlier depictions of impossible objects partly inspired it. Escher's Waterfall, Ascending and Descending were in turn inspired by Penrose. Together with mathematician, he went on to design a staircase that simultaneously loops up and down. An article followed and a copy was sent to Escher. Completing a cyclical flow of creativity, the Dutch master of geometrical illusions was inspired to produce his two masterpieces. One approach to this issue was by the use of perturbation theory, as developed under the leadership of John Archibald Wheeler at Princeton. Following up his "cosmic hypothesis", he went on, in 1979, to formulate a stronger version called the "strong censorship hypothesis". Together with issues of nonlinear stability, is one of the most important outstanding problems in general relativity. Penrose and James Terrell independently realised that objects travelling near the speed of light will appear to undergo a peculiar skewing or rotation.
Roger Penrose
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Roger Penrose, 2005
Roger Penrose
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Predicted view from outside the horizon of a black hole lit by a thin accretion disc
Roger Penrose
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Oil painting by Urs Schmid (1995) of a Penrose tiling using fat and thin rhombi.
Roger Penrose
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Prof. Penrose at a conference.
173.
Robert A. Millikan
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Millikan obtained his doctorate at Columbia University in 1895. In 1896 he became an assistant at the University of Chicago, where he became a full professor in 1910. In 1909 Millikan began a series of experiments to determine the electric charge carried by a single electron. He began by measuring the course of charged water droplets in an electric field. He obtained more precise results with his famous oil-drop experiment in which he replaced water with oil. In 1914 Millikan took up with similar skill the experimental verification of the equation introduced by Albert Einstein in 1905 to describe the photoelectric effect. He used this same research to obtain an accurate value of Planck’s constant. There he undertook a major study of the radiation that the physicist Victor Hess had detected coming from outer space. He named it "cosmic rays." He also served on the board of trustees for Science Service, now known as Society from 1921 to 1953. Robert Andrews Millikan was born on March 1868, in Morrison, Illinois. Millikan went in Maquoketa, Iowa. To my reply that I did not know any physics at all, his answer was, "Anyone who can do well in my Greek can teach physics." "All right," said I, "you will have to take the consequences, but I will try and see what I can do with it." I doubt if I have ever taught better in my life in my first course in physics in 1889.
Robert A. Millikan
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Robert A. Millikan
Robert A. Millikan
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Millikan’s original oil-drop apparatus, circa 1909–1910
Robert A. Millikan
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Robert A. Millikan around 1923
174.
Peter Higgs
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The Higgs mechanism is generally accepted as an important ingredient without which certain particles would have no mass. He was born in the Elswick district of Newcastle to Thomas Ware Higgs and his wife Gertrude Maude née Coghill. When his father relocated to Bedford, he was largely raised there. Higgs was awarded his PhD for a thesis entitled ` Some problems in the theory of molecular vibrations'. Higgs became a Fellow of the Royal Society of Edinburgh in 1983. He was promoted in 1980. Higgs became Emeritus professor at the University of Edinburgh. Professor Higgs received an honorary degree in 1997. In 2008 Higgs received an Honorary Fellowship in particle physics. He postulated that this field permeates space, giving that interact with it. The Higgs mechanism postulates the existence of the Higgs field which confers mass on leptons. However this causes only a tiny portion of the masses such as protons and neutrons. In these, gluons that bind quarks together confer most of the mass. The original basis of Higgs' work came from the University of Chicago. Higgs stated that there was no "moment" in the development of the theory.
Peter Higgs
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Higgs at a press conference, Stockholm, December 2013
Peter Higgs
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Portrait of Peter Higgs by Ken Currie, 2008
175.
Otto Hahn
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Otto Hahn, OBE, ForMemRS was a German chemist and pioneer in the fields of radioactivity and radiochemistry. He was exclusively awarded the Nobel Prize in Chemistry for the discovery and the radiochemical proof of nuclear fission. He is referred to as the father of nuclear chemistry. Hahn was an opponent of Jewish persecution by the Nazi Party. Albert Einstein did the best he could in these years of evil". After World War II, Hahn became a passionate campaigner as a weapon. Hahn was Charlotte Hahn, née Giese. Together with his brothers Karl, Heiner and Julius, Otto was raised in a sheltered environment. After taking his Abitur at the Klinger Oberrealschule in Frankfurt, Hahn began to study chemistry and mineralogy at the University of Marburg. His subsidiary subjects were philosophy. Hahn joined the Students' Association of Natural Sciences and Medicine, a forerunner of today's "Landsmannschaft Nibelungia". He spent his fourth semester studying under Adolf von Baeyer at the University of Munich. In 1901, Hahn received his doctorate for a dissertation entitled On Bromine Derivates of Isoeugenol, a topic in classical organic chemistry. Hahn's intention had been to work in industry. Here Hahn worked on radiochemistry, at that time a very new field.
Otto Hahn
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Otto Hahn
Otto Hahn
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Sir William Ramsay, London 1905
Otto Hahn
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Ernest Rutherford at McGill University, Montreal 1905
Otto Hahn
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Marble plaque in Latin by Professor Massimo Ragnolini, commemorating the honeymoon of Otto Hahn and his wife Edith at Punta San Vigilio, Lake Garda, Italy, in March and April 1913. (Unveiled by Count Guglielmo Guarienti di Brenzone in 1983).
176.
Tsung-Dao Lee
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He holds the rank of University Professor Emeritus at Columbia University, from which he retired in 2012. Lee was the youngest Nobel laureate after World War II until Malala Yousafzai was awarded the Nobel Peace Prize in 2014. He is the fourth youngest Nobel laureate in history after William L. Bragg, Malala Yousafzai. Lee and Yang were the Chinese laureates. Since he became a American citizen in 1962, Lee is also the youngest American ever to have won a Nobel Prize. Tsung-Dao Lee's ancestral hometown is Jiangsu Province. He was born in Shanghai. Lee's grandfather Chong-tan Lee was the first Methodist Episcopal senior pastor of St. John's Church in Suzhou. Lee has one sister. Educator Robert C.T. Lee is one of T. D.'s brothers. Brother Robert C. T. moved to Taiwan in the 1950s. They were jailed during the White Terror. Lee received his secondary education in Shanghai, Suzhou and Jiangxi. Due to the Sino-Japanese war, Lee's high school education was interrupted, thus he did not obtain his secondary diploma.
Tsung-Dao Lee
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T. D. Lee
Tsung-Dao Lee
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Signature
177.
Philipp Lenard
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Notably, he had labeled Albert Einstein's contributions as constituting "Jewish physics". Philipp Lenard was born on 7 June 1862. Lenard's parents were German-speakers. Philipp von Lenardis, was a wine-merchant in Pressburg. His mother was Antonie Baumann. As he writes it in his autobiography, this made a big impression on him. In 1880 he studied chemistry in Vienna and in Budapest. In Heidelberg he studied under the illustrious Robert Bunsen, obtained his doctoral degree in 1886. In 1887 he worked again under Loránd Eötvös as a demonstrator. In 1905 Lenard became a member of the Royal Swedish Academy in 1907 of the Hungarian Academy of Sciences. His early work included the conductivity of flames. As a physicist, Lenard's major contributions were in the study of cathode rays, which he began in 1888. Having made a window for the rays, he could pass them out into the laboratory, or, alternatively, into another chamber, completely evacuated. These windows have come to be known as Lenard windows. He was able to measure their intensity by means of paper sheets coated with phosphorescent materials.
Philipp Lenard
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Philipp Lenard in 1900
178.
Abdus Salam
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Mohammad Abdus Salam NI, SPk, KBE, was a Pakistani theoretical physicist. Salam made a major contribution at Imperial College London. Salam heavily contributed to the physics community in the world. Even until shortly before his death, Salam continued to advocate for the development of science in Third-World countries. Abdus Salam was born into an Ahmadi Muslim Punjabi family. Chaudhry Muhammad Hussain was Jat. Gul Muhammad, was a religious scholar apart from being a physician. Salam's father was an officer in the Department of Education of Punjab State in a poor farming district. Salam early established a reputation throughout the Punjab and later at the University of Cambridge for outstanding brilliance and academic achievement. At age 14, Salam scored the highest marks ever recorded at the Punjab University. He won a full scholarship to the Government College University of Lahore, Punjab State. Salam was a versatile scholar, interested in Urdu and English literature in which he excelled. But he soon picked up Mathematics as his concentration. His father wanted him to join Indian Civil Service. In those days, civil servants occupied a respected place in the civil society.
Abdus Salam
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Abdus Salam in 1987
Abdus Salam
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Abdus Salam lectures on G.U.T. at the University of Chicago's Oriental Institute
Abdus Salam
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The defaced grave of Abdus Salam at Rabwah, Punjab
Abdus Salam
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A commemorative stamp to honour the services of Dr. Abdus Salam.
179.
Gerard 't Hooft
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Gerardus't Hooft is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize "for elucidating the structure of electroweak interactions". His work concentrates on fundamental aspects of quantum mechanics. His contributions to physics include a proof that gauge theories are renormalizable, dimensional regularization, the holographic principle. He has Ellen. Saskia has translated one of her father's popular speculative books Planetenbiljart into English. The book's English title is Playing with Planets and was launched in Singapore in November 2008. Gerard't Hooft was born in Den Helder on July 5, 1946, but grew up in The Hague, the seat of government of the Netherlands. He was the middle child of a family of three. He comes from a family of scholars. Following his family's footsteps, he showed interest in science at an early age. When his primary school teacher asked him what he wanted to be when he grew up, he boldly declared, "a man who knows everything." After primary school Gerard attended the Dalton Lyceum, a school that applied the ideas of the Dalton Plan, an educational method that suited him well. He easily passed his science and mathematics courses, but struggled with his language courses. Nonetheless, he passed his classes in classical Greek and Latin.
Gerard 't Hooft
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November 2008
Gerard 't Hooft
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Gerardus 't Hooft at Harvard
180.
Murray Gell-Mann
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Murray Gell-Mann is an American physicist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles. Gell-Mann has spent several periods at CERN, among others as a John Simon Guggenheim Memorial Foundation Fellow in 1972. He introduced, independently of the quark -- constituents of all hadrons -- having first identified the SU symmetry of hadrons. This symmetry is now understood extending isospin to include a quantum number which he also discovered. He developed the V−A theory of the weak interaction in collaboration with Richard Feynman. This method led to model-independent sum rules confirmed by experiment and provided starting points underpinning the development of the standard theory of elementary particles. Gell-Mann, along with Maurice Lévy, developed the sigma model of pions, which describes low-energy pion interactions. In 1969 he received the Nobel Prize concerning the classification of their interactions. Gell-Mann is a proponent of the consistent histories approach to understanding quantum mechanics. Gell-Mann was born from the Austro-Hungarian Empire. His parents were Pauline and Arthur Isidore Gell-Mann, who taught English as a Second Language. At Yale, he participated in the William Lowell Putnam Mathematical Competition and was on the team representing Yale University that won the second prize in 1947. Gell-Mann earned a bachelor's degree from Massachusetts Institute of Technology in 1951. His supervisor at MIT was Victor Weisskopf. This work followed the experimental discovery of the violation of parity by Chien-Shiung Wu, as suggested by Chen Ning Yang and Tsung-Dao Lee, theoretically.
Murray Gell-Mann
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Gell-Mann at the World Economic Forum Annual Meeting, 2012
181.
J. J. Thomson
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Sir Joseph John Thomson OM PRS was an English physicist. Thus he is credited with the discovery and identification of the electron; and with the discovery of the first subatomic particle. Thomson was awarded the 1906 Nobel Prize in Physics for his work on the conduction of electricity in gases. Seven of his students, including his son George Paget Thomson, also became Nobel Prize winners either in physics or in chemistry. His record is comparable only to that of the German physicist Arnold Sommerfeld. Joseph John Thomson was born 18 December 1856 in Cheetham Hill, Manchester, Lancashire, England. His mother, Emma Swindells, came from a local textile family. His father, Joseph James Thomson, ran an antiquarian bookshop founded by a great-grandfather. He had a brother two years younger than he was, Frederick Vernon Thomson. His early education was in small private schools where he demonstrated outstanding talent and interest in science. In 1870 he was admitted to Owens College at the unusually young age of 14. He moved on to Trinity College, Cambridge, in 1876. In 1880 he obtained his BA in mathematics. He applied for and became a Fellow of Trinity College in 1881. Thomson received his MA in 1883.
J. J. Thomson
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Sir Joseph John Thomson
J. J. Thomson
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External video
J. J. Thomson
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In the bottom right corner of this photographic plate are markings for the two isotopes of neon: neon-20 and neon-22.
J. J. Thomson
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Plaque commemorating J. J. Thomson's discovery of the electron outside the old Cavendish Laboratory in Cambridge
182.
William Lawrence Bragg
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He was knighted in 1941. As of 2016, Lawrence Bragg is the youngest ever Nobel Laureate in physics, having received the award at the age of 25 years. He was born in South Australia. Bragg showed an early interest in mathematics. William Henry Bragg, was Elder Professor of Mathematics and Physics at the University of Adelaide. Shortly after starting school aged 5, William Lawrence Bragg broke his arm. This is the first recorded surgical use of X-rays in Australia. In the same year his father brought the family back to England. He received a major scholarship in mathematics, despite taking the exam while in bed with pneumonia. After initially excelling in mathematics, Bragg graduated with first class honours in 1911. In 1914 Bragg was elected at Trinity College -- a Fellowship at a Cambridge college involves the submission and defence of a thesis. Among Bragg's other interests was shell collecting; his personal collection amounted from some 500 species; all personally collected from South Australia. Bragg discovered a new species of cuttlefish -- Sepia braggi, named by Joseph Verco. He is most famous for his law on the diffraction of X-rays by crystals. Bragg made this discovery during his first year as a research student in Cambridge.
William Lawrence Bragg
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William L. Bragg in 1915
183.
John Bardeen
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Bardeen's developments in superconductivity, which won his second Nobel, are used in Nuclear Magnetic Resonance Spectroscopy or its medical sub-tool magnetic resonance imaging. In 1990, John Bardeen appeared on LIFE Magazine's list of the Century." John Bardeen was born on May 23, 1908. Bardeen was the son of the first dean of the University of Wisconsin Medical School. He graduated from Madison Central High School in 1923. Bardeen graduated at age fifteen even though he could have graduated several years earlier. His graduation was postponed due to taking additional courses at another high school and also because of his mother's death. Bardeen entered the University of Wisconsin -- Madison in 1923. While in college he joined the Zeta Psi fraternity. Bardeen raised the needed membership fees partly by playing billiards. Bardeen was initiated as a member of Tau Beta Pi engineering society. Bardeen chose engineering also because it is mathematical. Bardeen also felt that engineering had good job prospects. He received his Bachelor of Science degree from the University of Wisconsin -- Madison where he was a classmate of Grant Gale. Bardeen graduated despite taking a year off during his degree to work in Chicago.
John Bardeen
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John Bardeen
John Bardeen
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John Bardeen, William Shockley and Walter Brattain at Bell Labs, 1948.
John Bardeen
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A stylized replica of the first transistor invented at Bell Labs on December 23, 1947
John Bardeen
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A commemorative plaque remembering John Bardeen and the theory of superconductivity, at the University of Illinois at Urbana-Champaign.
184.
William Shockley
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William Bradford Shockley Jr. was an American physicist and inventor. Shockley was the manager of a group that included John Bardeen and Walter Brattain. The three scientists were jointly awarded the 1956 Nobel Prize in Physics. Shockley's attempts to commercialize a new design in the 1950s and 1960s led to California's "Silicon Valley" becoming a hotbed of electronics innovation. In his later life, Shockley became a proponent of eugenics. Shockley was raised in his family's hometown of Palo Alto, California, from age three. William Hillman Shockley, was a mining engineer who speculated in mines for a living, spoke eight languages. Mary, grew up in the American West, graduated from Stanford University, became the first female US Deputy mining surveyor. Shockley received his Bachelor of Science degree in 1932. Shockley received his Ph.D. degree in 1936. The title of his doctoral thesis was Electronic Bands in Sodium Chloride. His thesis topic was suggested by his thesis advisor, John C. Slater. After receiving his doctorate, Shockley joined a group headed by Clinton Davisson at Bell Labs in New Jersey. The few years were productive ones for Shockley.
William Shockley
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William Shockley
William Shockley
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John Bardeen, William Shockley and Walter Brattain at Bell Labs, 1948.
185.
James Chadwick
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Sir James Chadwick, CH, FRS was an English physicist, awarded the 1935 Nobel Prize in Physics for his discovery of the neutron in 1932. In 1941, Chadwick wrote the final draft of the MAUD Report, which inspired the U.S. government to begin atomic bomb research efforts. Chadwick was the head of the British team that worked during the Second World War. Chadwick was knighted for his achievements in physics. He graduated in 1911 where he studied under Ernest Rutherford. At Manchester, Chadwick continued to study under Rutherford until he was awarded his MSc in 1913. Chadwick was awarded an 1851 Research Fellowship from the Royal Commission for the Exhibition of 1851. Chadwick elected to study beta radiation under Hans Geiger in Berlin. Using Geiger's recently developed Geiger counter, he was able to demonstrate that beta radiation produced a continuous spectrum, not discrete lines as had been thought. Still in Germany when the First World War broke out in Europe, Chadwick spent the next four years in the Ruhleben camp. He followed his discovery of the neutron by measuring its mass. Chadwick anticipated that neutrons would become a major weapon in the fight against cancer. Chadwick surprised everyone by earning the almost-complete trust of Jr.. For his efforts, he received a knighthood on 1 January 1945. In July 1945, Chadwick viewed the Trinity nuclear test.
James Chadwick
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Sir James Chadwick
James Chadwick
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The Cavendish Laboratory was the home of some of the great discoveries in physics. It was founded in 1874 by the Duke of Devonshire (Cavendish was his family name), and its first professor was James Clerk Maxwell.
James Chadwick
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Sir Ernest Rutherford's laboratory
James Chadwick
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" Red brick " Victoria Building at the University of Liverpool
186.
Ernest O. Lawrence
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Ernest Orlando Lawrence was a pioneering American nuclear scientist and winner of the Nobel Prize in Physics in 1939 for his invention of the cyclotron. He is known for his work for founding the Lawrence Berkeley National Laboratory and the Lawrence Livermore National Laboratory. A graduate of the University of Minnesota, Lawrence obtained a PhD in physics at Yale in 1925. In 1928, he was hired at the University of California becoming the youngest full professor there two years later. In its library Lawrence was intrigued by a diagram of an accelerator that produced high-energy particles. He came up with an idea for a circular accelerating chamber between the poles of an electromagnet. The result was the first cyclotron. Lawrence went on to build a series of more expensive cyclotrons. His Radiation Laboratory became an official department of the University of California in 1936, as its director. In addition to the use of the cyclotron for physics, Lawrence also supported its use into medical uses of radioisotopes. During World War II, Lawrence developed electromagnetic separation at the Radiation Laboratory. It used devices known as a hybrid of the standard laboratory mass spectrometer and cyclotron. A electromagnetic separation plant was built at Oak Ridge, Tennessee, which came to be called Y-12. It worked. Lawrence strongly backed Edward Teller's campaign for a nuclear weapons laboratory, which Lawrence located in Livermore, California.
Ernest O. Lawrence
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Lawrence in 1939
Ernest O. Lawrence
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Meeting at Berkeley in 1940 concerning the planned 184-inch (4.67 m) cyclotron (seen on the blackboard): Lawrence, Arthur Compton, Vannevar Bush, James B. Conant, Karl T. Compton, and Alfred Lee Loomis
Ernest O. Lawrence
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The 60-inch (1.52 m) cyclotron soon after completion in 1939. The key figures in its development and use are shown, standing, left to right: D. Cooksey, D. Corson, Lawrence, R. Thornton, J, Backus, W.S. Sainsbury. In the background are Luis Walter Alvarez and Edwin McMillan.
Ernest O. Lawrence
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Giant electromagnet Alpha I racetrack for uranium enrichment at Y-12 plant, Oak Ridge, Tennessee, circa 1944–45. The calutrons Lawrence developed are located around the ring.
187.
Robert Hooke
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Robert Hooke FRS was an English natural philosopher, architect and polymath. These issues may have contributed to his historical obscurity. Allan Chapman has characterised him as "England's Leonardo". He studied at Oxford during the Protectorate where he became one of a tightly knit group of ardent Royalists led by John Wilkins. Hooke observed the rotations of Mars and Jupiter. In 1665 Hooke inspired the use of microscopes for scientific exploration with Micrographia. Based on his microscopic observations of fossils, he was an early proponent of biological evolution. Much of what is known of Hooke's early life comes from an autobiography that he commenced in 1696 but never completed. Richard Waller mentions it in his introduction to The Posthumous Works of M.D. S.R.S. printed in 1705. The work of Waller, along with John Ward's Lives of the Gresham Professors and John Aubrey's Brief Lives, form the major biographical accounts of Hooke. Robert Hooke was born in 1635 in Freshwater to John Hooke and Cecily Gyles. His two brothers were also ministers. Robert Hooke was expected to join the Church. Robert, too, grew up to be a staunch monarchist. As a youth, Robert Hooke was fascinated by observation, drawing, interests that he would pursue in various ways throughout his life.
Robert Hooke
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Modern portrait of Robert Hooke (Rita Greer 2004), based on descriptions by Aubrey and Waller; no contemporary depictions of Hooke are known to survive.
Robert Hooke
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Memorial portrait of Robert Hooke at Alum Bay, Isle of Wight, his birthplace, by Rita Greer (2012).
Robert Hooke
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Robert Boyle
Robert Hooke
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Diagram of a louse from Hooke's Micrographia
188.
Christiaan Huygens
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Christiaan Huygens, FRS was a prominent Dutch mathematician and scientist. He is known particularly as an astronomer, physicist, horologist. Huygens was a leading scientist of his time. He pioneered work on games of chance. Christiaan Huygens was born into a rich and influential Dutch family, the second son of Constantijn Huygens. Christiaan was named after his paternal grandfather. His mother was Suzanna van Baerle. She died in 1637, shortly after the birth of Huygens' sister. The couple had five children: Constantijn, Christiaan, Lodewijk, Philips and Suzanna. Constantijn Huygens was a advisor to the House of Orange, also a poet and musician. His friends included Galileo Galilei, René Descartes. Huygens was educated until turning sixteen years old. He liked to play with miniatures of other machines. His father gave a liberal education: he studied languages and music, history and geography, mathematics, logic and rhetoric, but also dancing, fencing and horse riding. In 1644 Huygens had as his mathematical tutor Jan Jansz de Jonge Stampioen, who set the 15-year-old a demanding reading list on contemporary science.
Christiaan Huygens
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Christiaan Huygens by Bernard Vaillant, Museum Hofwijck, Voorburg
Christiaan Huygens
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Correspondance
Christiaan Huygens
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The catenary in a manuscript of Huygens.
Christiaan Huygens
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Christiaan Huygens, relief by Jean-Jacques Clérion, around 1670?
189.
Leonhard Euler
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He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. Euler is also known for his work in mechanics, music theory. Euler was one of the most eminent mathematicians of the 18th century, is held to be one of the greatest in history. He is also widely considered to be the most prolific mathematician of all time. His collected works fill 60 to 80 quarto volumes, more than anybody in the field. He spent most of his adult life in St. Petersburg, Russia, in Berlin, then the capital of Prussia. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all." He had two younger sisters: Anna Maria and Maria Magdalena, a younger brother Johann Heinrich. Soon after the birth of Leonhard, the Eulers moved from Basel to the town of Riehen, where Euler spent most of his childhood. Euler's formal education started in Basel, where he was sent to live with his maternal grandmother. During that time, he was receiving Saturday afternoon lessons from Johann Bernoulli, who quickly discovered his new pupil's incredible talent for mathematics. In 1726, Euler completed a dissertation on the propagation of sound with the title De Sono. At that time, he was unsuccessfully attempting to obtain a position at the University of Basel. Pierre Bouguer, who became known as "the father of naval architecture", won and Euler took second place. Euler later won this annual prize twelve times.
Leonhard Euler
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Portrait by Jakob Emanuel Handmann (1756)
Leonhard Euler
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1957 Soviet Union stamp commemorating the 250th birthday of Euler. The text says: 250 years from the birth of the great mathematician, academician Leonhard Euler.
Leonhard Euler
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Stamp of the former German Democratic Republic honoring Euler on the 200th anniversary of his death. Across the centre it shows his polyhedral formula, nowadays written as " v − e + f = 2".
Leonhard Euler
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Euler's grave at the Alexander Nevsky Monastery
190.
Thomas Young (scientist)
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Thomas Young was an English polymath and physician. He made scientific contributions to the fields of vision, light, solid mechanics, energy, physiology, language, musical harmony, Egyptology. Young "made a number of insightful innovations" in the decipherment of Egyptian hieroglyphs before Jean-François Champollion eventually expanded on his work. Young was mentioned among others, William Herschel, Hermann von Helmholtz, James Clerk Maxwell, Albert Einstein. He has been described as "The Last Man Who Knew Everything". He belonged to a Quaker family of Milverton, Somerset, where he was born in the eldest of ten children. In 1797 Young entered Cambridge. He published many of his academic articles anonymously to protect his reputation as a physician. In 1801 he was appointed professor of natural philosophy at the Royal Institution. In two years Young delivered 91 lectures. In 1802, Young was appointed foreign secretary of the Royal Society, of which he had been elected a fellow in 1794. Young resigned his professorship in 1803, fearing that its duties would interfere with his medical practice. His lectures contain a number of anticipations of later theories. He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1822. In 1828, Young was elected a foreign member of the Royal Swedish Academy of Sciences.
Thomas Young (scientist)
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Thomas Young
Thomas Young (scientist)
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Signature
Thomas Young (scientist)
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Plate from "Lectures" of 1802 (RI), publ 1807
Thomas Young (scientist)
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Mathematical elements of natural philosophy
191.
Polymath
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The term was first used in the 17th century; polyhistor, is an ancient term with similar meaning. The term is often used to describe the Enlightenment who excelled at several fields in science and the arts. This term has now been applied to great thinkers living before and after the Renaissance. "Renaissance man" was first recorded in the early 20th century. It is now used to refer to great thinkers living before, after the Renaissance. Leonardo da Vinci has often been described of the Renaissance man a man of "unquenchable curiosity" and "feverishly inventive imagination". These polymaths had a rounded approach to education that reflected the ideals of the humanists of the time. The idea of a universal education was essential to achieving polymath ability, hence the university was used to describe a seat of learning. At this time, universities did not specialize in specific areas but rather trained students in a broad array of science, theology. This universal education gave a grounding from which they could continue into apprenticeship toward becoming a master of a specific field. Aside from "Renaissance man" as mentioned above, similar terms in use are Homo Universalis and Uomo Universale, which translate to "universal person" or "universal man". The related generalist -- contrasted with a specialist -- is used to describe a person with a general approach to knowledge. Versatile Genius is also used, with Leonardo da Vinci as the prime example again. When a person is described as having "encyclopedic knowledge", they exhibit a vast scope of knowledge. One whose accomplishments are limited to athletics would not be considered a "polymath" in the usual sense of the word.
Polymath
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Leonardo da Vinci, a polymath of the Renaissance era.
Polymath
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Abū Rayḥān al-Bīrūnī was a notable Persian polymath.
Polymath
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Galileo was one of the most influential polymaths.
Polymath
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Medieval German polymath Hildegard of Bingen, shown dictating to her scribe in an illumination from Liber Scivias
192.
Young's interference experiment
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This experiment played a major role in the general acceptance of the wave theory of light. In Young's own judgement, this was the most important of his many achievements. During this period, many scientists proposed a theory of light including Leonhard Euler. His idea was greeted with a certain amount of skepticism because it contradicted Newton's corpuscular theory. Nonetheless, he continued to develop his ideas. He demonstrated the phenomenon of interference in water waves. We are now to apply the same principles to the alternate union and extinction of colours. The figure shows the geometry for a far-field viewing plane. This expression applies when the light source has a single wavelength, whereas Young used sunlight, was therefore looking at white-light fringes which he describes above. A white light fringe pattern can be considered to be made up of a set of individual fringe patterns of different colours. Only two or three fringes can normally be observed. In the years 1803–1804, a series of unsigned attacks on Young's theories appeared in the Edinburgh Review. This incident prompted Young to focus more on his medical practice and less on physics. Augustin-Jean Fresnel submitted a thesis based on wave theory and whose substance consisted of a synthesis of the Huygens' principle and Young's principle of interference. Poisson studied Fresnel's theory in detail and of course looked for a way to prove it wrong being a supporter of the particle-theory of light.
Young's interference experiment
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From book publ 1807 relating lectures given by Young in 1802 to London's Royal Institution
193.
Wave theory of light
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Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to visible light, responsible for the sense of sight. This wavelength means a range of roughly 430 -- 750 terahertz. The main source of light on Earth is the Sun. This process of photosynthesis provides virtually all the energy used by living things. Historically, another important source of light for humans has been fire, to modern kerosene lamps. With the development of electric lights and power systems, electric lighting has effectively replaced firelight. Some species of animals generate their own light, a process called bioluminescence. For example, vampire squids use it to hide themselves from prey. Visible light, as with all types of electromagnetic radiation, is experimentally found to always move at this speed in a vacuum. In physics, the light sometimes refers to electromagnetic radiation of any wavelength, whether visible or not. In this sense, gamma rays, X-rays, radio waves are also light. Like all types of light, visible light exhibits properties of both waves and particles. This property is referred to as the wave–particle duality. The study of light, known as optics, is an important area in modern physics.
Wave theory of light
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An example of refraction of light. The straw appears bent, because of refraction of light as it enters liquid from air.
Wave theory of light
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A triangular prism dispersing a beam of white light. The longer wavelengths (red) and the shorter wavelengths (blue) get separated.
Wave theory of light
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A cloud illuminated by sunlight
Wave theory of light
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A city illuminated by artificial lighting
194.
Michael Faraday
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Michael Faraday FRS was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic induction, electrolysis. Although Faraday received formal education, he was one of the most influential scientists in history. Faraday also established that there was an underlying relationship between the two phenomena. He similarly discovered the laws of electrolysis. Faraday ultimately became the first and foremost Fullerian Professor of Chemistry at the Royal Institution of a lifetime position. The SI unit of capacitance is named in his honour: the farad. Albert Einstein kept a picture of Faraday alongside pictures of Isaac Newton and James Clerk Maxwell. Faraday was born in Newington Butts, now part of the London Borough of Southwark but was then a suburban part of Surrey. His family was not off. James, was a member of the Glassite sect of Christianity. Michael was born in the autumn of that year. The young Michael Faraday, the third of four children, having only the most basic school education, had to educate himself. At the age of 14 he became an apprentice in Blandford Street. He enthusiastically implemented the principles and suggestions contained therein.
Michael Faraday
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Michael Faraday, 1842
Michael Faraday
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External video
Michael Faraday
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Portrait of Faraday in his late thirties
Michael Faraday
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Michael Faraday, ca. 1861
195.
Cathode ray
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Cathode rays are streams of electrons observed in vacuum tubes. They were named by Eugen Goldstein Kathodenstrahlen, or cathode rays. Electrons were first discovered as the constituents of cathode rays. In 1897 British physicist J. J. Thomson showed the rays were composed of a previously unknown negatively charged particle, later named the electron. Cathode ray tubes use a focused beam of electrons deflected by magnetic fields to create the image in a classic set. Cathode rays are so named because they are emitted by cathode, in a tube. To release electrons into the tube, they first must be detached from the atoms of the cathode. The increased random motion of the filament knocks electrons out into the evacuated space of the tube. Since the electrons have a negative charge, they are repelled by the cathode and attracted to the anode. They travel in straight lines through the empty tube. The voltage applied between the electrodes accelerates these low mass particles to high velocities. The electric field of the wires deflects some of the electrons, preventing them from reaching the anode. Thus a small voltage on the grid can be made to control a much larger voltage on the anode. This is the principle used in vacuum tubes to amplify electrical signals. These are used in ray tubes, found in electron microscopes.
Cathode ray
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A beam of cathode rays bent into a circle by a magnetic field generated by a Helmholtz coil. Cathode rays are normally invisible; in this tube enough residual gas has been left that the gas atoms glow from fluorescence when struck by the fast moving electrons.
Cathode ray
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Crookes tube
196.
Gustav Kirchhoff
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Gustav Robert Kirchhoff was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, the emission of black-body radiation by heated objects. The Bunsen–Kirchhoff Award for spectroscopy is named after him and his colleague, Robert Bunsen. Gustav Kirchhoff was born in Königsberg, East Prussia, the son of Friedrich Kirchhoff, Johanna Henriette Wittke. In the same year, he moved to Berlin, where he stayed until he received a professorship at Breslau. Later, in 1857, He married the daughter of his mathematics professor Richelot. The couple had five children. Clara died in 1869. He married Luise Brömmel in 1872. Kirchhoff formulated his circuit laws, which are now ubiquitous in electrical engineering, in 1845, while still a student. He completed this study as a exercise; it later became his doctoral dissertation. In 1857 he calculated that an electric signal in a resistanceless wire travels along the wire at the speed of light. He gave a proof in 1861. He was called in 1854 where he collaborated in spectroscopic work with Robert Bunsen. Together Kirchhoff and Bunsen discovered rubidium in 1861. At Heidelberg he ran a mathematico-physical seminar, modelled on Neumann's, with the mathematician Leo Koenigsberger.
Gustav Kirchhoff
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Gustav Kirchhoff
Gustav Kirchhoff
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Gustav Kirchhoff (left) and Robert Bunsen (right)
Gustav Kirchhoff
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Spectroscope of Kirchhoff and Bunsen
Gustav Kirchhoff
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Tombstone at Alter St.-Matthäus-Kirchhof
197.
Ludwig Boltzmann
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Boltzmann was born in Vienna, the capital of the Austrian Empire. Ludwig Georg Boltzmann, was a official. Katharina Pauernfeind, was originally from Salzburg. He received his primary education from a private tutor at the home of his parents. Boltzmann attended high school in Linz, Upper Austria. When Boltzmann was 15, his father died. Boltzmann studied physics at the University of Vienna, starting in 1863. Among his teachers were Josef Loschmidt, Joseph Stefan, Andreas von Ettingshausen and Jozef Petzval. Boltzmann received his PhD degree in 1866 working under the supervision of Stefan; his dissertation was on kinetic theory of gases. In 1867 he became a Privatdozent. After obtaining his doctorate degree, Boltzmann worked two more years as Stefan's assistant. It was Stefan who introduced Boltzmann to Maxwell's work. In 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and there he stayed until 1876. In 1872, long before women were admitted to Austrian universities, he met an aspiring teacher in Graz. She was refused permission to audit lectures unofficially.
Ludwig Boltzmann
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Ludwig Boltzmann
Ludwig Boltzmann
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Ludwig Boltzmann and co-workers in Graz, 1887. (standing, from the left) Nernst, Streintz, Arrhenius, Hiecke, (sitting, from the left) Aulinger, Ettingshausen, Boltzmann, Klemenčič, Hausmanninger
Ludwig Boltzmann
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Boltzmann's 1898 I 2 molecule diagram showing atomic "sensitive region" (α, β) overlap.
Ludwig Boltzmann
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Boltzmann's bust in the courtyard arcade of the main building, University of Vienna.
198.
Wien approximation
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Wien's approximation is a law of physics used to describe the spectrum of thermal radiation. This law was first derived by Wilhelm Wien in 1896. Wien derived his law from several years before Planck introduced the quantization of radiation. Details are contained in. T is the temperature of the black body. H is Planck's constant. C is the speed of light. K is Boltzmann's constant. The Wien approximation was originally proposed as a description of the complete spectrum of thermal radiation, although it failed to accurately describe long emission. However, it was soon superseded by Planck's law, developed by Max Planck. Unlike the Wien approximation, Planck's law accurately describes the complete spectrum of thermal radiation. Wien's displacement law Sakuma–Hattori equation ASTM Subcommittee E20.02 on Radiation Thermometry Ultraviolet catastrophe
Wien approximation
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Comparison of Wien's Distribution law with the Rayleigh–Jeans Law and Planck's law, for a body of 8 mK temperature.
199.
Maxwell's equations
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One important consequence of the equations is that fluctuating electric and magnetic fields can propagate at the speed of light. This electromagnetic radiation manifests itself in manifold ways from radio waves to light and X- or γ-rays. The equations have two major variants. The microscopic Maxwell equations have universal applicability but may be infeasible to calculate with. They relate the magnetic fields including the complicated currents in materials at the atomic scale. The "macroscopic" Maxwell equations define two new auxiliary fields that describe the large-scale behaviour of matter without having to consider atomic scale details. However, their use requires experimentally determining parameters for a phenomenological description of the electromagnetic response of materials. The term "Maxwell's equations" is often used for equivalent alternative formulations. The space-time formulations, are commonly used in high energy and gravitational physics because they make the compatibility of the equations with special and general relativity manifest. In many situations, though, deviations from Maxwell's equations are immeasurably small. Exceptions include many other phenomena related to photons or virtual photons. In the electric and magnetic field formulation there are four equations. The two inhomogeneous equations describe how the fields vary in space due to sources. Gauss's law describes how electric fields emanate from electric charges. Gauss's law for magnetism describes magnetic fields as closed field lines not due to magnetic monopoles.
Maxwell's equations
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Maxwell's equations (mid-left) as featured on a monument in front of Warsaw University's Centre of New Technologies
Maxwell's equations
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Electromagnetism
Maxwell's equations
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In a geomagnetic storm, a surge in the flux of charged particles temporarily alters Earth's magnetic field, which induces electric fields in Earth's atmosphere, thus causing surges in electrical power grids. Artist's rendition; sizes are not to scale.
Maxwell's equations
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Magnetic core memory (1954) is an application of Ampère's law. Each core stores one bit of data.
200.
Planck's law
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Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T. The law is named after Max Planck, who proposed it in 1900. It is a pioneering result of modern physics and quantum theory. The spectral radiance of a body, Bν, describes the amount of energy it gives off as radiation of different frequencies. The spectral radiance can also be measured per unit wavelength instead of per unit frequency. In this case, it is given by B λ = 2 h c 2 λ 5 1 e h c λ k B T − 1. The SI units of Bν are W·sr−1·m−2·Hz−1, while those of Bλ are W·sr−1·m−3. In the limit of low frequencies, Planck's law tends to the Rayleigh–Jeans law, while in the limit of high frequencies it tends to the Wien approximation. As an energy distribution, it is one of a family of thermal equilibrium distributions which include the Bose–Einstein distribution, the Fermi–Dirac distribution and the Maxwell–Boltzmann distribution. Every physical body spontaneously and continuously emits electromagnetic radiation. Near thermodynamic equilibrium, the emitted radiation is nearly described by Planck's law. Because of its dependence on temperature, Planck radiation is said to be thermal radiation. The higher the temperature of a body the more radiation it emits at every wavelength. Planck radiation has a maximum intensity at a specific wavelength that depends on the temperature. For example, at room temperature, a body emits thermal radiation, mostly infrared and invisible.
Planck's law
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Planck's law (colored curves) accurately described black body radiation and resolved the ultraviolet catastrophe (black curve).
201.
Atomic theory
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In chemistry and physics, atomic theory is a scientific theory of the nature of matter, which states that matter is composed of discrete units called atoms. The atom comes from the Ancient Greek adjective atomos, meaning "indivisible". 19th century chemists began using the term in connection with the growing number of irreducible chemical elements. In fact, in extreme environments, such as neutron stars, extreme temperature and pressure prevents atoms from existing at all. Since atoms were found to be divisible, physicists later invented the term "elementary particles" to describe the "uncuttable", though not indestructible, parts of an atom. The idea that matter is made up of discrete units is a very old one, appearing in ancient cultures such as Greece and India. However, these ideas were founded rather than evidence and experimentation. Because of this, they could not convince everybody, so atomism was but one of a number of competing theories on the nature of matter. Near the end of the 18th century, two laws about chemical reactions emerged without referring to the notion of an atomic theory. The second was the law of definite proportions. For example: Proust had found that their masses were either 88.1 % tin and 11.9 % oxygen or 78.7 % tin and 21.3 % oxygen. Dalton noted from these percentages that 100g of tin will combine either with 27g of oxygen; 13.5 and 27 form a ratio of 1:2. Dalton found that an atomic theory of matter could elegantly explain this common pattern in chemistry. In the case of Proust's tin oxides, one atom will combine with either one or two oxygen atoms. Dalton hypothesized this was due to the differences in complexity of the gases' respective particles.
Atomic theory
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The cathode rays (blue) were emitted from the cathode, sharpened to a beam by the slits, then deflected as they passed between the two electrified plates.
Atomic theory
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The current theoretical model of the atom involves a dense nucleus surrounded by a probabilistic "cloud" of electrons
202.
Electromagnetic radiation
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Electromagnetic radiation is the radiant energy released by certain electromagnetic processes. Visible light is electromagnetic radiation, as is invisible light, infrared, X-rays. Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of magnetic fields that propagate at the speed of light through a vacuum. The oscillations of the two fields are perpendicular to perpendicular to the direction of energy and wave propagation, forming a transverse wave. These waves can subsequently interact with any charged particles. EM waves can impart those quantities to matter with which they interact. They are still affected by gravity. Thus, EMR is sometimes referred to as the far field. In this language, the near field refers to EM current that directly produced them, specifically, electromagnetic induction and electrostatic induction phenomena. In the theory of electromagnetism, EMR consists of photons, the elementary particles responsible for all electromagnetic interactions. Quantum effects provide additional sources such as the transition of electrons to lower energy levels in an atom and black-body radiation. The energy of an individual photon is greater for photons of higher frequency. A single gamma photon, for example, might carry ~ 100,000 times the energy of a single photon of visible light. The effects of EMR upon biological organisms depend both upon the radiation's power and its frequency. EMR of visible or lower frequencies is called non-ionizing radiation, because its photons do not individually have enough energy to ionize molecules.
Electromagnetic radiation
203.
Elliptical orbit
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In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0 and less than 1. In a wider sense it is a Kepler orbit with negative energy. This includes the radial elliptic orbit, with eccentricity equal to 1. In a two-body problem with negative energy both bodies follow elliptic orbits with the same orbital period around their common barycenter. Also the relative position of one body with respect to the other follows an elliptic orbit. Examples of elliptic orbits include: Hohmann transfer orbit, Molniya orbit. A is the length of the semi-major axis. Conclusions: For a given semi-major axis the specific orbital energy is independent of the eccentricity. ν is the local true anomaly. Here ϕ is defined as the angle which differs by 90 degrees from this, so the cosine appears in place of the sine. This set of six variables, together with time, are called the orbital state vectors. Given the masses of the two bodies they determine the full orbit. The two most general cases with these 6 degrees of freedom are the elliptic and the hyperbolic orbit. Special cases with fewer degrees of freedom are the circular and parabolic orbit. Another set of six parameters that are commonly used are the orbital elements.
Elliptical orbit
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A small body in space orbits a large one (like a planet around the sun) along an elliptical path, with the large body being located at one of the ellipse foci.
204.
Frequency
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Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example, if a newborn baby's heart beats at a frequency of a minute, its period -- the interval between beats -- is half a second. For cyclical processes, such as waves, frequency is defined as a number of cycles per unit time. Period X Ordinary frequency = 1 cycle. Therefore, the period, usually denoted by T, is the reciprocal of the frequency f: f = 1 T. The SI unit of frequency is the hertz, named after the German physicist Heinrich Hertz; one hertz means that an event repeats once per second. A previous name for this unit was cycles per second. The SI unit for period is the second. A traditional unit of measure used with rotating mechanical devices is revolutions per abbreviated rpm. 60 rpm equals one hertz. As a matter of convenience, slower waves, such as surface waves, tend to be described by wave period rather than frequency. Fast waves, like radio, are usually described by their frequency instead of period. Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes.
Frequency
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A resonant-reed frequency meter, an obsolete device used from about 1900 to the 1940s for measuring the frequency of alternating current. It consists of a strip of metal with reeds of graduated lengths, vibrated by an electromagnet. When the unknown frequency is applied to the electromagnet, the reed which is resonant at that frequency will vibrate with large amplitude, visible next to the scale.
Frequency
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As time elapses – represented here as a movement from left to right, i.e. horizontally – the five sinusoidal waves shown vary regularly (i.e. cycle), but at different rates. The red wave (top) has the lowest frequency (i.e. varies at the slowest rate) while the purple wave (bottom) has the highest frequency (varies at the fastest rate).
Frequency
Frequency
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Modern frequency counter
205.
Planck constant
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The Planck constant is a physical constant, the quantum of action, central in quantum mechanics. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called the photon. This leads to another relationship involving the Planck constant. With p denoting the linear momentum of a particle, the de Broglie wavelength λ of the particle is given by λ = h p. In applications where it is natural to use the angular frequency it is often useful to absorb a factor of 2π into the Planck constant. The resulting constant is called the reduced Planck constant or Dirac constant. It is equal to the Planck constant divided by 2π, is denoted ħ: ℏ = h 2 π. This was confirmed by experiments soon afterwards. This holds throughout quantum theory, including electrodynamics. These two relations are the temporal and spatial component parts of the special relativistic expression using 4-Vectors. P μ = = ℏ K μ = ℏ Classical statistical mechanics requires the existence of h. Eventually, following upon Planck's discovery, it was recognized that physical action cannot take on an arbitrary value. Instead, it must be some multiple of a very small quantity, the "quantum of action", now called the Planck constant. Thus there is no value of the action as classically defined.
Planck constant
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Plaque at the Humboldt University of Berlin: "Max Planck, discoverer of the elementary quantum of action h, taught in this building from 1889 to 1928."
206.
Electromagnetic wave
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Electromagnetic radiation is the radiant energy released by certain electromagnetic processes. Visible light is electromagnetic radiation, as is invisible light, infrared, X-rays. Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of magnetic fields that propagate at the speed of light through a vacuum. The oscillations of the two fields are perpendicular to perpendicular to the direction of energy and wave propagation, forming a transverse wave. These waves can subsequently interact with any charged particles. EM waves can impart those quantities to matter with which they interact. They are still affected by gravity. Thus, EMR is sometimes referred to as the far field. In this language, the near field refers to EM current that directly produced them, specifically, electromagnetic induction and electrostatic induction phenomena. In the theory of electromagnetism, EMR consists of photons, the elementary particles responsible for all electromagnetic interactions. Quantum effects provide additional sources such as the transition of electrons to lower energy levels in an atom and black-body radiation. The energy of an individual photon is greater for photons of higher frequency. A single gamma photon, for example, might carry ~ 100,000 times the energy of a single photon of visible light. The effects of EMR upon biological organisms depend both upon the radiation's power and its frequency. EMR of visible or lower frequencies is called non-ionizing radiation, because its photons do not individually have enough energy to ionize molecules.
Electromagnetic wave
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The electromagnetic waves that compose electromagnetic radiation can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This diagram shows a plane linearly polarized EMR wave propagating from left to right. The electric field is in a vertical plane and the magnetic field in a horizontal plane. The electric and magnetic fields in EMR waves are always in phase and at 90 degrees to each other.
207.
Photon
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A photon is an elementary particle, the quantum of all forms of electromagnetic radiation including light. It is the carrier for electromagnetic force, even when static via virtual photons. Like all elementary particles, photons are currently best explained by exhibit wave -- particle duality, exhibiting properties of both waves and particles. The quanta in a light wave cannot be spatially localized. Some defined physical parameters of a photon are listed. The model accounted for anomalous observations, including the properties of black-body radiation, that others had tried to explain using semiclassical models. Material objects emitted and absorbed light in quantized amounts. In 1926 the chemist Gilbert N. Lewis coined the name photon for these particles. The intrinsic properties such as charge, mass and spin, are determined by this gauge symmetry. It has been applied to photochemistry, measurements of molecular distances. Recently, photons have been studied for applications in optical imaging and optical communication such as quantum cryptography. In his 1901 article in Annalen der Physik he called these packets "energy elements". The quanta was used before 1900 to mean particles or amounts of different quantities, including electricity. In 1905, Albert Einstein suggested that electromagnetic waves could only exist as discrete wave-packets. He called such a wave-packet the light quantum.
Photon
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Large Hadron Collider tunnel at CERN
208.
Solvay Conference
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The Institutes coordinate conferences, workshops, colloquia. Following the initial success of 1911, the Solvay Conferences have been devoted to preeminent open problems in both physics and chemistry. There have been larger gaps. Hendrik A. Lorentz was chairman of the first Solvay Conference held in the autumn of 1911. The subject was the Quanta. This conference looked at the problems of having two approaches, namely the classical physics and theory. Albert Einstein was the second youngest present. Other members of the Solvay Congress included such luminaries as Henri Poincaré. The first Solvay Conference following World War I was held in April 1921. Most German scientists were barred from attending. The leading figures were Niels Bohr. Bragg, H.A. Kramers, P.A.M. Dirac, A.H. Compton, L. de Broglie, M. Born, N. Bohr;I. Langmuir, M. Planck, M. Skłodowska-Curie, H.A.
Solvay Conference
Solvay Conference
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Third Conference, 1921
Solvay Conference
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Fourth Conference, 1924
209.
Brussels
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Brussels, officially the Brussels-Capital Region, is a region of Belgium comprising 19 municipalities, including the City of Brussels, the capital of Belgium. The region has a population of 1.2 million and a metropolitan area with a population of over 1.8 million, the largest in Belgium. Brussels is the de facto capital of the European Union as it hosts a number of principal EU institutions. The secretariat of the Benelux and the headquarters of the North Atlantic Treaty Organization are also located in Brussels. It has seen a shift from the 19th century onwards. Today the majority language is French, the Brussels-Capital Region is an officially bilingual enclave within the Flemish Region. Many services are shown in both languages. Brussels is increasingly becoming multilingual with increasing numbers of migrants, expatriates and minority groups speaking their own languages. The bishop of Cambrai made the recorded reference in 695 when it was still a hamlet. Charles would construct the first permanent fortification in the city, doing so on that same island. Lambert I of Leuven, Count of Leuven gained the County of Brussels around 1000 by marrying Charles' daughter. As it grew to a population of around 30,000, the surrounding marshes were drained to allow for further expansion. The Counts of Leuven became Dukes of Brabant at about this time. In the 13th century, the city got its first walls. After the construction of the city walls in the early 13th century, Brussels grew significantly.
Brussels
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A collage with several views of Brussels, Top: View of the Northern Quarter business district, 2nd left: Floral carpet event in the Grand Place, 2nd right: Brussels City Hall and Mont des Arts area, 3rd: Cinquantenaire Park, 4th left: Manneken Pis, 4th middle: St. Michael and St. Gudula Cathedral, 4th right: Congress Column, Bottom: Royal Palace of Brussels
Brussels
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Charles of Lorraine founded what would become Brussels c. 979
Brussels
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Grand Place after the 1695 bombardment by the French army
Brussels
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Episode of the Belgian Revolution of 1830, Wappers (1834)
210.
Quantum physics
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Quantum mechanics, including quantum field theory, is a fundamental branch of physics concerned with processes involving, for example, atoms and photons. Systems such as these which obey quantum mechanics can be in a quantum superposition of different states, unlike in classical physics. Early quantum theory was profoundly reconceived in the mid-1920s. The reconceived theory is formulated in various specially developed mathematical formalisms. In one of them, the function, provides information about the amplitude of position, momentum, other physical properties of a particle. This experiment played a major role in the general acceptance of the wave theory of light. In 1838, Michael Faraday discovered cathode rays. Planck's hypothesis that energy is radiated and absorbed in discrete "quanta" precisely matched the observed patterns of black-body radiation. In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation, known as Wien's law in his honor. Ludwig Boltzmann independently arrived at this result by considerations of Maxwell's equations. However, it was valid only at high frequencies and underestimated the radiance at low frequencies. Following Max Planck's solution in 1900 to the black-body radiation problem, Albert Einstein offered a quantum-based theory to explain the photoelectric effect. Robert Andrews Millikan studied the photoelectric effect experimentally, Albert Einstein developed a theory for it. In 1913, Peter Debye extended Niels Bohr's theory of atomic structure, introducing elliptical orbits, a concept also introduced by Arnold Sommerfeld. This phase is known as old quantum theory.
Quantum physics
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Max Planck is considered the father of the quantum theory.
Quantum physics
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Solution to Schrödinger's equation for the hydrogen atom at different energy levels. The brighter areas represent a higher probability of finding an electron
Quantum physics
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The 1927 Solvay Conference in Brussels.
211.
Subatomic particles
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In the physical sciences, subatomic particles are particles much smaller than atoms. There are two types of subatomic particles: elementary particles, which according to current theories are not made of other particles; and composite particles. Nuclear physics study these particles and how they interact. In particle physics, the concept of a particle is one of several concepts inherited from classical physics. The idea of a particle underwent serious rethinking when experiments showed that light could behave like a stream of particles well as exhibit wave-like properties. This led to the new concept of wave -- duality to reflect that quantum-scale "particles" behave like both particles and waves. The uncertainty principle, states that some of their properties taken together, such as their simultaneous position and momentum, can not be measured exactly. In more recent times, wave -- duality has been shown to apply not only to photons but to increasingly massive particles as well. Interactions of particles in the framework of quantum theory are understood as creation and annihilation of quanta of corresponding fundamental interactions. This blends particle physics with theory. Any subatomic particle, like any particle in the 3-dimensional space that obeys laws of quantum mechanics, can be either a fermion. Various extensions of the Standard Model predict the existence of many other elementary particles. Composite subatomic particles are bound states of two or more elementary particles. The neutron is made up quark. Composite particles include all hadrons: these include mesons.
Subatomic particles
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Large Hadron Collider tunnel at CERN
212.
Periodic table
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The periodic table is a tabular arrangement of the chemical elements, ordered by their atomic number, electron configurations, recurring chemical properties. This ordering shows periodic trends, such as elements with similar behaviour in the same column. It also shows four rectangular blocks with some approximately similar chemical properties. In general, within one row the elements are metals on the left, non-metals on the right. The rows of the table are called periods; the columns are called groups. Six groups have names as well as numbers: for example, group 17 elements are the halogens; and group 18, the noble gases. The periodic table provides a useful framework for analyzing chemical behaviour, is widely used in chemistry and other sciences. Dmitri Mendeleev published in 1869 the first widely recognized periodic table. He developed his table to illustrate periodic trends in the properties of the then-known elements. Mendeleev also predicted some properties of then-unknown elements that would be expected to fill gaps in this table. Most of his predictions were proved correct when the elements in question were subsequently discovered. The first 94 elements exist naturally, although some are found only in trace amounts and were synthesized in laboratories before being found in nature. Elements with atomic numbers from 95 to 118 have only been synthesized in laboratories or nuclear reactors. Synthesis of elements having higher atomic numbers is being pursued. Numerous synthetic radionuclides of naturally occurring elements have also been produced in laboratories.
Periodic table
–
Dmitri Mendeleev
Periodic table
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Standard form of the periodic table (color legend below)
Periodic table
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Glenn T. Seaborg who, in 1945, suggested a new periodic table showing the actinides as belonging to a second f-block series
213.
Chemical bond
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A chemical bond is a lasting attraction between atoms that enables the formation of chemical compounds. The bond may result as in the covalent bonds. The nuclei will be attracted toward electrons in this position. This attraction constitutes the chemical bond. This phenomenon limits the distance between atoms in a bond. In general, strong bonding is associated with the sharing or transfer of electrons between the participating atoms. , in practice, simplification rules allow chemists to predict the strength, directionality, polarity of bonds. The octet rule and theory are two examples. Electrostatics are used to describe the effects they have on chemical substances. A bond is an attraction between atoms. This attraction may be seen as the result of different behaviors of the valence electrons of atoms. These behaviors merge into each other seamlessly in various circumstances, so that there is no clear line to be drawn between them. However it remains customary to differentiate between different types of bond, which result in different properties of condensed matter. In the simplest view of a covalent bond, one or more electrons are drawn into the space between the two atomic nuclei. Energy is released by formation.
Chemical bond
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Examples of Lewis dot -style representations of chemical bonds between carbon (C), hydrogen (H), and oxygen (O). Lewis dot diagrams were an early attempt to describe chemical bonding and are still widely used today.
214.
Superfluid
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Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without loss of kinetic energy. When stirred a superfluid forms cellular vortices that continue to rotate indefinitely. Superfluidity occurs in two isotopes of helium, helium-4, when they are liquified by cooling to cryogenic temperatures. It is also a property of various exotic states of matter theorized to exist in astrophysics, high-energy physics, theories of quantum gravity. Superfluidity was originally discovered by Pyotr Kapitsa and John F. Allen. It has since been described through microscopic theories. In liquid helium-4, the superfluidity occurs at far higher temperatures than it does in helium-3. Each atom of helium-4 is a particle, by virtue of its integer spin. A helium-3 atom is a particle; it can form bosons only by pairing with itself at much lower temperatures. This process is similar to the electron pairing in superconductivity. Such vortices had previously been observed in an bosonic gas using 87Rb in 2000, more recently in two-dimensional gases. As early as 1999 Lene Hau created such a condensate later stopping it completely. With a light-roadblock setup, we can generate controlled collisions between shock waves resulting in completely unexpected, nonlinear excitations. We have observed hybrid structures consisting of vortex rings embedded in solitonic shells. The vortex rings act as'phantom propellers' leading to very rich excitation dynamics."
Superfluid
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Fig. 2. The liquid helium is in the superfluid phase. As long as it remains superfluid, it creeps up the wall of the cup as a thin film. It comes down on the outside, forming a drop which will fall into the liquid below. Another drop will form—and so on—until the cup is empty.
Superfluid
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Fig. 1. Helium II will "creep" along surfaces in order to find its own level—after a short while, the levels in the two containers will equalize. The Rollin film also covers the interior of the larger container; if it were not sealed, the helium II would creep out and escape.
215.
Latin language
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Latin is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from Greek alphabets. Latin was originally spoken in the Italian Peninsula. Through the power of the Roman Republic, it became the dominant language, initially in Italy and subsequently throughout the Roman Empire. Vulgar Latin developed such as Italian, Portuguese, Spanish, French, Romanian. Latin, Italian and French have contributed many words to the English language. Ancient Greek roots are used in theology, biology, medicine. By the late Roman Republic, Old Latin had been standardised into Classical Latin. Vulgar Latin was the colloquial form attested in inscriptions and the works of comic playwrights like Plautus and Terence. Later, Early Modern Latin and Modern Latin evolved. Latin was used until well into the 18th century, when it began to be supplanted by vernaculars. Ecclesiastical Latin remains the Roman Rite of the Catholic Church. Many students, scholars and members of the Catholic clergy speak Latin fluently. It is taught around the world. The language has been passed down through various forms.
Latin language
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Latin inscription, in the Colosseum
Latin language
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Julius Caesar 's Commentarii de Bello Gallico is one of the most famous classical Latin texts of the Golden Age of Latin. The unvarnished, journalistic style of this patrician general has long been taught as a model of the urbane Latin officially spoken and written in the floruit of the Roman republic.
Latin language
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A multi-volume Latin dictionary in the University Library of Graz
Latin language
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Latin and Ancient Greek Language - Culture - Linguistics at Duke University in 2014.
216.
Atom
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An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element. Plasma is composed of neutral or ionized atoms. Atoms are very small; typical sizes are around 100 picometers. Through the development of physics, atomic models have incorporated quantum principles to better predict the behavior. Every atom is composed of one or more electrons bound to the nucleus. The nucleus is made of typically a similar number of neutrons. Neutrons are called nucleons. More than 99.94% of an atom's mass is in the nucleus. The protons have a electric charge, the electrons have a negative electric charge, the neutrons have no electric charge. If the number of electrons are equal, that atom is electrically neutral. It is called an ion. The electrons of an atom are attracted by this electromagnetic force. The number of protons in the nucleus defines to what the atom belongs: for example, all copper atoms contain 29 protons. The number of neutrons defines the isotope of the element. The number of electrons influences the magnetic properties of an atom.
Atom
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Scanning tunneling microscope image showing the individual atoms making up this gold (100) surface. The surface atoms deviate from the bulk crystal structure and arrange in columns several atoms wide with pits between them (See surface reconstruction).
Atom
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Helium atom
217.
Mathematical
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Mathematics is the study of topics such as quantity, structure, space, change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of logic, mathematics developed from counting, the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity from as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Galileo Galilei said, "The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. Without these, one is wandering about in a dark labyrinth." Carl Friedrich Gauss referred to mathematics as "the Queen of the Sciences". Benjamin Peirce called mathematics "the science that draws necessary conclusions". David Hilbert said of mathematics: "We are not speaking here of arbitrariness in any sense. Mathematics is not like a game whose tasks are determined by arbitrarily stipulated rules.
Mathematical
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Euclid (holding calipers), Greek mathematician, 3rd century BC, as imagined by Raphael in this detail from The School of Athens.
Mathematical
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Greek mathematician Pythagoras (c. 570 – c. 495 BC), commonly credited with discovering the Pythagorean theorem
Mathematical
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Leonardo Fibonacci, the Italian mathematician who established the Hindu–Arabic numeral system to the Western World
Mathematical
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Carl Friedrich Gauss, known as the prince of mathematicians
218.
Chemistry
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Chemistry is a branch of physical science that studies the composition, structure, properties and change of matter. Chemistry is sometimes called the central science because it bridges natural sciences, including physics, biology. For the differences between physics see comparison of physics. Scholars disagree about the etymology of the word chemistry. The history of chemistry can be traced to alchemy, practiced for several millennia in various parts of the world. The chemistry comes from alchemy, which referred to an earlier set of practices that encompassed elements of chemistry, metallurgy, philosophy, astrology, astronomy, medicine. An alchemist was called a'chemist' in popular speech, later the suffix "-ry" was added to this to describe the art of the chemist as "chemistry". The modern alchemy in turn is derived from the Arabic al-kīmīā. In origin, the term is borrowed from the Greek χημία or χημεία. Alternately, al-kīmīā may derive from χημεία, meaning "cast together". In retrospect, the definition of chemistry has changed over time, as new discoveries and theories add to the functionality of the science. The term "chymistry", in the view of noted scientist Robert Boyle in 1661, meant the subject of the material principles of mixed bodies. In 1837, Jean-Baptiste Dumas considered the word "chemistry" to refer to the science concerned with the laws and effects of molecular forces. More recently, in 1998, Professor Raymond Chang broadened the definition of "chemistry" to mean the study of matter and the changes it undergoes. Early civilizations, such as the Egyptians Babylonians, Indians amassed practical knowledge concerning the arts of metallurgy, pottery and dyes, but didn't develop a systematic theory.
Chemistry
–
Solutions of substances in reagent bottles, including ammonium hydroxide and nitric acid, illuminated in different colors
Chemistry
–
Democritus ' atomist philosophy was later adopted by Epicurus (341–270 BCE).
Chemistry
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Antoine-Laurent de Lavoisier is considered the "Father of Modern Chemistry".
Chemistry
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Laboratory, Institute of Biochemistry, University of Cologne.
219.
Solid-state physics
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Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the large-scale properties of solid materials result from their atomic-scale properties. Thus, solid-state physics forms a theoretical basis of materials science. It also has direct applications, for example in the technology of transistors and semiconductors. Solid materials are formed from densely packed atoms, which interact intensely. These interactions produce the mechanical, thermal, optical properties of solids. Depending on the conditions in which it was formed, the atoms may be arranged in a geometric pattern or irregularly. The bulk of solid-state physics, as a general theory, is focused on crystals. Primarily, this is because the periodicity of atoms in a crystal — its defining characteristic — facilitates mathematical modeling. Likewise, crystalline materials often have electrical, mechanical properties that can be exploited for engineering purposes. The forces between the atoms in a crystal can take a variety of forms. In a crystal of chloride, the crystal is made up of ionic sodium and chlorine, held together with ionic bonds. In others, the atoms share electrons and form covalent bonds. In metals, electrons are shared amongst the whole crystal in metallic bonding.
Solid-state physics
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An example of a simple cubic lattice
220.
Computational physics
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Computational physics is the study and implementation of numerical analysis to solve problems in physics for which a quantitative theory already exists. Historically, computational physics is now a subset of computational science. In physics, different theories based on mathematical models provide very precise predictions on how systems behave. Unfortunately, it is often the case that solving the mathematical model for a particular system in order to produce a useful prediction is not feasible. This can occur, for instance, when the solution is too complicated. In such cases, numerical approximations are required. There is a debate about the status of computation within the scientific method. While computers can be used in experiments for the recording of data, this clearly does not constitute a computational approach. Physics problems are in general very difficult to solve exactly. This is due to several reasons: lack of algebraic and/or analytic solubility, chaos. On the more advanced side, mathematical theory is also sometimes used. In addition, the computational cost and complexity for many-body problems tend to grow quickly. A macroscopic system typically has a size of the order of 23 constituent particles, so it is somewhat of a problem. For classical N-body it is of order N-squared. Because computational physics uses a broad class of problems, it is generally divided amongst the mathematical problems it numerically solves, or the methods it applies.
Computational physics
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Computational physics
221.
Computational chemistry
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Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into efficient computer programs, to calculate the properties of molecules and solids. While computational results normally complement the information obtained by chemical experiments, it can in some cases predict hitherto unobserved chemical phenomena. It is widely used in the design of new materials. The methods used cover both dynamic situations. In all cases, other resources increase rapidly with the size of the system being studied. That system can be one molecule, a solid. Computational chemistry methods range from very approximate to highly accurate; the latter are usually feasible for small systems only. Ab initio methods are based entirely on basic physical constants. Other methods are called semi-empirical because they use additional empirical parameters. Semi-empirical approaches involve approximations. In principle, initio methods eventually converge to the exact solution of the underlying equations as the number of approximations is reduced. In practice, residual error inevitably remains. The goal of computational chemistry is to minimize this residual error while keeping the calculations tractable. In some cases, the details of electronic structure are less important than the long-time phase behavior of molecules.
Computational chemistry
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Diagram illustrating various ab initio electronic structure methods in terms of energy. Spacings are not to scale.
222.
Circular motion
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In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body. Without this acceleration, the object would move according to Newton's laws of motion. In physics, circular motion describes the motion of a body traversing a circular path at constant speed. Since the body describes circular motion, its distance from the axis of rotation remains constant at all times. Though the body's speed is constant, its velocity is not constant: a vector quantity, depends on both the body's speed and its direction of travel. This changing velocity indicates the presence of an acceleration; this centripetal acceleration is of constant magnitude and directed at all times towards the axis of rotation. This acceleration is, in turn, directed towards the axis of rotation. Note: The magnitude of the angular velocity is the angular speed. For motion in a circle of radius r, the circumference of the circle is C = 2π r. The axis of rotation is shown as a vector perpendicular to the plane of the orbit and with a magnitude ω = dθ / dt. The direction of ω is chosen using the right-hand rule. In the simplest case the mass and radius are constant.
Circular motion
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Figure 1: Velocity v and acceleration a in uniform circular motion at angular rate ω; the speed is constant, but the velocity is always tangent to the orbit; the acceleration has constant magnitude, but always points toward the center of rotation
223.
Probability
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Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1. The higher the probability of an event, the more certain that the event will occur. A simple example is the tossing of a fair coin. Since the coin is unbiased, the two outcomes are both equally probable; the probability of "head" equals the probability of "tail." Since no other outcomes are possible, the probability is 1/2, of either "head" or "tail". This type of probability is also called a priori probability. Probability theory is also used to describe the underlying mechanics and regularities of complex systems. For example, tossing a fair coin twice will yield "head-head", "tail-tail" outcomes. The probability of getting an outcome of "head-head" is 1 out of 0.25. This interpretation considers probability to be the relative frequency "in the long run" of outcomes. Subjectivists assign numbers per subjective probability, i.e. as a degree of belief. The most popular version of subjective probability is Bayesian probability, which includes knowledge well as experimental data to produce probabilities. The knowledge is represented by some prior distribution. These data are incorporated in a likelihood function.
Probability
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Christiaan Huygens probably published the first book on probability
Probability
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Gerolamo Cardano
Probability
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Carl Friedrich Gauss
224.
Atomic orbital
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This function can be used to calculate the probability of finding any electron of an atom in any specific region around the atom's nucleus. Each such orbital can be occupied by a maximum of two electrons, each with its own spin number s. These names, together with the value of n, are used to describe the electron configurations of atoms. They are derived from the description as sharp, principal, diffuse, fundamental. The lowest possible energy an electron can take is therefore analogous to the fundamental frequency of a wave on a string. Higher energy states are then similar to harmonics of the fundamental frequency. Particle-like properties: There is always an integer number of electrons orbiting the nucleus. Electrons jump between orbitals in a particle-like fashion. For example, if a single photon strikes the electrons, only a single electron changes states in response to the photon. The electrons retain particle-like properties such as: each state has the same electrical charge as the electron particle. Each state has a single discrete spin. This can depend upon its superposition. Thus, despite the popular analogy to planets revolving around the Sun, electrons cannot be described simply as solid particles. In addition, atomic orbitals do not closely resemble a planet's elliptical path in ordinary atoms. A more accurate analogy might be that of a often oddly shaped "atmosphere", distributed around a relatively tiny planet.
Atomic orbital
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The shapes of the first five atomic orbitals: 1s, 2s, 2p x, 2p y, and 2p z. The two colors show the phase or sign of the wave function in each region. These are graphs of ψ(x, y, z) functions which depend on the coordinates of one electron. To see the elongated shape of ψ(x, y, z) 2 functions that show probability density more directly, see the graphs of d-orbitals below.
Atomic orbital
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False-color density images of some hydrogen-like atomic orbitals (f orbitals and higher are not shown)
225.
Spectrum
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A spectrum is a condition, not limited to a specific set of values but can vary infinitely within a continuum. The word was first used scientifically within the field of optics to describe the rainbow of colors in visible light when separated using a prism. As scientific understanding of light advanced, it came to apply to the electromagnetic spectrum. Spectrum has since been applied to topics outside of optics. Thus, one might talk about the spectrum of political opinion, or the autism spectrum. In these uses, values within a spectrum may not be associated with definitions. Such uses imply a broad range of behaviors grouped together and studied under a single title for ease of discussion. In most modern usages of spectrum there is a unifying theme between extremes at either end. They led to modern ones through a sequence of events set out below. This may be difficult to recognize. In Latin spectrum means "image" or "apparition", including the meaning "spectre". Spectral evidence is testimony about what was done not present physically, or hearsay evidence about what ghosts or apparitions of Satan said. It was used to convict a number of persons of witchcraft at Salem, Massachusetts in the 17th century. The word "spectrum" was strictly used to designate a ghostly optical afterimage in On Vision and Colors. The prefix "spectro-" is used to form words relating to spectra.
Spectrum
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The spectrum in a rainbow
Spectrum
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Electromagnetic spectrum of a quasar.
Spectrum
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Mass spectrum of Titan 's ionosphere
Spectrum
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Spectrogram of dolphin vocalizations.
226.
Isotope
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Isotopes are variants of a particular chemical element which differ in neutron number. All isotopes of a given element have the same number of protons in each atom. The number of protons within the atom's nucleus is equal to the number of electrons in the neutral atom. Each isotope of a given element has a different mass number. For example, carbon-12, carbon-14 are three isotopes of the element carbon with mass numbers 12, 13 and 14 respectively. Nuclide refers to a nucleus rather than to an atom. Identical nuclei belong for example each nucleus of the carbon-13 nuclide is composed of 6 protons and 7 neutrons. The nuclide concept emphasizes nuclear properties over chemical properties, whereas the isotope concept emphasizes chemical over nuclear. Its effect on chemical properties is negligible for most elements. An isotope nuclide is specified by the name of the particular element followed by a hyphen and the mass number. When a symbol is used, e.g.. The m is sometimes appended after the mass number to indicate a nuclear isomer, a metastable or energetically-excited nuclear state, for example 180m 73Ta. For example, 14C is a radioactive form of carbon, whereas 13C are stable isotopes. There are about 339 naturally meaning that they have existed since the Solar System's formation. Primordial nuclides include 32 nuclides with 254 that are formally considered as "stable nuclides", because they have not been observed to decay.
Isotope
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The three naturally-occurring isotopes of hydrogen. The fact that each isotope has one proton makes them all variants of hydrogen: the identity of the isotope is given by the number of neutrons. From left to right, the isotopes are protium (1 H) with zero neutrons, deuterium (2 H) with one neutron, and tritium (3 H) with two neutrons.
Isotope
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Nuclear physics
Isotope
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In the bottom right corner of J. J. Thomson 's photographic plate are the separate impact marks for the two isotopes of neon: neon-20 and neon-22.
227.
Chemical element
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A chemical element or element is a species of atoms having the same number of protons in their atomic nuclei. There are 118 elements of which the first 94 occur naturally on Earth with the remaining 24 being synthetic elements. There are 80 elements that have 38 that have exclusively radioactive isotopes, which decay over time into other elements. Iron is the most abundant element making up Earth, while oxygen is the most common element in the Earth's crust. Chemical elements constitute all of the ordinary matter of the universe. Hydrogen and helium, were mostly formed in the Big Bang and are the most common elements in the universe. The next three elements are thus rarer than those that follow. Formation of elements with from 6 to 26 protons continues to occur in main sequence stars via stellar nucleosynthesis. The high abundance of oxygen, iron on Earth reflects their common production in such stars. The term "element" is used for atoms with a given number of protons well as for a pure chemical substance consisting of a single element. When different elements are chemically combined, with the atoms held together by chemical bonds, they form chemical compounds. Only a minority of elements are found uncombined as relatively pure minerals. Among the more common of such native elements are copper, silver, gold, carbon, sulfur. While about 32 of the chemical elements occur in native uncombined forms, most of these occur as mixtures. The history of the use of the elements began with primitive human societies that found native elements like carbon, sulfur, copper and gold.
Chemical element
Chemical element
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Top: The periodic table of the chemical elements. Below: Examples of certain chemical elements. From left to right: hydrogen, barium, copper, uranium, bromine, and helium.
Chemical element
Chemical element
228.
Unit vector
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In mathematics, a unit vector in a normed vector space is a vector of length 1. A vector is often denoted by a lowercase letter with a circumflex, or "hat": ı ^. The term direction vector is used to describe a unit vector being used to represent spatial direction, such quantities are commonly denoted as d. Two 2D direction vectors, d1 and d2 are illustrated. 2D spatial directions represented this way are equivalent numerically to points on the circle. The same construct is used to specify spatial directions in 3D. As illustrated, each unique direction is equivalent numerically to a point on the sphere. The term normalized vector is sometimes used as a synonym for vector. Unit vectors are often chosen to form the basis of a space. Every vector in the space may be written as a linear combination of unit vectors. In a Euclidean space the dot product of two unit vectors is a scalar value amounting to the cosine of the smaller subtended angle. Unit vectors may be used to represent the axes of a coordinate system. They are often denoted using normal notation rather than standard unit vector notation. In most contexts it can be assumed that j, k, are versors of a 3-D Cartesian coordinate system. The notations, or, without hat, are also used, particularly in contexts where i, j, k might lead to confusion with another quantity.
Unit vector
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Examples of two 2D direction vectors
229.
Complex number
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In this expression, b is the imaginary part of the complex number. A + bi can be identified with the point in the complex plane. As as their use within mathematics, complex numbers have practical applications in many fields, including physics, chemistry, biology, economics, electrical engineering, statistics. The Italian mathematician Gerolamo Cardano is the first known to have introduced complex numbers. He called them "fictitious" during his attempts to find solutions to cubic equations in the 16th century. Complex numbers allow solutions to certain equations that have no solutions in real numbers. For example, the equation = − 9 has no real solution, since the square of a real number can not be negative. Complex numbers provide a solution to this problem. According to the fundamental theorem of algebra, all polynomial equations with complex coefficients in a single variable have a solution in complex numbers. For example, 3.5 + 2i is a complex number. By this convention the imaginary part does not include the imaginary unit: hence b, not bi, is the imaginary part. For example, Re = − 3.5 Im = 2. Hence, in imaginary parts, a complex number z is equal to Re + Im ⋅ i. This expression is sometimes known as the Cartesian form of z. A can be regarded as a complex number a + 0i whose imaginary part is 0.
Complex number
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A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. "Re" is the real axis, "Im" is the imaginary axis, and i is the imaginary unit which satisfies i 2 = −1.
230.
Hilbert space
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The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. A Hilbert space is an abstract space possessing the structure of an inner product that allows length and angle to be measured. Furthermore, Hilbert spaces are complete: there are enough limits in the space to allow the techniques of calculus to be used. Hilbert spaces arise frequently in mathematics and physics, typically as infinite-dimensional function spaces. They are indispensable tools in the theories of partial differential equations, -- ergodic theory, which forms the mathematical underpinning of thermodynamics. John von Neumann coined the term space for the abstract concept that underlies many of these diverse applications. The success of Hilbert space methods ushered in a very fruitful era for functional analysis. Geometric intuition plays an important role in many aspects of Hilbert theory. Exact analogs of the Pythagorean theorem and law hold in a Hilbert space. At a deeper level, projection onto a subspace plays a significant role in optimization problems and other aspects of the theory. The latter space is often in the older literature referred to as the Hilbert space. The product takes two vectors x and y, produces a real number x · y. The product satisfies the properties: It is symmetric in x and y: x · y = y · x. It is positive definite: for all vectors x · x ≥ 0, with equality if and only if x = 0. An operation on pairs of vectors that, like the product, satisfies these three properties is known as a inner product.
Hilbert space
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David Hilbert
Hilbert space
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The state of a vibrating string can be modeled as a point in a Hilbert space. The decomposition of a vibrating string into its vibrations in distinct overtones is given by the projection of the point onto the coordinate axes in the space.
231.
Projective space
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In mathematics, a projective space can be thought of as the set of lines through the origin of a vector space V. All points that lie on a projection line, intersecting with the entrance pupil of the camera, are projected onto a common image point. In this case, the projective space corresponds to the image points. Projective spaces are also used in various applied fields, geometry in particular. Geometric objects, such as points, planes, can be given a representation as elements in projective spaces based on homogeneous coordinates. As a result, various relations between these objects can be described in a simpler way than is possible without homogeneous coordinates. Furthermore, various statements in geometry can be made more consistent and without exceptions. In the standard Euclidean geometry for the plane, two lines always intersect at a point except when the lines are parallel. Mathematical fields where projective spaces play a significant role are topology, the theory of Lie groups and algebraic groups, their representation theories. As outlined above, projective space is a geometric object that formalizes statements like "Parallel lines intersect at infinity." For concreteness, we give the construction of the projective plane P2 in some detail. There are three equivalent definitions: The set of all lines in R3 passing through the origin. Every such line meets the sphere of radius one centered in the origin twice, say in P = and its antipodal point. P2 can also be described on the sphere S2, where every point P and its antipodal point are not distinguished. For example, the point is identified with, etc.
Projective space
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In graphical perspective, parallel lines in the plane intersect in a vanishing point on the horizon.
232.
Complex projective space
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In mathematics, complex projective space is the projective space with respect to the field of complex numbers. Formally, a complex space is the space of complex lines through the origin of an - dimensional complex vector space. The space is denoted variously as P, Pn or CPn. When n = 2, CP2 is the complex projective plane. In modern times, both the geometry of complex projective space are well-understood and closely related to that of the sphere. Indeed, in a certain sense the -sphere can be regarded as a family of circles parametrized by CPn: this is the Hopf fibration. Complex space carries a metric, called the Fubini -- Study metric, in terms of which it is a Hermitian symmetric space of rank 1. Complex space has many applications in both mathematics and quantum physics. In algebraic geometry, complex space is the home of projective varieties, a well-behaved class of algebraic varieties. In topology, the complex space plays an important role as a classifying space for complex line bundles: families of complex lines parametrized by another space. In this context, the infinite union of projective spaces, denoted CP ∞, is the classifying K. The horizon is sometimes called a line at infinity. By the same construction, projective spaces can be considered in higher dimensions. For instance, the real 3-space is a Euclidean space together with a plane at infinity that represents the horizon that an artist would see. These real projective spaces can be constructed in a slightly more rigorous way as follows.
Complex projective space
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Parallel lines in the plane intersect at the vanishing point in the line at infinity.
Complex projective space
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The Riemann sphere, the one-dimensional complex projective space, i.e. the complex projective line.
233.
Eigenstate
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In quantum physics, quantum state refers to the state of an isolated quantum system. A state provides a probability distribution for the value of each observable, i.e. for the outcome of each possible measurement on the system. Knowledge of the state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. A mixture of quantum states is again a state. Quantum states that cannot be written as a mixture of other states are called pure quantum states, all other states are called mixed quantum states. Mathematically, a pure state can be represented by a ray in a Hilbert space over the complex numbers. Its phase factor can be chosen freely anyway. Nevertheless, such factors are important when state vectors are added together to form a superposition. It contains all possible pure quantum states of the given system. A mixed state corresponds to a probabilistic mixture of pure states; however, different distributions of pure states can generate equivalent mixed states. Mixed states are described by so-called density matrices. For example, if the spin of an electron is measured in e.g. with a Stern -- Gerlach experiment, there are two possible results: up or down. The Hilbert space for the electron's spin is therefore two-dimensional. A mixed state, in this case, is a 2 × 2 matrix, Hermitian, positive-definite, has 1. This reflects a core difference between classical and quantum physics.
Eigenstate
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Probability densities for the electron of a hydrogen atom in different quantum states.
234.
Eigenvector
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There is a correspondence between n by n square matrices and linear transformations from an n-dimensional vector space to itself. For this reason, it is equivalent to define eigenvalues and eigenvectors using either the language of matrices or the language of linear transformations. If the eigenvalue is negative, the direction is reversed. Eigenvalues and eigenvectors feature prominently in the analysis of linear transformations. The prefix eigen- is adopted from the German word eigen for "proper", "inherent"; "own", "individual", "special"; "specific", "peculiar", or "characteristic". In essence, an eigenvector v of a linear transformation T is a non-zero vector that, when T is applied to it, does not change direction. Applying T to the eigenvector only scales the eigenvector by the scalar value λ, called an eigenvalue. This condition can be written as the equation T = λ v, referred to as the eigenvalue equation or eigenequation. In general, λ may be any scalar. For example, λ may be negative, in which case the eigenvector reverses direction as part of the scaling, or it may be zero or complex. The Mona Lisa example pictured at right provides a simple illustration. Each point on the painting can be represented as a vector pointing from the center of the painting to that point. The linear transformation in this example is called a shear mapping. The vectors pointing to each point in the original image are therefore tilted right or left and made longer or shorter by the transformation. Notice that points along the horizontal axis do not move at all when this transformation is applied.
Eigenvector
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In this shear mapping the red arrow changes direction but the blue arrow does not. The blue arrow is an eigenvector of this shear mapping because it doesn't change direction, and since its length is unchanged, its eigenvalue is 1.
235.
Eigenvalue
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There is a correspondence between n by n square matrices and linear transformations from an n-dimensional vector space to itself. For this reason, it is equivalent to define eigenvalues and eigenvectors using either the language of matrices or the language of linear transformations. If the eigenvalue is negative, the direction is reversed. Eigenvalues and eigenvectors feature prominently in the analysis of linear transformations. The prefix eigen- is adopted from the German word eigen for "proper", "inherent"; "own", "individual", "special"; "specific", "peculiar", or "characteristic". In essence, an eigenvector v of a linear transformation T is a non-zero vector that, when T is applied to it, does not change direction. Applying T to the eigenvector only scales the eigenvector by the scalar value λ, called an eigenvalue. This condition can be written as the equation T = λ v, referred to as the eigenvalue equation or eigenequation. In general, λ may be any scalar. For example, λ may be negative, in which case the eigenvector reverses direction as part of the scaling, or it may be zero or complex. The Mona Lisa example pictured at right provides a simple illustration. Each point on the painting can be represented as a vector pointing from the center of the painting to that point. The linear transformation in this example is called a shear mapping. The vectors pointing to each point in the original image are therefore tilted right or left and made longer or shorter by the transformation. Notice that points along the horizontal axis do not move at all when this transformation is applied.
Eigenvalue
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In this shear mapping the red arrow changes direction but the blue arrow does not. The blue arrow is an eigenvector of this shear mapping because it doesn't change direction, and since its length is unchanged, its eigenvalue is 1.
236.
Vector space
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A vector space is a collection of objects called vectors, which may be added together and multiplied by numbers, called scalars in this context. There are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of vector scalar multiplication must satisfy certain requirements, called axioms, listed below. Euclidean vectors are an example of a space. In the same vein, but in a more geometric sense, vectors representing displacements in three-dimensional space also form vector spaces. Infinite-dimensional vector spaces arise naturally as function spaces, whose vectors are functions. These vector spaces are generally endowed with additional structure, which may be a topology, allowing the consideration of issues of continuity. Among these topologies, those that are defined by inner product are more commonly used, as having a notion of distance between two vectors. This is particularly the case of Banach spaces and Hilbert spaces, which are fundamental in mathematical analysis. Vector spaces are applied throughout mathematics, science and engineering. Furthermore, vector spaces furnish an coordinate-free way of dealing with geometrical and physical objects such as tensors. This in turn allows the examination of local properties of manifolds by linearization techniques. Vector spaces may be generalized in several ways, leading in geometry and abstract algebra. This is used in physics to describe velocities. Given any two such arrows, w, the parallelogram spanned by these two arrows contains one diagonal arrow that starts at the origin, too.
Vector space
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Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2 w.
237.
Thought experiment
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A thought experiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences. Perhaps the key experiment in the history of modern science is Galileo's demonstration that falling objects must fall at the same rate regardless of their masses. The'experiment' is described by Galileo in Discorsi e dimostrazioni matematiche thus: Salviati. Do you not agree with me in this opinion? Simplicio. You are unquestionably right. Salviati. Hence the heavier body moves with less speed than the lighter; an effect, contrary to your supposition. Instead, many philosophers prefer to consider'Thought Experiments' to be merely the use of a hypothetical scenario to help understand the way things actually are. Thought experiments have been used in a variety including philosophy, law, physics, mathematics. In philosophy, they have been used at least since some pre-dating Socrates. In law, they were well-known to Roman lawyers quoted in the Digest. Johann Witt-Hansen established that Hans Christian Ørsted was the first to use the Latin-German mixed term Gedankenexperiment 1812. Ørsted was also the first to use Gedankenversuch, in 1820. It first appeared in the 1897 English translation of one of Mach's papers.
Thought experiment
–
Temporal representation of a prefactual thought experiment.
Thought experiment
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A famous example, Schrödinger's cat (1935), presents a cat that might be alive or dead, depending on an earlier random event. It illustrates the problem of the Copenhagen interpretation applied to everyday objects.
Thought experiment
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Temporal representation of a counterfactual thought experiment.
Thought experiment
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Temporal representation of a semifactual thought experiment.
238.
Interpretation of quantum mechanics
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An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature. Although quantum mechanics has held up to thorough experimental testing, many of these experiments are open to different interpretations. This question is to philosophers of physics as physicists continue to show a strong interest in the subject. The definition such as wavefunctions and matrix mechanics, progressed through many stages. Although the Copenhagen interpretation was originally most popular, decoherence has gained popularity. Thus the many-worlds interpretation has been gaining acceptance. The authors reference a similarly informal poll carried out at the "Fundamental Problems in Quantum Theory" conference in August 1997. In Tegmark's poll, the Everett interpretation received 17% of the vote, similar to the number of votes in our poll." A general law is a regularity of outcomes, whereas a causal mechanism may regulate the outcomes. A phenomenon can receive interpretation either epistemic. For instance, indeterminism may be explained as a real existing maybe encoded in the universe. In a broad sense, scientific theory might be perceived with antirealism. A stance seeks the epistemic and the ontic, whereas an antirealist stance seeks epistemic but not the ontic. In the 20th century's first half, antirealism was mainly logical positivism, which sought to exclude unobservable aspects of reality from scientific theory. The view is carried by the famous quote of David Mermin, "Shut up and calculate", often misattributed to Richard Feynman.
Interpretation of quantum mechanics
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Schrödinger
Interpretation of quantum mechanics
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Born
Interpretation of quantum mechanics
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Everett
239.
Relative state interpretation
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The many-worlds interpretation is an interpretation of quantum mechanics that asserts the objective reality of the universal wavefunction and denies the actuality of wavefunction collapse. Many-worlds implies that all possible alternate histories and futures are real, each representing an actual "world". The theory is also referred to as the theory of the universal wavefunction, many-universes interpretation, or just many-worlds. The original relative state formulation is due to Hugh Everett in 1957. Later, this formulation was popularized and renamed many-worlds by Bryce Seligman DeWitt in the 1960s and 1970s. The decoherence approaches to interpreting quantum theory have been further explored and developed, becoming quite popular. MWI is one of many multiverse hypotheses in physics and philosophy. It is currently considered a interpretation along with hidden variable theories such as the Bohmian mechanics. Before many-worlds, reality had always been viewed as a single unfolding history. Many-worlds, however, views reality as a many-branched tree, wherein every possible quantum outcome is realised. Many-worlds reconciles the observation of non-deterministic events, such as random radioactive decay, with the fully deterministic equations of quantum physics. It was that, when his Nobel equations seem to be describing several different histories, they are "not alternatives but all really happen simultaneously". This is the earliest known reference to the many-worlds. "Under scrutiny of the environment, only pointer states remain unchanged. Other states decohere into mixtures of stable pointer states that can persist, and, in this sense, exist: They are einselected."
Relative state interpretation
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Hugh Everett III (1930–1982) was the first physicist who proposed the many-worlds interpretation (MWI) of quantum physics, which he termed his "relative state" formulation.
Relative state interpretation
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The quantum-mechanical " Schrödinger's cat " paradox according to the many-worlds interpretation. In this interpretation, every event is a branch point; the cat is both alive and dead, even before the box is opened, but the "alive" and "dead" cats are in different branches of the universe, both of which are equally real, but which do not interact with each other.
240.
Quantum Entanglement
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Measurements of physical properties such as position, polarization, performed on entangled particles are found to be appropriately correlated. Later, however, the counterintuitive predictions of quantum mechanics were verified experimentally. Recent experiments have measured entangled particles within less than one hundredth of a percent of the travel time of light between them. According to the formalism of quantum theory, the effect of measurement happens instantly. It is not possible, however, to use this effect to transmit classical information at faster-than-light speeds. Research is also focused on the utilization of entanglement effects in communication and computation. In this study, they formulated a experiment that attempted to show that quantum mechanical theory was incomplete. They wrote: "We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete." However, they did not coin the word entanglement, nor did they generalize the special properties of the state they considered. He thereafter published a seminal paper terming it "entanglement." Einstein famously derided entanglement at a distance." The EPR paper inspired much discussion about the foundations of quantum mechanics, but produced little other published work. Until recently each had left open at least one loophole by which it was possible to question the validity of the results. However, in 2015 the first loophole-free experiment was performed, which ruled out a large class of local realism theories with certainty. The work of Bell raised the possibility of using these super-strong correlations as a resource for communication.
Quantum Entanglement
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May 4, 1935 New York Times article headline regarding the imminent EPR paper.
Quantum Entanglement
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Spontaneous parametric down-conversion process can split photons into type II photon pairs with mutually perpendicular polarization.
241.
Probability distribution
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In more technical terms, the probability distribution is a description of a random phenomenon in terms of the probabilities of events. Examples of random phenomena can include the results of an experiment or survey. A distribution is defined in terms of an underlying space, the set of all possible outcomes of the random phenomenon being observed. Probability distributions are generally divided into two classes. A discrete distribution can be encoded by a discrete list of the probabilities of the outcomes, known as a probability function. On the other hand, a continuous distribution is typically described by density functions. The normal distribution represents a commonly encountered continuous probability distribution. More complex experiments, such as those involving stochastic processes defined in continuous time, may demand the use of more general probability measures. Important and commonly encountered univariate probability distributions include the normal distribution. The normal distribution is a commonly encountered distribution. To define probability distributions for the simplest cases, one needs to distinguish between discrete and continuous random variables. Continuous probability distributions can be described in several ways. The cumulative function is the antiderivative of the probability function provided that the latter function exists. As theory is used in quite diverse applications, terminology is not sometimes confusing. The following terms are used for random variables.
Probability distribution
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The probability mass function (pmf) p (S) specifies the probability distribution for the sum S of counts from two dice. For example, the figure shows that p (11) = 1/18. The pmf allows the computation of probabilities of events such as P (S > 9) = 1/12 + 1/18 + 1/36 = 1/6, and all other probabilities in the distribution.
242.
Bohr model
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After the cubic model, the Rutherford model came the Rutherford -- Bohr model or just Bohr model for short. The improvement to the Rutherford model is mostly a quantum physical interpretation of it. The model's key success lay in explaining the Rydberg formula for the spectral emission lines of atomic hydrogen. While the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. The Bohr model is a relatively primitive model of the atom, compared to the valence atom. A related model was originally proposed by Arthur Erich Haas in 1910, but was rejected. The laws of classical mechanics, predict that the electron will release electromagnetic radiation while orbiting a nucleus. Because the electron would lose energy, it would rapidly spiral inwards, collapsing into the nucleus on a timescale of around 16 picoseconds. This atom model is disastrous, because it predicts that all atoms are unstable. Also, as the electron spirals inward, the emission would rapidly increase in frequency as the orbit got smaller and faster. This would produce a continuous smear, in frequency, of electromagnetic radiation. However, 19th century experiments with electric discharges have shown that atoms will only emit light at discrete frequencies. To overcome this difficulty, Niels Bohr proposed, in 1913, what is now called the Bohr model of the atom. He suggested that electrons could only have certain classical motions: Electrons in atoms orbit the nucleus. The electrons can only orbit stably, without radiating, at a discrete set of distances from the nucleus.
Bohr model
243.
German language
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German is a West Germanic language, mainly spoken in Central Europe. Major languages which are most similar to German include other members of the West Germanic branch, such as Afrikaans, Dutch, English. It is the second most widely spoken Germanic language, after English. German derives most of its vocabulary from the Germanic branch of the Indo-European family. Fewer are borrowed from French and English. With slightly different standardized variants, German is a pluricentric language. Like English, German is also notable with many unique varieties existing in Europe and also other parts of the world. The history of the German language begins with the German consonant shift during the migration period, which separated Old High German dialects from Old Saxon. When Martin Luther translated the Bible, he based his translation primarily on the bureaucratic language used in Saxony, also known as Meißner Deutsch. Copies of Luther's Bible featured a long list of glosses for each region that translated words which were unknown in the region into the regional dialect. It was not until the middle of the 18th century that a widely accepted standard was created, ending the period of Early New High German. Until about 1800, standard German was mainly a written language: in northern Germany, the local Low German dialects were spoken. Standard German, markedly different, was often learned as a foreign language with uncertain pronunciation. German pronunciation was considered the standard in prescriptive pronunciation guides though; however, the actual pronunciation of Standard German varies from region to region. German was the language in the Habsburg Empire, which encompassed a large area of Central and Eastern Europe.
German language
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Old Frisian (Alt-Friesisch)
German language
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The widespread popularity of the Bible translated into German by Martin Luther helped establish modern German
German language
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Examples of German language in Namibian everyday life
German language
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German-language newspapers in the U.S. in 1922
244.
Total energy
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In physics, energy is a property of objects which can be transferred to other objects or converted into different forms. It is misleading because energy is not necessarily available to do work. All of the many forms of energy are convertible to other kinds of energy. This means that it is impossible to destroy energy. This creates a limit to the amount of energy that can do work in a cyclic process, a limit called the available energy. Other forms of energy can be transformed in the other direction into thermal energy without such limitations. The total energy of a system can be calculated by adding up all forms of energy in the system. Lifting against gravity performs mechanical work on the object and stores gravitational potential energy in the object. Energy are closely related. With a sensitive enough scale, one could measure an increase in mass after heating an object. Living organisms require available energy to stay alive, such as the energy humans get from food. Civilisation gets the energy it needs from energy resources such as fossil fuels, renewable energy. The processes of Earth's ecosystem are driven by the radiant energy Earth receives from the sun and the geothermal energy contained within the earth. In biology, energy can be thought of as what's needed to keep entropy low. The total energy of a system can be classified in various ways.
Total energy
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In a typical lightning strike, 500 megajoules of electric potential energy is converted into the same amount of energy in other forms, mostly light energy, sound energy and thermal energy.
Total energy
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Thermal energy is energy of microscopic constituents of matter, which may include both kinetic and potential energy.
Total energy
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Thomas Young – the first to use the term "energy" in the modern sense.
Total energy
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A Turbo generator transforms the energy of pressurised steam into electrical energy
245.
Determinism
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Determinism is the philosophical position that for every event there exist conditions that could cause no other event. "There are many determinisms, depending on what pre-conditions are considered to be determinative of an action." Deterministic theories throughout the history of philosophy have sprung from considerations. Some forms of determinism can be empirically tested with the philosophy of physics. The opposite of determinism is some kind of indeterminism. Determinism is often contrasted with free will. Determinism often is taken to mean causal determinism, which in physics is known as cause-and-effect. This meaning can be distinguished from other varieties of determinism mentioned below. Historical debates involve many philosophical positions and varieties of determinism. They include debates concerning determinism and free will, technically denoted as incompatibilistic. Determinism should not be confused by reasons, motives, desires. Determinism rarely requires that perfect prediction be practically possible. Below are some of the more common viewpoints confused with "determinism". Causal determinism is "the idea that every event is necessitated by antecedent conditions together with the laws of nature". Causal determinism proposes that there is an unbroken chain of prior occurrences stretching back to the origin of the universe.
Determinism
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Many philosophical theories of determinism frame themselves with the idea that reality follows a sort of predetermined path
Determinism
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Adequate determinism focuses on the fact that, even without a full understanding of microscopic physics, we can predict the distribution of 1000 coin tosses
Determinism
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Nature and nurture interact in humans. A scientist looking at a sculpture after some time does not ask whether we are seeing the effects of the starting materials or of environmental influences.
Determinism
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A technological determinist might suggest that technology like the mobile phone is the greatest factor shaping human civilization.
246.
Random
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Randomness is the lack of pattern or predictability in events. A random sequence of events, steps has no order and does not follow an intelligible pattern or combination. In many cases the frequency of different outcomes over a large number of events is predictable. For example, when throwing two dice, a sum of 7 will occur twice as often as 4. In this view, randomness is a measure of uncertainty of an outcome, rather than applies to concepts of chance, probability, information entropy. The fields of mathematics, statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an space. This association facilitates the calculation of probabilities of the events. Random variables can appear in random sequences. A random process is a sequence of random variables whose outcomes do not follow an evolution described by probability distributions. Other constructs are extremely useful in probability theory and the various applications of randomness. Randomness is most often used in statistics to signify statistical properties. Monte Carlo methods, which rely on random input, are important techniques in science, as, for instance, in computational science. By analogy, quasi-Monte Carlo methods use number generators. With a bowl containing just 10 red marbles and 90 blue marbles, a random selection mechanism would choose a red marble with probability 1/10.
Random
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Ancient fresco of dice players in Pompei.
Random
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A pseudorandomly generated bitmap.
Random
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The ball in a roulette can be used as a source of apparent randomness, because its behavior is very sensitive to the initial conditions.
247.
Newton's second law
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Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between the forces acting upon it, its motion in response to those forces. They can be summarised as follows. The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica, first published in 1687. Newton used them to investigate the motion of many physical objects and systems. In this way, even a planet can be idealised around a star. In their original form, Newton's laws of motion are not adequate to characterise the motion of rigid bodies and deformable bodies. Euler's laws can, however, be taken as axioms describing the laws of any particle structure. Newton's laws hold only to a certain set of frames of reference called Newtonian or inertial reference frames. Other authors do treat the first law as a corollary of the second. The explicit concept of an inertial frame of reference was not developed after Newton's death. In the given mass, acceleration, momentum, force are assumed to be externally defined quantities. Not the only interpretation of the way one can consider the laws to be a definition of these quantities. The first law states that if the net force is zero, then the velocity of the object is constant. The first law can be stated mathematically when the mass is a constant, as, ∑ F = 0 ⇔ d v d t = 0.
Newton's second law
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Newton's First and Second laws, in Latin, from the original 1687 Principia Mathematica.
Newton's second law
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Isaac Newton (1643–1727), the physicist who formulated the laws
248.
Probability density function
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The probability density function is nonnegative everywhere, its integral over the entire space is equal to one. The terms "function" and "function" have sometimes been used to denote the probability density function. However, this use is not standard among probabilists and statisticians. Further confusion of terminology exists because density function has also been used for what is here called the "probability mass function". In general though, the PMF is used in the context of discrete random variables, while PDF is used in the context of continuous random variables. Suppose a species of bacteria typically lives 4 to 6 hours. What is the probability that a bacterium lives exactly 5 hours? The answer is 0%. A lot of bacteria live for approximately 5 hours, but there is no chance that any given bacterium dies at exactly 5.0000000000... hours. Instead we might ask: What is the probability that the bacterium dies between 5 hours and 5.01 hours? Let's say the answer is 0.02. Next: What is the probability that the bacterium dies between 5 hours and 5.001 hours? The answer is probably around 0.002, since this is 1/10th of the previous interval. The probability that the bacterium dies between 5 hours and 5.0001 hours is probably about 0.0002, so on. In these three examples, the ratio / is approximately constant, equal to 2 per hour.
Probability density function
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Boxplot and probability density function of a normal distribution N (0, σ 2).
249.
Chladni's figures
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Ernst Florens Friedrich Chladni was a German physicist and musician. He also undertook pioneering work in the study of meteorites and so is also regarded by some as the father of meteoritics. Chladni has therefore been identified as German, Hungarian and Slovak. Chladni came from an educated family of academics and learned men. Chladni's great-grandfather, the Lutheran clergyman Georg Chladni, had left Kremnica in 1673 during the Counter Reformation. Chladni's grandfather, Martin Chladni, was also a Lutheran theologian and, in 1710, became professor of theology at the University of Wittenberg. He was dean of the theology faculty in 1720–1721 and later became the university's rector. Justus Georg Chladni, was a professor at the university. Johann Martin Chladni, was a theologian, a professor at the University of Erlangen and the University of Leipzig. Ernst Martin Chladni, was a law rector of the University of Wittenberg. He had joined the law faculty there in 1746. Chladni's mother was Johanna Sophia and he was an only child. His father disapproved of his son's interest in science and insisted that Chladni become a lawyer. Chladni studied philosophy in Wittenberg and Leipzig, obtaining a law degree in 1782. He turned in earnest.
Chladni's figures
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Ernst Chladni
Chladni's figures
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Martin Chladni, Ernst Chladni's grandfather
Chladni's figures
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Chladni figure on a rectangular plate supported in center
250.
Acoustics
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The application of acoustics is present in almost all aspects of modern society with the most obvious being the control industries. Accordingly, the science of acoustics spreads across many facets of human society -- music, medicine, architecture, more. Likewise, animal species such as frogs use sound and marking territories. Art, technology have provoked one another to advance the whole, as in many other fields of knowledge. Robert Bruce Lindsay's'Wheel of Acoustics' is a well accepted overview of the various fields in acoustics. The Latin synonym is "sonic", after which the term sonics used to be a synonym for acoustics and later a branch of acoustics. Frequencies above and below the audible range are called "ultrasonic" and "infrasonic", respectively. If, for example, a string of a certain length would sound particularly harmonious with a string of twice the length. In modern parlance, if a string sounds C when plucked, a string twice long will sound a C an octave lower. The physical understanding of acoustical processes advanced rapidly during and after the Scientific Revolution. Mainly Galileo Galilei but also Marin Mersenne, independently, discovered the complete laws of vibrating strings. Experimental measurements of the speed of sound in air were carried out successfully by a number of prominently Mersenne. Meanwhile, Newton derived the relationship in a cornerstone of physical acoustics. The eighteenth century saw major advances in acoustics as mathematicians applied the new techniques of calculus to elaborate theories of sound wave propagation. Also in the 19th century, Wheatstone, Ohm, Henry developed the analogy between electricity and acoustics.
Acoustics
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Principles of acoustics were applied since ancient times: Roman theatre in the city of Amman.
Acoustics
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Artificial omni-directional sound source in an anechoic chamber
Acoustics
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Jay Pritzker Pavilion
Acoustics
251.
Angular momentum
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In physics, angular momentum is the rotational analog of linear momentum. This definition can be applied to each point in continua like solids or fluids, or physical fields. Unlike momentum, angular momentum does depend on where the origin is chosen, since the particle's position is measured from it. The angular momentum of an object can also be connected to the angular velocity ω of the object via the moment of inertia I. Angular momentum is additive; the total angular momentum of a system is the vector sum of the angular momenta. For continua or fields one uses integration. Torque can be defined as the rate of change of angular momentum, analogous to force. Applications include the gyrocompass, control moment gyroscope, Earth's rotation to name a few. In general, conservation does limit the possible motion of a system, but does not uniquely determine what the exact motion is. In quantum mechanics, angular momentum is an operator with quantized eigenvalues. Angular momentum is subject to the Heisenberg uncertainty principle, meaning only one component can be measured with definite precision, the other two cannot. Also, the "spin" of elementary particles does not correspond to literal spinning motion. Angular momentum is a vector quantity that represents the product of a body's rotational inertia and rotational velocity about a particular axis. Angular momentum can be considered a rotational analog of linear momentum. Unlike linear speed, which occurs in a straight line, angular speed occurs about a center of rotation.
Angular momentum
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This gyroscope remains upright while spinning due to the conservation of its angular momentum.
Angular momentum
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An ice skater conserves angular momentum – her rotational speed increases as her moment of inertia decreases by drawing in her arms and legs.
252.
Resonant frequency
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Frequencies at which the response amplitude is a relative maximum are known as the system's resonant frequencies or resonance frequencies. At resonant frequencies, small periodic driving forces have the ability to produce large amplitude oscillations, due to the storage of vibrational energy. Resonance occurs when a system is able to store and easily transfer energy between two or more different storage modes. However, there are some losses from cycle to cycle, called damping. When damping is small, the resonant frequency is approximately equal to the natural frequency of the system, a frequency of unforced vibrations. Some systems have resonant frequencies. Resonant systems can be used to generate vibrations of a specific frequency, or pick out specific frequencies from a complex vibration containing many frequencies. Resonance occurs widely in nature, is exploited in many manmade devices. It is the mechanism by which virtually all sinusoidal waves and vibrations are generated. Many sounds we hear, such as when hard objects of wood are struck, are caused by brief resonant vibrations in the object. Other short electromagnetic radiation is produced by resonance on an atomic scale, such as electrons in atoms. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including trains, aircraft. Avoiding resonance disasters is a major concern in bridge construction project. As a countermeasure, shock mounts can be installed to absorb resonant frequencies and thus dissipate the absorbed energy. The Taipei 101 building relies on a 660-tonne pendulum —a tuned mass damper—to cancel resonance.
Resonant frequency
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Pushing a person in a swing is a common example of resonance. The loaded swing, a pendulum, has a natural frequency of oscillation, its resonant frequency, and resists being pushed at a faster or slower rate.
Resonant frequency
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Increase of amplitude as damping decreases and frequency approaches resonant frequency of a driven damped simple harmonic oscillator.
Resonant frequency
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NMR Magnet at HWB-NMR, Birmingham, UK. In its strong 21.2- tesla field, the proton resonance is at 900 MHz.
253.
Atomic nucleus
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After the discovery of the neutron in 1932, models for a nucleus composed of neutrons were quickly developed by Werner Heisenberg. Almost all of the mass of an atom is located with a very small contribution from the cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force. The diameter of the nucleus is in the range of 6985175000000000000♠1.75 fm for hydrogen to about 6986150000000000000♠15 fm for the heaviest atoms, such as uranium. These dimensions are much smaller than the diameter of the atom itself, by a factor of about 23,000 to about 145,000. The nucleus was discovered as a result of Ernest Rutherford's efforts to test Thomson's "plum model" of the atom. The electron had already been discovered earlier by J.J. Thomson himself. Knowing that atoms are electrically neutral, Thomson postulated that there must be a positive charge as well. In his model, Thomson suggested that an atom consisted of negative electrons randomly scattered within a sphere of positive charge. To his surprise, many of the particles were deflected at very large angles. This justified the idea of a nuclear atom with a dense center of positive charge and mass. The nucleus is from a diminutive of nux, meaning the kernel inside a watery type of fruit. In 1844, Michael Faraday used the term to refer to the "central point of an atom". The modern atomic meaning was proposed by Ernest Rutherford in 1912.
Atomic nucleus
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Nuclear physics
254.
Spherical coordinate system
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It can be seen as the three-dimensional version of the polar coordinate system. The radial distance is also called the radius or radial coordinate. The polar angle may be called angle. The use of symbols and the order of the coordinates differs between sources. In both systems ρ is often used instead of r. Other conventions are also used, so great care needs to be taken to check which one is being used. A number of different spherical coordinate systems following other conventions are used outside mathematics. In a geographical coordinate system positions are measured in latitude, longitude and height or altitude. There are a number of different celestial coordinate systems based on different fundamental planes and with different terms for the various coordinates. The polar angle is often replaced by the elevation angle measured from the reference plane. Elevation angle of zero is at the horizon. The spherical coordinate system generalises the two-dimensional polar coordinate system. It can also be extended to higher-dimensional spaces and is then referred to as a hyperspherical coordinate system. To define a spherical coordinate system, one must choose two orthogonal directions, the zenith and the azimuth reference, an origin point in space. These choices determine a reference plane that contains the origin and is perpendicular to the zenith.
Spherical coordinate system
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Spherical coordinates (r, θ, φ) as commonly used in physics: radial distance r, polar angle θ (theta), and azimuthal angle φ (phi). The symbol ρ (rho) is often used instead of r.
255.
Phase (waves)
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Phase is the position of a point in time on a waveform cycle. A complete cycle is defined as the interval required for the waveform to return to its arbitrary initial value. The graphic to the right shows how one cycle constitutes ° of phase. The graphic also shows how phase is sometimes expressed in radians, where one radian of phase equals approximately 57.3°. Phase can also be an expression of relative displacement between two corresponding features of two waveforms having the same frequency. In sinusoidal functions or in waves "phase" has two different, but closely related, meanings. One is sometimes called phase offset or phase difference. Another usage is the fraction of the cycle that has elapsed relative to the origin. Shift is any change that occurs in the phase of one quantity, or in the phase difference between two or more quantities. This symbol: φ is sometimes referred to as a phase shift or phase offset, because it represents a "shift" from zero phase. For long sinusoids, a change in φ is the same as a shift in time, such as a time delay. It has been shifted by 2 radians. Difference is the difference, expressed in degrees or time, between two waves having the same frequency and referenced to the same point in time. Two oscillators that have no phase difference are said to be in phase. If the difference is 180 degrees, then the two oscillators are said to be in antiphase.
Phase (waves)
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Illustration of phase shift. The horizontal axis represents an angle (phase) that is increasing with time.
256.
Quantum harmonic oscillator
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The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Furthermore, it is one of the quantum-mechanical systems for which an exact, analytical solution is known. The second term represents its corresponding possible potential energy states. One may solve the equation representing this eigenvalue problem in the coordinate basis, for the wave function ⟨ x | ψ ⟩ = ψ, using a spectral method. It turns out that there is a family of solutions. In this basis, they amount to ψ n = 2 n n! ⋅ 1 / 4 ⋅ e − m ω x 2 2 ℏ ⋅ H n, n = 0, 1, 2, …. The functions Hn are the physicists' Hermite polynomials, H n = n z 2 d n d z n. The corresponding energy levels are n = ℏ ω = ℏ 2 ω. This spectrum is noteworthy for three reasons. First, the energies are quantized, meaning that only discrete energy values are possible; this is a general feature of quantum-mechanical systems when a particle is confined. Second, these discrete energy levels are equally spaced, in the Bohr model of the atom, or the particle in a box. Third, the lowest energy is not equal to the minimum of the potential well, but ħω / 2 above it; this is called zero-point energy. This zero-point energy further has important implications in quantum field theory and gravity. As the energy increases, the density becomes concentrated at the classical "turning points", where the state's energy coincides with the potential energy.
Quantum harmonic oscillator
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Wavefunction representations for the first eight bound eigenstates, n = 0 to 7. The horizontal axis shows the position x. Note: The graphs are not normalized, and the signs of some of the functions differ from those given in the text.
257.
Particle in a box
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In quantum mechanics, the particle in a box model describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between quantum systems. However, when the well becomes very narrow, quantum effects become important. The particle may only occupy positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never "sit still". Additionally, it is more likely to be found at certain positions than at others, depending on its level. The particle may never be detected at certain positions, known as spatial nodes. The particle in a model provides one of the very few problems in quantum mechanics which can be solved analytically, without approximations. Due to its simplicity, the model allows insight without the need for complicated mathematics. The simplest form of the particle in a model considers a one-dimensional system. Here, the particle may only move backwards and forwards at either end. The walls of a one-dimensional box may be visualised with an infinitely large potential energy. Conversely, the interior of the box has a constant, potential energy. It can move freely in that region. However, large forces repel the particle if it touches the walls of the box, preventing it from escaping.
Particle in a box
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The barriers outside a one-dimensional box have infinitely large potential, while the interior of the box has a constant, zero potential.
258.
Dihydrogen cation
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The hydrogen molecular ion, dihydrogen cation, or H+ 2, is the simplest molecular ion. One negatively charged electron, can be formed from ionization of a neutral hydrogen molecule. The analytical solutions for the energy eigenvalues are a generalization of the Lambert W function. Thus, the case of clamped nuclei can be completely done analytically using a computer system within an experimental mathematics approach. Consequently, it is included as an example in most quantum chemistry textbooks. Earlier attempts using the old theory had been published in 1922 by Karel Niessen and Wolfgang Pauli, in 1925 by Harold Urey. In 1928, Linus Pauling published a review putting together the work of Burrau on the hydrogen molecule. Bonding in H + 2 can be described as a one-electron bond, which has a formal bond order of one half. The ion is important in the chemistry of the interstellar medium. An additive term 1/R, constant for fixed internuclear R, has been omitted from the potential V, since it merely shifts the eigenvalue. The distances between the nuclei are denoted ra and rb. In atomic units the equation is ψ = E ψ with V = − 1 r a − 1 r b. We can choose the midpoint between the nuclei as the origin of coordinates. It follows from general symmetry principles that the wave functions can be characterized by their symmetry behavior to space inversion. The symmetry-adapted wave functions satisfy the same Schrödinger equation.
Dihydrogen cation
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Hydrogen molecular ion H 2 + with clamped nuclei A and B, internuclear distance R and plane of symmetry M.
259.
Hydrogen atom
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A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the elemental mass of the universe. In everyday life on Earth, isolated hydrogen atoms are extremely rare. Instead, hydrogen tends to combine with itself to form ordinary hydrogen gas, H2. "hydrogen atom" in ordinary English use have overlapping, yet distinct, meanings. For example, a molecule contains two hydrogen atoms, but does not contain atomic hydrogen. Attempts to develop a theoretical understanding of the atom have been important to the history of quantum mechanics. Hydrogen-1, protium, or light hydrogen, contains no neutrons and is just a proton and an electron. Protium makes up 99.9885 % of naturally occurring hydrogen by absolute number. Deuterium contains one proton. Deuterium makes up 0.0115 % of naturally occurring hydrogen and is used in industrial processes like nuclear reactors and Nuclear Magnetic Resonance. Tritium is not stable, decaying with a half-life of 12.32 years. Because of the short life, Tritium does not exist in nature except in trace amounts. Higher isotopes of hydrogen have half lives around the order of 10 − 22 seconds.
Hydrogen atom
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Full table
260.
Helium
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Helium is a chemical element with symbol He and atomic number 2. It is the first in the noble gas group in the periodic table. Its boiling point is the lowest among all the elements. Its abundance is similar in Jupiter. This is due to the very high nuclear binding energy of helium-4 with respect after helium. This binding energy also accounts for why it is a product of both nuclear fusion and radioactive decay. Most helium in the universe is believed to have been formed during the Big Bang. Large amounts of new helium are being created in stars. Helium is named for the Greek god of the Sun, Helios. It was first detected as an unknown yellow spectral line signature in sunlight by French astronomer Jules Janssen. Janssen is jointly credited with detecting the element along with Norman Lockyer. Janssen observed during the solar eclipse of 1868 while Lockyer observed from Britain. Lockyer was the first to propose that the line was due to a new element, which he named. Liquid helium is used in cryogenics, with the main commercial application being in MRI scanners. A minor use is as a lifting gas in balloons and airships.
Helium
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Helium, 2 He
Helium
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Spectral lines of helium
Helium
Helium
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Sir William Ramsay, the discoverer of terrestrial helium
261.
Potential energy
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In physics, potential energy is energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, other factors. The unit for energy in the International System of Units is the joule, which has the symbol J. Potential energy is the stored energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is often associated with restoring forces such as the force of gravity. The action of lifting the mass is performed by an external force that works against the force field of the potential. This work is stored in the field, said to be stored as potential energy. Suppose a ball which it is in h position in height. If the acceleration of free fall is g, the weight of the ball is mg. There are various types of potential energy, each associated with a particular type of force. Thermal energy usually has the potential energy of their mutual positions. Forces derivable from a potential are also called conservative forces. The negative sign provides the convention while work done by the force field decreases potential energy. Common notations for potential energy are U, V, also Ep. Potential energy is closely linked with forces.
Potential energy
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In the case of a bow and arrow, when the archer does work on the bow, drawing the string back, some of the chemical energy of the archer's body is transformed into elastic potential-energy in the bent limbs of the bow. When the string is released, the force between the string and the arrow does work on the arrow. Thus, the potential energy in the bow limbs is transformed into the kinetic energy of the arrow as it takes flight.
Potential energy
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A trebuchet uses the gravitational potential energy of the counterweight to throw projectiles over two hundred meters
Potential energy
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Springs are used for storing elastic potential energy
Potential energy
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Archery is one of humankind's oldest applications of elastic potential energy
262.
Nobel Prize in Physics
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This award is administered by the Nobel Foundation and widely regarded as the most prestigious award that a scientist can receive in physics. It is presented at an annual ceremony on December 10, the anniversary of Nobel's death. Through 2016, a total of 203 individuals have been awarded the prize. Only two women have won the Nobel prize in physics, Marie Curie in 1903. Nobel bequeathed 94 % of million Swedish kronor, to endow the five Nobel Prizes. Due to the level of skepticism surrounding the will, it was not until April 26, 1897 that it was approved by the Storting. The executors of his will were Ragnar Sohlman and Rudolf Lilljequist, who formed the Nobel Foundation to take care of Nobel's fortune and organise the prizes. The members of the Norwegian Nobel Committee who were to award the Peace Prize were appointed shortly after the will was approved. The prize-awarding organisations followed: the Karolinska Institutet on June 7, the Swedish Academy on June 9, the Royal Swedish Academy of Sciences on June 11. The Nobel Foundation then reached an agreement on guidelines for how the Nobel Prize should be awarded. In 1900, the Nobel Foundation's newly created statutes were promulgated by King Oscar II. According to Nobel's will, The Royal Swedish Academy of sciences were to award the Prize in Physics. A maximum of two different works may be selected for the Nobel Prize in Physics. Compared with other Nobel Prizes, the nomination and process for the prize in Physics is long and rigorous. This is a key reason why it has grown in importance over the years to become the most important prize in Physics.
Nobel Prize in Physics
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Wilhelm Röntgen (1845–1923), the first recipient of the Nobel Prize in Physics.
Nobel Prize in Physics
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The Nobel Prize in Physics
Nobel Prize in Physics
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Three Nobel Laureates in Physics. Front row from left: Albert A. Michelson (1907), Albert Einstein (1921) and Robert A. Millikan (1923).
263.
Continuous function
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In mathematics, a continuous function is, roughly speaking, a function for which sufficiently small changes in the input result in arbitrarily small changes in the output. Otherwise, a function is said to be a discontinuous function. A continuous function with a continuous inverse function is called a homeomorphism. Continuity of functions is one of the core concepts of topology, treated in full generality below. The introductory portion of this article focuses on the special case where the inputs and outputs of functions are real numbers. In addition, this article discusses the definition for the more general case of functions between two metric spaces. Especially in theory, one considers a notion of continuity known as Scott continuity. Other forms of continuity do exist but they are not discussed in this article. As an example, consider the h, which describes the height of a growing flower at t. This function is continuous. A form of the epsilon–delta definition of continuity was first given by Bernard Bolzano in 1817. Cauchy defined infinitely small quantities in terms of variable quantities, his definition of continuity closely parallels the infinitesimal definition used today. All three of those nonequivalent definitions of pointwise continuity are still in use. Eduard Heine provided the first published definition of uniform continuity in 1872, but based these ideas on lectures given by Peter Gustav Lejeune Dirichlet in 1854. Such a point is called a discontinuity.
Continuous function
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Illustration of the ε-δ-definition: for ε=0.5, c=2, the value δ=0.5 satisfies the condition of the definition.
264.
Discrete mathematics
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Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets. However, there is no exact definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included by what is excluded: related notions. The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business. Conversely, computer implementations are significant in applying ideas from discrete mathematics to real-world problems, such as in operations research. Although the main objects of study in discrete mathematics are discrete objects, analytic methods from continuous mathematics are often employed as well. In curricula, "Discrete Mathematics" appeared in the 1980s, initially as a computer science course; its contents were somewhat haphazard at the time. Some discrete mathematics textbooks have appeared well. At this level, discrete mathematics is sometimes seen as a preparatory course, not unlike precalculus in this respect. The Fulkerson Prize is awarded for outstanding papers in discrete mathematics. The history of discrete mathematics has involved a number of challenging problems which have focused attention within areas of the field.
Discrete mathematics
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Graphs like this are among the objects studied by discrete mathematics, for their interesting mathematical properties, their usefulness as models of real-world problems, and their importance in developing computer algorithms.
265.
Feynman
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For his contributions to the development of quantum electrodynamics, Feynman, jointly with Julian Schwinger and Sin'ichirō Tomonaga, received the Nobel Prize in Physics in 1965. Feynman developed a widely used pictorial scheme for the mathematical expressions governing the behavior of subatomic particles, which later became known as Feynman diagrams. During his lifetime, Feynman became one of the best-known scientists in the world. In addition to his work in theoretical physics, Feynman has been credited with introducing the concept of nanotechnology. He held the Richard C. Tolman professorship in theoretical physics at the California Institute of Technology. By his youth Feynman described himself as an "avowed atheist". Like Edward Teller, Feynman was a late talker, by his third birthday had yet to utter a single word. He retained a Brooklyn accent as an adult. From his mother he gained the sense of humor that he had throughout his life. As a child, he had a talent for engineering, delighted in repairing radios. When he was in school, he created a home burglar alarm system while his parents were out for the day running errands. Four years later, the family moved to Far Rockaway, Queens. Though separated by nine years, Joan and Richard were close, as they both shared a natural curiosity about the world. Their mother thought that women did not have the cranial capacity to comprehend such things.
Feynman
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Richard Feynman
Feynman
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Feynman (center) with Robert Oppenheimer (right) relaxing at a Los Alamos social function during the Manhattan Project
Feynman
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The Feynman section at the Caltech bookstore
Feynman
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Mention of Feynman's prize on the monument at the American Museum of Natural History in New York City. Because the monument is dedicated to American Laureates, Tomonaga is not mentioned.
266.
Superposition principle
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So that if A produces response X and input B produces response Y then input produces response. The additivity properties together are called the superposition principle. A linear function is one that satisfies the properties of superposition. It is defined for scalar a. This principle has many applications in engineering because many physical systems can be modeled as linear systems. Because physical systems are generally approximately linear, the superposition principle is only an approximation of the true physical behaviour. The principle applies to any linear system, including algebraic equations, linear differential equations, systems of equations of those forms. The responses could be numbers, functions, vectors, vector fields, time-varying signals, or any other object which satisfies certain axioms. Note that when vectors or vector fields are involved, a superposition is interpreted as a sum. By writing a very general stimulus as the superposition of stimuli of a simple form, often the response becomes easier to compute. In Fourier analysis, the stimulus is written as the superposition of infinitely many sinusoids. Due to the superposition principle, its individual response can be computed. According to the principle, the response to the original stimulus is the sum of all the individual sinusoidal responses. Fourier analysis is particularly common for waves. In electromagnetic theory, ordinary light is described as a superposition of plane waves.
Superposition principle
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Superposition of almost plane waves (diagonal lines) from a distant source and waves from the wake of the ducks. Linearity holds only approximately in water and only for waves with small amplitudes relative to their wavelengths.
267.
List of unsolved problems in physics
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Some of the major unsolved problems in physics are theoretical, meaning that existing theories seem incapable of explaining a certain observed phenomenon or experimental result. The others are experimental, meaning that there is a difficulty in creating an experiment to investigate a phenomenon in greater detail. The following is a list of unsolved problems grouped into broad area of physics. Entropy Why did the universe have such low entropy in the past, resulting in the distinction between past and future and the second law of thermodynamics? Why are CP violations observed in certain weak force decays, but not elsewhere? Are CP violations somehow a product of the Second Law of Thermodynamics, or are they a separate arrow of time? Are there exceptions to the principle of causality? Is there a single possible past? Is the present moment physically distinct from the past and future or is it merely an emergent property of consciousness? Why does time have a direction? What links the quantum arrow of time to the thermodynamic arrow? Another way of stating this question regards the problem: What constitutes a "measurement" which apparently causes the wave function to collapse into a definite state? Grand Unification Theory Is there a theory which explains the values of all physical constants? Is the theory string theory? Do "fundamental physical constants" vary over time?
List of unsolved problems in physics
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A simulation of how a detection of the Higgs particle would appear in the CMS detector at CERN
List of unsolved problems in physics
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Estimated distribution of dark matter and dark energy in the universe
List of unsolved problems in physics
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Relativistic jet. The environment around the AGN where the relativistic plasma is collimated into jets which escape along the pole of the supermassive black hole
List of unsolved problems in physics
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A sample of a cuprate superconductor (specifically BSCCO). The mechanism for superconductivity of these materials is unknown.
268.
Theory of relativity
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The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity. Special relativity applies to their interactions, describing all their physical phenomena except gravity. General relativity explains the law of its relation to other forces of nature. It applies to the astrophysical realm, including astronomy. The theory transformed theoretical astronomy during the 20th century, superseding a 200-year-old theory of mechanics created primarily by Isaac Newton. It introduced concepts including spacetime as a unified entity of space and time, length contraction. In the field of physics, relativity improved the science of their fundamental interactions, along with ushering in the nuclear age. With relativity, cosmology and astrophysics predicted astronomical phenomena such as neutron stars, black holes, gravitational waves. Max Planck, others did subsequent work. Einstein developed general relativity between 1907 and 1915, after 1915. The final form of general relativity was published in 1916. In the section of the same paper, Alfred Bucherer used for the first time the expression "theory of relativity". By the 1920s, the community understood and accepted special relativity. It rapidly became a necessary tool for theorists and experimentalists in the new fields of atomic physics, nuclear physics, quantum mechanics. By comparison, general relativity did not appear to be as useful, beyond making minor corrections to predictions of Newtonian theory.
Theory of relativity
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USSR stamp dedicated to Albert Einstein
Theory of relativity
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Key concepts
269.
Kinetic energy
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In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done in decelerating from its current speed to a state of rest. In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a v is 1 2 m v 2. In relativistic mechanics, this is a good approximation only when v is much less than the speed of light. The standard unit of kinetic energy is the joule. The kinetic has its roots in the Greek word κίνησις kinesis, meaning "motion". The dichotomy between potential energy can be traced back to Aristotle's concepts of actuality and potentiality. Willem's Gravesande of the Netherlands provided experimental evidence of this relationship. Émilie du Châtelet published an explanation. Work in their present scientific meanings date back to the mid-19th century. William Thomson, later Lord Kelvin, is given the credit for coining 1849 -- 51. 1849–51. Energy occurs in many forms, including chemical energy, thermal energy, electromagnetic radiation, gravitational energy, electric energy, elastic energy, rest energy.
Kinetic energy
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The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. When they start rising, the kinetic energy begins to be converted to gravitational potential energy. The sum of kinetic and potential energy in the system remains constant, ignoring losses to friction.
270.
Harmonic oscillator
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If a frictional force proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the coefficient, the system can: Oscillate lower in an amplitude decreasing with time. Decay to the equilibrium position, without oscillations. The boundary solution between an underdamped oscillator and an overdamped oscillator occurs at a particular value of the friction coefficient and is called "critically damped." If an external time dependent force is present, the harmonic oscillator is described as a driven oscillator. Mechanical examples include pendulums, masses connected to springs, acoustical systems. Other analogous systems include electrical harmonic oscillators such as RLC circuits. Harmonic oscillators occur widely in nature and are exploited in many manmade devices, such as clocks and radio circuits. They are the source of virtually all sinusoidal vibrations and waves. A simple harmonic oscillator is an oscillator, neither driven nor damped. The motion is periodic, repeating itself in a sinusoidal fashion with constant amplitude, A. The position at a given time t also depends on the phase, φ, which determines the starting point on the sine wave. The velocity and acceleration of a simple harmonic oscillator oscillate with the same frequency as the position but with shifted phases. The velocity is maximum for zero displacement, while the acceleration is in the opposite direction as the displacement. The potential energy stored in a simple harmonic oscillator at position x is U = 1 2 k x 2.
Harmonic oscillator
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Another damped harmonic oscillator
Harmonic oscillator
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Dependence of the system behavior on the value of the damping ratio ζ
271.
Electric charge
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Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges: negative. Like charges repel and unlike attract. An object is negatively charged if it is otherwise positively charged or uncharged. The SI derived unit of electric charge is the coulomb. In electrical engineering, it is also common to use the ampere-hour, and, in chemistry, it is common to use the elementary charge as a unit. The Q often denotes charge. Early knowledge of how charged substances interact is still accurate for problems that don't require consideration of quantum effects. The electric charge is a conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, produces, electromagnetic fields. The interaction between an electromagnetic field is the source of the electromagnetic force, one of the four fundamental forces. The electron has a charge of − e. The study of charged particles, how their interactions are mediated by photons, is called quantum electrodynamics. Charge is the fundamental property of forms of matter that exhibit electrostatic repulsion in the presence of other matter. Electric charge is a characteristic property of subatomic particles.
Electric charge
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Electric field of a positive and a negative point charge.
272.
Electromagnetic field
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An electromagnetic field is a physical field produced by electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field describes the electromagnetic interaction. It is one of the four fundamental forces of nature. The field can be viewed as the combination of a magnetic field. The electric field is produced by moving charges; these two are often described as the sources of the field. The way in which currents interact with the electromagnetic field is described by Maxwell's equations and the Lorentz force law. The electromagnetic field may be viewed in two distinct ways: a discrete structure. Classically, magnetic fields are thought of as being produced by smooth motions of charged objects. For example, oscillating charges produce magnetic fields that may be viewed in a ` smooth', continuous, wavelike fashion. In this case, energy is viewed as being transferred continuously through the electromagnetic field between any two locations. For instance, the metal atoms in a transmitter appear to transfer energy continuously. Problems are found at high frequencies. The electromagnetic field may be thought of in a more'coarse' way. Experiments reveal that in some circumstances electromagnetic transfer is better described as being carried in the form of packets called quanta with a fixed frequency.
Electromagnetic field
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Electromagnetism
273.
Electric field
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Electric fields converge and can be induced by time-varying magnetic fields. The electric field combines with the magnetic field to form the electromagnetic field. A particle of charge q would be subject to a force F = q ⋅ E. Its SI units are newtons per coulomb or, equivalently, volts per metre, which in terms of SI base units are kg⋅m⋅s−3⋅A−1. Electric fields are caused by varying magnetic fields. In the special case of a steady state, the Maxwell-Faraday effect disappears. The permittivity of vacuum, must be substituted if charges are considered in non-empty media. The equations of electromagnetism are best described in a continuous description. A q located at r 0 can be described mathematically as a charge density ρ = q δ, where the Dirac delta function is used. Conversely, a distribution can be approximated by many small point charges. Electric fields satisfy the principle, because Maxwell's equations are linear. This principle is useful to calculate the field created by multiple point charges. If charges q 1, q 2. . .
Electric field
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Electric field lines emanating from a point positive electric charge suspended over an infinite sheet of conducting material.
274.
Electric potential
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By dividing out the charge on the particle a remainder is obtained, a property of the electric field itself. This value volts. The electric potential at infinity is assumed to be zero. This can not be so simply calculated. The magnetic vector potential together form a four vector, so that the two kinds of potential are mixed under Lorentz transformations. Classical mechanics explores concepts such as force, energy, etc.. Potential energy are directly related. A net force acting on any object will cause it to accelerate. As it rolls downhill its potential energy decreases, being translated to motion, inertial energy. Two such force fields are an electric field. Such fields must affect objects due to the position of the object. An electric field exerts a force on charged objects. The magnitude of the force is given by the quantity of the charge multiplied by the magnitude of the electric vector. When the curl ∇ × E is zero, the integral above does not depend on the specific path C chosen but only on its endpoints. The concept of electric potential is closely linked with potential energy.
Electric potential
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Electromagnetism
Electric potential
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The electric potential created by a charge Q is V = Q /(4πε o r). Different values of Q will make different values of electric potential V (shown in the image).
275.
Field (physics)
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In physics, a field is a physical quantity, typically a number or tensor, that has a value for each point in space and time. On a weather map, the surface wind velocity is described by assigning a vector to each point on a map. Each vector represents the direction of the movement of air at that point. When a test electric charge is placed in this electric field, the particle accelerates due to a force. This led physicists to consider electromagnetic fields to be a physical entity, making a supporting paradigm of the edifice of modern physics. In practice, the strength of most fields has been found to diminish to the point of being undetectable. One consequence is that the Earth's gravitational field quickly becomes undetectable on cosmic scales. In fact in this theory an representation of field is a field particle, namely a boson. To Isaac Newton his law of universal gravitation simply expressed the gravitational force that acted between any pair of massive objects. In the eighteenth century, a new quantity was devised to simplify the bookkeeping of all these gravitational forces. The development of the independent concept of a field truly began with the development of the theory of electromagnetism. The independent nature of the field became more apparent with James Clerk Maxwell's discovery that waves in these fields propagated at a finite speed. Maxwell, at first, did not adopt the modern concept of a field as fundamental quantity that could independently exist. Instead, he supposed that the electromagnetic field expressed the deformation of some underlying medium -- the luminiferous aether -- much like the tension in a membrane. If that were the case, the observed velocity of the electromagnetic waves should depend to the aether.
Field (physics)
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Illustration of the electric field surrounding a positive (red) and a negative (blue) charge.
276.
Strong nuclear force
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The nuclear force is the force between protons and neutrons, subatomic particles that are collectively called nucleons. The nuclear force is responsible for binding neutrons into atomic nuclei. Protons are affected by the nuclear force almost identically. The mass of a nucleus is less than the total of the individual masses of the protons and neutrons which form it. The difference in mass between bound and unbound nucleons is known as the mass defect. It is this energy, used in nuclear power and nuclear weapons. At distances less than 0.7 fm, the nuclear force becomes repulsive. This repulsive component is responsible for the physical size of nuclei, since the nucleons can come no closer than the force allows. By comparison, the size of an atom, measured in angstroms, is five orders of magnitude larger. A quantitative description of the nuclear force potentials. The constants for the equations are phenomenological, determined by fitting the equations to experimental data. The internucleon potentials attempt to describe the properties of nucleon -- interaction. Once determined, any given potential can be used in, e.g. the Schrödinger equation to determine the mechanical properties of the nucleon system. The discovery of the neutron in 1932 revealed that atomic nuclei were made of neutrons, held together by an attractive force. By 1935 the nuclear force was conceived to be transmitted by particles called mesons.
Strong nuclear force
Strong nuclear force
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Nuclear physics
Strong nuclear force
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Corresponding potential energy (in units of MeV) of two nucleons as a function of distance as computed from the Reid potential. The potential well is a minimum at a distance of about 0.8 fm. With this potential nucleons can become bound with a negative "binding energy."
277.
Weak nuclear force
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In particle physics, the weak interaction is one of the four known fundamental interactions of nature, alongside the strong interaction, electromagnetism, gravitation. The weak interaction is responsible for radioactive decay, which plays an essential role in nuclear fission. However the term QFD is rarely used because the weak force is best understood in terms of electro-weak theory. The Standard Model of particle physics, which does not address gravity, provides a uniform framework for understanding how strong interactions work. An interaction occurs when two particles, typically but not necessarily force-carrying bosons. The fermions involved in such exchanges can be either elementary or composite, although at the deepest levels, all weak interactions ultimately are between elementary particles. In the case of the weak interaction, fermions can exchange three distinct types of force carriers known as Z bosons. During the epoch of the early universe, the force separated into the electromagnetic and weak forces. Important examples of the weak interaction include the fusion of hydrogen into deuterium that powers the Sun's process. Most fermions will decay by a weak interaction over time. Such decay makes radiocarbon dating possible, as carbon-14 decays through the weak interaction to nitrogen-14. It can also create commonly used in illumination, in the related field of betavoltaics. The weak interaction is unique in that it allows for quarks to swap their flavour for another. The swapping of those properties is mediated by the bosons. Also, similarly, the only one to break charge symmetry.
Weak nuclear force
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Large Hadron Collider tunnel at CERN
Weak nuclear force
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The radioactive beta decay is possible due to the weak interaction, which transforms a neutron into: a proton, an electron, and an electron antineutrino.
278.
Quark
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A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. For this reason, much of what is known about quarks has been drawn from observations of the hadrons themselves. Quarks have intrinsic properties, including electric charge, mass, color charge, spin. There are six types of quarks, known as flavors: up, down, strange, top, bottom. Up and down quarks have the lowest masses of all quarks. The model was independently proposed by physicists Murray Gell-Mann and George Zweig in 1964. Accelerator experiments have provided evidence for all six flavors. The top quark was the last to be discovered in 1995. The Standard Model is the theoretical framework describing the currently known elementary particles. This model contains six flavors of quarks, named up, down, top. Antiparticles of quarks are denoted by a bar over the symbol for the corresponding quark, such as u for an up antiquark. Quarks are spin- 1⁄2 particles, implying that they are fermions according to the spin-statistics theorem. They are subject to the Pauli principle, which states that no two identical fermions can simultaneously occupy the same quantum state. This is to bosons, any number of which can be in the same state.
Quark
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Murray Gell-Mann at TED in 2007. Gell-Mann and George Zweig proposed the quark model in 1964.
Quark
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A proton is composed of two up quarks, one down quark and the gluons that mediate the forces "binding" them together. The color assignment of individual quarks is arbitrary, but all three colors must be present.
279.
Gluon
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In lay terms, they "glue" quarks together, forming neutrons. In technical terms, gluons are gauge bosons that mediate strong interactions of quarks in quantum chromodynamics. Gluons themselves carry the color charge of the strong interaction. This is unlike the photon, which lacks an electric charge. Gluons therefore participate in the strong interaction in addition to mediating it, making QCD significantly harder to analyze than QED. The gluon is a boson; like the photon, it has a spin of 1. In quantum theory, unbroken gauge invariance requires that gauge bosons have zero mass. The gluon has intrinsic parity. Unlike Z bosons of the weak interaction, there are eight independent types of gluon in QCD. This may be difficult to understand intuitively. Quarks carry three types of charge; antiquarks carry three types of anticolor. A relevant illustration in the case at hand would be a gluon with a color state described by: 2. This is read as "red–antiblue plus blue–antired". The color state is: / 3. In words, if one could measure the color of the state, there would be equal probabilities of it being red-antired, green-antigreen.
Gluon
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Large Hadron Collider tunnel at CERN
Gluon
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Diagram 1: In Feynman diagrams, emitted gluons are represented as helices. This diagram depicts the annihilation of an electron and positron.
280.
Electromagnetic force
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Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually is one of the four fundamental interactions in nature. The other three fundamental interactions are the strong interaction, gravitation. The electromagnetic force plays a major role in determining the internal properties of most objects encountered in daily life. Ordinary matter is a manifestation of the electromagnetic force. The electromagnetic force governs the processes involved in chemistry, which arise from interactions between the electrons of neighboring atoms. There are mathematical descriptions of the electromagnetic field. In classical electrodynamics, electric fields are described as electric current. Although electromagnetism is considered one of the four fundamental forces, at high energy electromagnetic force are unified as a single electroweak force. During the quark epoch the unified force broke into the two separate forces as the universe cooled. Originally, magnetism were considered to be two separate forces. An electric current inside a wire creates a corresponding magnetic field outside the wire. Its direction depends on the direction of the current in the wire. While preparing for an lecture on 21 April 1820, Hans Christian Ørsted made a surprising observation. However, he began more intensive investigations.
Electromagnetic force
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Lightning is an electrostatic discharge that travels between two charged regions.
Electromagnetic force
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Electromagnetism
Electromagnetic force
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Hans Christian Ørsted.
Electromagnetic force
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André-Marie Ampère
281.
Electroweak theory
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In particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 100 GeV, they would merge into a single electroweak force. Thus, if the universe is hot enough, then the electromagnetic force and weak force merge into a combined electroweak force. During the electroweak epoch, the electroweak force separated from the strong force. During the quark epoch, the electroweak force split into the electromagnetic and weak force. In 1999, Gerardus't Hooft and Martinus Veltman were awarded the Nobel prize for showing that the electroweak theory is renormalizable. Mathematically, the unification is accomplished under an SU × U gauge group. The axes representing the particles have essentially just been rotated, in the plane, by the angle θW. The L g term describes the interaction between the three W particles and the B particle. L f is the kinetic term for the Standard Model fermions. The interaction of the gauge bosons and the fermions are through the gauge covariant derivative. C. The Lagrangian reorganizes itself after the Higgs boson acquires a vacuum expectation value. Due to its complexity, this Lagrangian is best described by breaking it up into several parts as follows.
Electroweak theory
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Large Hadron Collider tunnel at CERN
282.
Sheldon Glashow
–
Sheldon Lee Glashow is a Nobel Prize winning American theoretical physicist. Sheldon Lee Glashow was born to Jewish immigrants from Russia, Bella and Lewis Gluchovsky, a plumber. He graduated in 1950. Afterwards, Glashow joined the University of California, Berkeley where he was an associate professor from 1962 to 1966. He was named Higgins Professor of Physics in 1979; he became emeritus in 2000. In 1961, Glashow extended unification models due to Schwinger by including a short range neutral current, the Z0. SU × U, forms the basis of the accepted theory of the electroweak interactions. For this discovery, Glashow along with Abdus Salam, was awarded the 1979 Nobel Prize in Physics. In collaboration with James Bjorken, Glashow was the first to predict the charm quark, in 1964. This was at a time when 4 leptons had been only 3 quarks proposed. In 1973, Glashow and Howard Georgi proposed the first unified theory. They discovered how to fit the gauge forces in the quarks and leptons into two simple representations. This work was the foundation for all unifying work. Glashow shared the 1977 J. Robert Oppenheimer Memorial Prize with Feza Gürsey. Glashow is a skeptic of Superstring theory due to its lack of experimentally testable predictions.
Sheldon Glashow
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Sheldon Lee Glashow
Sheldon Glashow
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Professor Glashow's KHC PY 101 Energy class, at Boston University's Kilachand Honors College (Spring 2011)
283.
Steven Weinberg
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Weinberg holds the Josey Regental Chair in Science at the University of Texas at Austin, where he is a member of the Physics and Astronomy Departments. Weinberg's articles on various subjects occasionally appear in The New York Review of other periodicals. He has served as consultant at the U. S. Steven Weinberg was born in 1933 in New York City-his parents were Jewish immigrants. Weinberg graduated in 1950. He received his bachelor's degree from Cornell University in 1954, living at the Cornell Branch of the Telluride Association. Weinberg went to the Niels Bohr Institute in Copenhagen where he started his graduate studies and research. After one Weinberg returned to Princeton University where he earned his PhD degree in physics in 1957, for research supervised by Sam Treiman. Both textbooks are among the most influential texts in the scientific community in their subjects. In 1966, he accepted a lecturer position at Harvard. In 1967 Weinberg was a visiting professor at MIT. One of its fundamental aspects was the prediction of the existence of the Higgs boson. The 1973 experimental discovery of neutral currents was one verification of the electroweak unification. The paper by Weinberg in which he presented this theory is one of the most cited works ever in high energy physics. In the years after 1967, the full Standard Model of elementary theory was developed through the work of many contributors.
Steven Weinberg
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Steven Weinberg at the 2010 Texas Book Festival
Steven Weinberg
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Queen Beatrix meets Nobel laureates in 1983, Weinberg is next to the queen
284.
Gravity
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Gravity, or gravitation, is a natural phenomenon by which all things with mass are brought toward one another, including planets, stars and galaxies. Since mass are equivalent, all forms of energy, including light, also cause gravitation and are under the influence of it. On Earth, gravity causes the ocean tides. Gravity has an infinite range, although its effects become increasingly weaker on farther objects. The most extreme example of this curvature of spacetime is a black hole, from which nothing can escape once past its horizon, not even light. More gravity results in gravitational time dilation, where time lapses more slowly at a lower gravitational potential. Gravity is the weakest of the four fundamental interactions of nature. As a consequence, gravity plays no role in determining the internal properties of everyday matter. On the other hand, gravity is the cause of the formation, shape and trajectory of astronomical bodies. While the European thinkers are rightly credited with development of gravitational theory, there were pre-existing ideas which had identified the force of gravity. Later, the works of Brahmagupta referred to the presence of this force. Modern work on gravitational theory began in the late 16th and early 17th centuries. This was a major departure from Aristotle's belief that heavier objects have a higher gravitational acceleration. Galileo postulated resistance as the reason that objects with less mass may fall slower in an atmosphere. Galileo's work set the stage for the formulation of Newton's theory of gravity.
Gravity
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Sir Isaac Newton, an English physicist who lived from 1642 to 1727
Gravity
Gravity
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Two-dimensional analogy of spacetime distortion generated by the mass of an object. Matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. White lines do not represent the curvature of space but instead represent the coordinate system imposed on the curved spacetime, which would be rectilinear in a flat spacetime.
Gravity
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Ball falling freely under gravity. See text for description.
285.
Fundamental force
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Fundamental interactions, also known as fundamental forces, are the interactions in physical systems that do not appear to be reducible to more basic interactions. There are four conventionally accepted fundamental interactions -- weak nuclear. Each one is understood as the dynamics of a field. The gravitational force is modelled as a classical field. The other three exhibit a measurable unit or elementary particle. The two nuclear interactions produce strong forces at subatomic distances. The nuclear interaction is responsible for the binding of atomic nuclei. The nuclear interaction also acts on the nucleus, mediating radioactive decay. Gravity produce significant forces at macroscopic scales where the effects can be seen directly in everyday life.. . Other theorists seek to unite strong fields within a Grand Unified Theory. Thus Newton's theory violated the first principle of mechanical philosophy, as stated at a distance. Conversely, during the 1820s, when explaining magnetism, Michael Faraday inferred a field transmitting that force. Faraday conjectured that ultimately, all forces unified into one. The Standard Model of particle physics was developed throughout the latter half of the 20th century.
Fundamental force
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The Standard Model of elementary particles, with the fermions in the first three columns, the gauge bosons in the fourth column, and the Higgs boson in the fifth column
286.
Hawking radiation
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Hawking radiation is blackbody radiation, predicted to be released by black holes, due to quantum effects near the event horizon. Hawking radiation reduces the mass and energy of black holes and is therefore also known as black hole evaporation. Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish. Micro black holes are predicted to be larger net emitters of radiation than larger black holes and should shrink and dissipate faster. In June 2008, NASA launched the Fermi space telescope, searching for the terminal gamma-ray flashes expected from evaporating primordial black holes. However, the results remain unverified and debatable. Other projects have been launched to look for this radiation within the framework of analog gravity. Black holes are sites of immense gravitational attraction. Classically, the gravitation is so powerful that nothing, not even electromagnetic radiation, can escape from the black hole. It is yet unknown how gravity can be incorporated into quantum mechanics. Hawking showed that quantum effects allow black holes to emit exact black body radiation. The electromagnetic radiation is produced as if emitted by a black body with a temperature inversely proportional to the mass of the black hole. Physical insight into the process may be gained by imagining that particle–antiparticle radiation is emitted from just beyond the event horizon. As the particle–antiparticle pair was produced by the black hole's gravitational energy, the escape of one of the particles lowers the mass of the black hole. An alternative view of the process is that vacuum fluctuations cause a particle–antiparticle pair to appear close to the event horizon of a black hole.
Hawking radiation
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Simulated view of a black hole (center) in front of the Large Magellanic Cloud. Note the gravitational lensing effect, which produces two enlarged but highly distorted views of the Cloud. Across the top, the Milky Way disk appears distorted into an arc.
287.
Complex domain
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In this expression, a is the real part and b is the imaginary part of the complex number. The complex number a + bi can be identified with the point in the complex plane. As as their use within mathematics, complex numbers have practical applications including physics, chemistry, biology, economics, electrical engineering, statistics. The Italian mathematician Gerolamo Cardano is the first known to have introduced complex numbers. He called them "fictitious" during his attempts to find solutions to cubic equations in the 16th century. Complex numbers allow solutions to certain equations that have no solutions in real numbers. For example, the equation 2 = − 9 has no real solution, since the square of a real number cannot be negative. Complex numbers provide a solution to this problem. According to the fundamental theorem of algebra, all polynomial equations with real or complex coefficients in a single variable have a solution in complex numbers. For example, −3.5 + 2i is a complex number. By this convention the imaginary part does not include the imaginary unit: hence b, not bi, is the imaginary part. For example, Re = − 3.5 Im = 2. Hence, in imaginary parts, a complex z is equal to Re + Im ⋅ i. This expression is sometimes known as the Cartesian form of z. A real number a can be regarded as a complex number a + 0i whose imaginary part is 0.
Complex domain
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A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. "Re" is the real axis, "Im" is the imaginary axis, and i is the imaginary unit which satisfies i 2 = −1.
288.
Chaos theory
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Small differences in initial conditions yield widely diverging outcomes for dynamical systems, rendering long-term prediction of their behavior impossible in general. This happens even though these systems are deterministic, meaning that their future behavior is fully determined with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos. The approximate present does not approximately determine the future. Chaotic behavior exists in natural systems, such as weather and climate. It also occurs spontaneously in some systems such as road traffic. This behavior can be studied through analytical techniques such as recurrence plots and Poincaré maps. Chaos theory has applications including meteorology, sociology, physics, environmental science, computer science, engineering, economics, biology, ecology, philosophy. Chaos theory concerns deterministic systems whose behavior can in principle be predicted. Chaotic systems are predictable for a while and then'appear' to become random. Some examples of Lyapunov times are: about 1 millisecond; weather systems, a few days; the solar system, 50 million years. In chaotic systems, the uncertainty in a forecast increases exponentially with elapsed time. Mathematically, doubling the forecast time more than squares the proportional uncertainty in the forecast. This means, in practice, a meaningful prediction can not be made over three times the Lyapunov time.
Chaos theory
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The Lorenz attractor displays chaotic behavior. These two plots demonstrate sensitive dependence on initial conditions within the region of phase space occupied by the attractor.
Chaos theory
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A plot of Lorenz attractor for values r = 28, σ = 10, b = 8/3
Chaos theory
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Turbulence in the tip vortex from an airplane wing. Studies of the critical point beyond which a system creates turbulence were important for chaos theory, analyzed for example by the Soviet physicist Lev Landau, who developed the Landau-Hopf theory of turbulence. David Ruelle and Floris Takens later predicted, against Landau, that fluid turbulence could develop through a strange attractor, a main concept of chaos theory.
Chaos theory
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A conus textile shell, similar in appearance to Rule 30, a cellular automaton with chaotic behaviour.
289.
Quantum coherence
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In physics, two wave sources are perfectly coherent if they have a constant phase difference and the same frequency. It is an ideal property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between several waves or wave packets. Interference is nothing more than the addition, in the mathematical sense, of wave functions. This is still an addition of two waves. Two waves always interfere, even if the result of the addition is complicated or not remarkable. Two waves are said to be coherent if they have a relative phase. Spatial coherence describes the correlation between waves at different points in space, either longitudinal. Temporal coherence describes the correlation between waves observed at different moments in time. Both are observed in Young's interference experiment. Similarly, finally the fringes disappear, showing spatial coherence. In both cases, the amplitude slowly disappears, as the path difference increases past the coherence length. The property of coherence is the basis for commercial applications such as holography, the Sagnac gyroscope, radio antenna arrays, telescope interferometers. A precise definition is given at degree of coherence. The power spectral density are defined as the Fourier transforms of the cross-correlation and the autocorrelation signals, respectively.
Quantum coherence
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Figure 1: The amplitude of a single frequency wave as a function of time t (red) and a copy of the same wave delayed by τ(green). The coherence time of the wave is infinite since it is perfectly correlated with itself for all delays τ.
290.
EPR paradox
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This consequence had not previously been noticed and seemed unreasonable at the time; the phenomenon involved is now known as quantum entanglement. However, the outcomes for each subsystem separately at each repetition of the experiment will not be well defined or predictable. This modern resolution eliminates the need for hidden variables, action at a distance or other structures introduced over time in order to explain the phenomenon. A preference for the latter resolution is supported by experiments suggested by Bell's theorem of 1964, which exclude some classes of hidden variable theory. At the time the EPR article discussed below was written, it was known from experiments that the outcome of an experiment sometimes cannot be uniquely predicted. An example of such indeterminacy can be seen when a beam of light is incident on a half-silvered mirror. One half of the beam will reflect, the other will pass. The routine explanation of this effect was, at that time, provided by Heisenberg's uncertainty principle. Physical quantities come in pairs called conjugate quantities. Examples of such conjugate pairs are position and momentum of a particle and components of spin measured around different axes. When one quantity was measured, became determined, the conjugated quantity became indeterminate. Heisenberg explained this as a disturbance caused by measurement. The EPR paper, written in 1935, was intended to illustrate that this explanation is inadequate. Heisenberg's principle was an attempt to provide a classical explanation of a quantum effect sometimes called non-locality. According to EPR there were two possible explanations.
EPR paradox
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Albert Einstein
291.
Quantum interference
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In physics, interference is a phenomenon in which two waves superpose to form a resultant wave of greater, lower, or the same amplitude. Interference effects can be observed for example, light, radio, acoustic, surface water waves or matter waves. Consider, for example, what happens when two identical stones are dropped at different locations. Each stone generates a circular wave propagating outwards from the point where the stone was dropped. When the two waves overlap, the net displacement at a particular point is the sum of the displacements of the individual waves. At some points, these will produce a maximum displacement. In other places, there will be no net displacement at these points. Thus, parts of the surface will be stationary -- these are seen to the right as stationary blue-green lines radiating from the center. The above can be demonstrated by deriving the formula for the sum of two waves. Constructive interference: If the difference is an even multiple of pi: ϕ =... − 4 π, − 2 π, 0, 2 π, 4 π... . . − 4 π, − 2 π, 0, 2 π, 4 π. . .
Quantum interference
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Swimming pool interference
Quantum interference
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Magnified-image of coloured interference-pattern in soap-film. The black areas ("holes") are areas where the film is very thin and there is a nearly total destructive interference.
Quantum interference
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Interference fringes in overlapping plane waves
Quantum interference
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White light interference in a soap bubble
292.
Absolute zero
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The corresponding Kelvin and Rankine temperature scales set their zero points by definition. In the quantum-mechanical description, matter at absolute zero is in its state, the point of lowest internal energy. And a system at absolute zero still possesses the energy of its ground state at absolute zero. The kinetic energy of the state can not be removed. Technologists routinely achieve temperatures close to absolute zero, where matter exhibits quantum effects such as superconductivity and superfluidity. At temperatures near 0 K, nearly all molecular motion ΔS = 0 for any adiabatic process, where S is the entropy. In such a circumstance, pure substances can form perfect crystals as T → 0. Max Planck's strong form of the third law of thermodynamics states the entropy of a perfect crystal vanishes at absolute zero. The Nernst postulate identifies the isotherm T = 0 as coincident with the adiabat S = 0, although other adiabats are distinct. As no two intersect, no other adiabat can intersect the T = 0 isotherm. Consequently no adiabatic process initiated at temperature can lead to zero temperature. A perfect crystal is one in which the internal structure extends uninterrupted in all directions. The perfect order can be represented by translational symmetry along three axes. Every element of the structure is in its proper place, whether it is a single atom or a molecular grouping. For substances that exist in two crystalline forms, such as diamond and graphite for carbon, there is a kind of chemical degeneracy.
Absolute zero
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Robert Boyle pioneered the idea of an absolute zero.
Absolute zero
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Velocity-distribution data of a gas of rubidium atoms at a temperature within a few billionths of a degree above absolute zero. Left: just before the appearance of a Bose–Einstein condensate. Center: just after the appearance of the condensate. Right: after further evaporation, leaving a sample of nearly pure condensate.
Absolute zero
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The rapid expansion of gases leaving the Boomerang Nebula causes the lowest observed temperature outside a laboratory: 1 K
293.
Molecule
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A molecule is an electrically neutral group of two or more atoms held together by chemical bonds. Molecules are distinguished from ions by their lack of electrical charge. However, in quantum physics, biochemistry, the term molecule is often used less strictly, also being applied to polyatomic ions. In the kinetic theory of gases, the molecule is often used for any gaseous particle regardless of its composition. According to this definition, noble gas atoms are considered molecules as they are in monoatomic molecules. Complexes connected by non-covalent interactions, such as hydrogen bonds or ionic bonds, are generally not considered single molecules. Molecules as components of matter are common in organic substances. They also make up most of atmosphere. The theme of repeated unit-cellular-structure also holds with metallic bonding, which means that solid metals are also not made of molecules. The science of molecules is called molecular physics, depending on whether the focus is on chemistry or physics. In practice, however, this distinction is vague. In molecular sciences, a molecule consists of a stable system composed of two or more atoms. Polyatomic ions may sometimes be usefully thought as electrically charged molecules. According to the Online Etymology Dictionary, the word "molecule" derives from the Latin "moles" or small unit of mass. Molecule -- "extremely minute particle", from French molécule, from diminutive of Latin moles "mass, barrier".
Molecule
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Atomic force microscopy image of a PTCDA molecule, which contains five carbon rings in a non-linear arrangement.
Molecule
Molecule
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A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings.
Molecule
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Arrangement of polyvinylidene fluoride molecules in a nanofiber – transmission electron microscopy image.
294.
Speed of light
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The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. According to special relativity, c is the maximum speed at which all matter and hence information in the universe can travel. It is the speed at which all massless particles and changes of the associated fields travel in vacuum. Such waves travel at c regardless of the inertial refer