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 continued postgraduate studies there, he became a professor there in 1932. In 1919–1923 and 1928–1941 he collaborated with the Vavilov State Optical Institute, in 1924–1936 with the Leningrad Institute of Physics and Technology, in 1934–1941 and 1944–1953 with the Lebedev Physical Institute, his primary scientific contribution lies in the development of quantum physics and the theory of gravitation, although he contributed to the fields of mechanics, theoretical optics, physics of continuous media. In 1926, he derived the Klein–Gordon equation, he gave his name to Fock space, the Fock representation and Fock state, developed the Hartree–Fock method in 1930. He made many subsequent scientific contributions, during the rest of his life. Fock developed the electromagnetic methods for geophysical exploration in a book The theory of the study of the rocks resistance by the carottage method.
Fock made significant contributions to general relativity theory for the many body problems. Fock criticised on scientific grounds both Einstein's general principle of relativity as being devoid of physical substance and the equivalence principle as interpreted as the equivalence of gravitation and acceleration as having only a local validity. In Leningrad, Fock created a scientific school in theoretical physics and raised the physics education in the USSR through his books, he wrote the first textbook on quantum mechanics Fundamentals of Quantum Mechanics and a influential monograph The Theory of Space and Gravitation. Historians of science, 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 the USSR Academy of Sciences and a member of the International Academy of Quantum Molecular Science.
List of things named after Vladimir Fock Graham, L.. "The reception of Einstein's ideas: Two examples from contrasting political cultures." In Holton, G. and Elkana, Y. Albert Einstein: Historical and cultural perspectives. Princeton, NJ: Princeton UP, pp. 107–136 Fock, V. A.. "The Theory of Space and Gravitation". Macmillan
In physics, a continuous spectrum means a set of attainable values for some physical quantity, best described as an interval of real numbers, as opposed to a discrete spectrum, a set of attainable values, discrete in the mathematical sense, where there is a positive gap between each value and the next one. The classical example of a continuous spectrum, from which the name is derived, is the part of the spectrum of the light emitted by excited atoms of hydrogen, due to free electrons becoming bound to a hydrogen ion and emitting photons, which are smoothly spread over a wide range of wavelengths, in contrast to the discrete lines due to electrons falling from some bound quantum state to a state of lower energy; as in that classical example, the term is most used when the range of values of a physical quantity may have both a continuous and a discrete part, whether at the same time or in different situations. In quantum systems, continuous spectra are associated with free particles, such as atoms in a gas, electrons in an electron beam, or conduction band electrons in a metal.
In particular, the position and momentum of a free particle has a continuous spectrum, but when the particle is confined to a limited space its spectrum becomes discrete. A continuous spectrum may be just a convenient model for a discrete spectrum whose values are too close to be distinguished, as in the phonons in a crystal; the continuous and discrete spectra of physical systems can be modeled in functional analysis as different parts in the decomposition of the spectrum of a linear operator acting on a function space, such as the Hamiltonian operator. Astronomical spectroscopy Synchrotron radiation Inverse Compton scattering Discrete spectra Emission spectrum Absorption spectrum ContinuousSpectrum.com
Physics is the natural science that studies matter, its motion, behavior through space and time, that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, its main goal is to understand how the universe behaves. Physics is one of the oldest academic disciplines and, through its inclusion of astronomy the oldest. Over much of the past two millennia, chemistry and certain branches of mathematics, were a part of natural philosophy, but during the scientific revolution in the 17th century these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, the boundaries of physics which are not rigidly defined. New ideas in physics explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics enable advances in new technologies.
For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have transformed modern-day society, such as television, domestic appliances, nuclear weapons. Astronomy is one of the oldest natural sciences. Early civilizations dating back to beyond 3000 BCE, such as the Sumerians, ancient Egyptians, the Indus Valley Civilization, had a predictive knowledge and a basic understanding of the motions of the Sun and stars; the stars and planets were worshipped, believed to represent gods. While the explanations for the observed positions of the stars were unscientific and lacking in evidence, these early observations laid the foundation for astronomy, as the stars were found to traverse great circles across the sky, which however did not explain the positions of the planets. According to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, all Western efforts in the exact sciences are descended from late Babylonian astronomy.
Egyptian astronomers left monuments showing knowledge of the constellations and the motions of the celestial bodies, while Greek poet Homer wrote of various celestial objects in his Iliad and Odyssey. Natural philosophy has its origins in Greece during the Archaic period, when pre-Socratic philosophers like Thales rejected non-naturalistic explanations for natural phenomena and proclaimed that every event had a natural cause, they proposed ideas verified by reason and observation, many of their hypotheses proved successful in experiment. The Western Roman Empire fell in the fifth century, this resulted in a decline in intellectual pursuits in the western part of Europe. By contrast, the Eastern Roman Empire resisted the attacks from the barbarians, continued to advance various fields of learning, including physics. In the sixth century Isidore of Miletus created an important compilation of Archimedes' works that are copied in the Archimedes Palimpsest. In sixth century Europe John Philoponus, a Byzantine scholar, questioned Aristotle's teaching of physics and noting its flaws.
He introduced the theory of impetus. Aristotle's physics was not scrutinized until John Philoponus appeared, unlike Aristotle who based his physics on verbal argument, Philoponus relied on observation. On Aristotle's physics John Philoponus wrote: “But this is erroneous, our view may be corroborated by actual observation more than by any sort of verbal argument. For if you let fall from the same height two weights of which one is many times as heavy as the other, you will see that the ratio of the times required for the motion does not depend on the ratio of the weights, but that the difference in time is a small one, and so, if the difference in the weights is not considerable, that is, of one is, let us say, double the other, there will be no difference, or else an imperceptible difference, in time, though the difference in weight is by no means negligible, with one body weighing twice as much as the other”John Philoponus' criticism of Aristotelian principles of physics served as an inspiration for Galileo Galilei ten centuries during the Scientific Revolution.
Galileo cited Philoponus in his works when arguing that Aristotelian physics was flawed. In the 1300s Jean Buridan, a teacher in the faculty of arts at the University of Paris, developed the concept of impetus, it was a step toward the modern ideas of momentum. Islamic scholarship inherited Aristotelian physics from the Greeks and during the Islamic Golden Age developed it further placing emphasis on observation and a priori reasoning, developing early forms of the scientific method; the most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn al-Haytham, in which he conclusively disproved the ancient Greek idea about vision, but came up with a new theory. In the book, he presented a study of the phenomenon of the camera obscura (his thousand-year-old
Enrico Fermi was an Italian and naturalized-American physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and the "architect of the atomic bomb", he was one of few physicists to excel in both theoretical physics and experimental physics. Fermi held several patents related to the use of nuclear power, was awarded the 1938 Nobel Prize in Physics for his work on induced radioactivity by neutron bombardment and for the discovery of transuranium elements, he made significant contributions to the development of statistical mechanics, quantum theory, nuclear and particle physics. Fermi's first major contribution involved the field of statistical mechanics. After Wolfgang Pauli formulated his exclusion principle in 1925, Fermi followed with a paper in which he applied the principle to an ideal gas, employing a statistical formulation now known as Fermi–Dirac statistics. Today, particles that obey the exclusion principle are called "fermions".
Pauli postulated the existence of an uncharged invisible particle emitted along with an electron during beta decay, to satisfy the law of conservation of energy. Fermi took up this idea, developing a model that incorporated the postulated particle, which he named the "neutrino", his theory referred to as Fermi's interaction and now called weak interaction, described one of the four fundamental interactions in nature. Through experiments inducing radioactivity with the discovered neutron, Fermi discovered that slow neutrons were more captured by atomic nuclei than fast ones, he developed the Fermi age equation to describe this. After bombarding thorium and uranium with slow neutrons, he concluded that he had created new elements. Although he was awarded the Nobel Prize for this discovery, the new elements were revealed to be nuclear fission products. Fermi left Italy in 1938 to escape new Italian racial laws that affected his Jewish wife, Laura Capon, he emigrated to the United States, where he worked on the Manhattan Project during World War II.
Fermi led the team that designed and built Chicago Pile-1, which went critical on 2 December 1942, demonstrating the first human-created, self-sustaining nuclear chain reaction. He was on hand when the X-10 Graphite Reactor at Oak Ridge, went critical in 1943, when the B Reactor at the Hanford Site did so the next year. At Los Alamos, he headed F Division, part of which worked on Edward Teller's thermonuclear "Super" bomb, he 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, Fermi served under J. Robert Oppenheimer on the General Advisory Committee, which advised the Atomic Energy Commission on nuclear matters. After the detonation of the first Soviet fission bomb in August 1949, he opposed the development of a hydrogen bomb on both moral and technical grounds, he was among the scientists who testified on Oppenheimer's behalf at the 1954 hearing that resulted in the denial of Oppenheimer's security clearance. Fermi did important work in particle physics related to pions and muons, he speculated that cosmic rays arose when material was accelerated by magnetic fields in interstellar space.
Many awards and institutions are named after Fermi, including the Enrico Fermi Award, the Enrico Fermi Institute, the Fermi National Accelerator Laboratory, the Fermi Gamma-ray Space Telescope, the Enrico Fermi Nuclear Generating Station, the synthetic element fermium, making him one of 16 scientists who have elements named after them. Enrico Fermi was born in Rome, Italy, on 29 September 1901, he was the third child of Alberto Fermi, a division head in the Ministry of Railways, Ida de Gattis, an elementary school teacher. His sister, was two years older than he, his brother Giulio a year older. After the two boys were sent to a rural community to be wet nursed, Enrico rejoined his family in Rome when he was two and a half. Although he was baptised a Roman Catholic in accordance with his grandparents' wishes, his family was not religious; as a young boy he shared the same interests as his brother Giulio, building electric motors and playing with electrical and mechanical toys. Giulio died during an operation on a throat abscess in 1915 and Maria died in an airplane crash near Milan in 1959.
At a local market Fermi found a physics book, the 900-page Elementorum physicae mathematicae. Written in Latin by Jesuit Father Andrea Caraffa, a professor at the Collegio Romano, it presented mathematics, classical mechanics, astronomy and acoustics as they were understood at the time of its 1840 publication. With scientifically inclined friend, Enrico Persico, Fermi pursued projects such as building gyroscopes and measuring the acceleration of Earth's gravity. A colleague of Fermi's father gave him books on physics and mathematics which he assimilated quickly. Fermi graduated from high school in July 1918, at Amidei's urging applied to the Scuola Normale Superiore in Pisa. Having lost one son, his parents only reluctantly allowed him to live in the school's lodgings for four years. Fermi took first place in the difficult entrance exam, which included an essay on the theme of "Specific characteristics of Sounds". At the Scuola Normale Superiore Fermi played pranks with fellow student Franco Rasetti.
Fermi was advised by Luigi Puccianti, director of the physics laborat
Princeton University is a private Ivy League research university in Princeton, New Jersey. Founded in 1746 in Elizabeth as the College of New Jersey, Princeton is the fourth-oldest institution of higher education in the United States and one of the nine colonial colleges chartered before the American Revolution; the institution moved to Newark in 1747 to the current site nine years and renamed itself Princeton University in 1896. Princeton provides undergraduate and graduate instruction in the humanities, social sciences, natural sciences, engineering, it offers professional degrees through the Woodrow Wilson School of Public and International Affairs, the School of Engineering and Applied Science, the School of Architecture and the Bendheim Center for Finance. The university has ties with the Institute for Advanced Study, Princeton Theological Seminary and the Westminster Choir College of Rider University. Princeton has the largest endowment per student in the United States. From 2001 to 2018, Princeton University was ranked either first or second among national universities by U.
S. News & World Report, holding the top spot for 16 of those 18 years; as of October 2018, 65 Nobel laureates, 15 Fields Medalists and 13 Turing Award laureates have been affiliated with Princeton University as alumni, faculty members or researchers. In addition, Princeton has been associated with 21 National Medal of Science winners, 5 Abel Prize winners, 5 National Humanities Medal recipients, 209 Rhodes Scholars, 139 Gates Cambridge Scholars and 126 Marshall Scholars. Two U. S. Presidents, twelve U. S. Supreme Court Justices and numerous living billionaires and foreign heads of state are all counted among Princeton's alumni body. Princeton has graduated many prominent members of the U. S. Congress and the U. S. Cabinet, including eight Secretaries of State, three Secretaries of Defense and three of the past five Chairs of the Federal Reserve. New Light Presbyterians founded the College of New Jersey in 1746; the college was the religious capital of Scottish Presbyterian America. In 1754, trustees of the College of New Jersey suggested that, in recognition of Governor Jonathan Belcher's interest, Princeton should be named as Belcher College.
Belcher replied: "What a name that would be!" In 1756, the college moved to New Jersey. Its home in Princeton was Nassau Hall, named for the royal House of Orange-Nassau of William III of England. Following the untimely deaths of Princeton's first five presidents, John Witherspoon became president in 1768 and remained in that office until his death in 1794. During his presidency, Witherspoon shifted the college's focus from training ministers to preparing a new generation for secular leadership in the new American nation. To this end, he solicited investment in the college. Witherspoon's presidency constituted a long period of stability for the college, interrupted by the American Revolution and the Battle of Princeton, during which British soldiers occupied Nassau Hall. In 1812, the eighth president of the College of New Jersey, Ashbel Green, helped establish the Princeton Theological Seminary next door; the plan to extend the theological curriculum met with "enthusiastic approval on the part of the authorities at the College of New Jersey".
Today, Princeton University and Princeton Theological Seminary maintain separate institutions with ties that include services such as cross-registration and mutual library access. Before the construction of Stanhope Hall in 1803, Nassau Hall was the college's sole building; the cornerstone of the building was laid on September 17, 1754. During the summer of 1783, the Continental Congress met in Nassau Hall, making Princeton the country's capital for four months. Over the centuries and through two redesigns following major fires, Nassau Hall's role shifted from an all-purpose building, comprising office, dormitory and classroom space; the class of 1879 donated twin lion sculptures that flanked the entrance until 1911, when that same class replaced them with tigers. Nassau Hall's bell rang after the hall's construction; the bell was recast and melted again in the fire of 1855. James McCosh took office as the college's president in 1868 and lifted the institution out of a low period, brought about by the American Civil War.
During his two decades of service, he overhauled the curriculum, oversaw an expansion of inquiry into the sciences, supervised the addition of a number of buildings in the High Victorian Gothic style to the campus. McCosh Hall is named in his honor. In 1879, the first thesis for a Doctor of Philosophy Ph. D. was submitted by James F. Williamson, Class of 1877. In 1896, the college changed its name from the College of New Jersey to Princeton University to honor the town in which it resides. During this year, the college underwent large expansion and became a university. In 1900, the Graduate School was established. In 1902, Woodrow Wilson, graduate of the Class of 1879, was elected the 13th president of the university. Under Wilson, Princeton introduced the preceptorial system in 1905, a then-unique concept in the US that augmented the standard lecture method of teaching with a more personal form in which small groups of students, or precepts, could interact with a single instructor, or preceptor, in their field of interest.
In 1906, the reservoir Lake Carnegie was created by Andrew Carnegie. A collection of historical photographs of the build
In mechanical systems, resonance is a phenomenon that occurs when the frequency at which a force is periodically applied is equal or nearly equal to one of the natural frequencies of the system on which it acts. This causes the system to oscillate with larger amplitude than when the force is applied at other frequencies. Frequencies at which the response amplitude is a relative maximum are known as resonant frequencies or resonance frequencies of the system. Near resonant frequencies, small periodic forces have the ability to produce large amplitude oscillations, due to the storage of vibrational energy. In other systems, such as electrical or optical, phenomena occur which are described as resonance but depend on interaction between different aspects of the system, not on an external driver. For example, electrical resonance occurs in a circuit with capacitors and inductors because the collapsing magnetic field of the inductor generates an electric current in its windings that charges the capacitor, the discharging capacitor provides an electric current that builds the magnetic field in the inductor.
Once the circuit is charged, the oscillation is self-sustaining, there is no external periodic driving action. This is analogous to a mechanical pendulum, where mechanical energy is converted back and forth between kinetic and potential, both systems are forms of simple harmonic oscillators. In optical cavities, light confined in the cavity reflects forth multiple times; this produces standing waves, only certain patterns and frequencies of radiation are sustained, due to the effects of interference, while the others are suppressed by destructive interference. Once the light enters the cavity, the oscillation is self-sustaining, there is no external periodic driving action; some behavior is mistaken for resonance but instead is a form of self-oscillation, such as aeroelastic flutter, speed wobble, or Hunting oscillation. In these cases, the external energy source does not oscillate, but the components of the system interact with each other in a periodic fashion. Resonance occurs when a system is able to store and 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 equal to the natural frequency of the system, a frequency of unforced vibrations; some systems have multiple, resonant frequencies. Resonance phenomena occur with all types of vibrations or waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance, electron spin resonance and resonance of quantum wave functions. Resonant systems can be used to generate vibrations of a specific frequency, or pick out specific frequencies from a complex vibration containing many frequencies; the term resonance originates from the field of acoustics observed in musical instruments, e.g. when strings started to vibrate and to produce sound without direct excitation by the player. A familiar example is a playground swing. Pushing a person in a swing in time with the natural interval of the swing makes the swing go higher and higher, while attempts to push the swing at a faster or slower tempo produce smaller arcs.
This is because the energy the swing absorbs is maximized when the pushes match the swing's natural oscillations. Resonance occurs in nature, is exploited in many manmade devices, it is the mechanism by which all sinusoidal waves and vibrations are generated. Many sounds we hear, such as when hard objects of metal, glass, or wood are struck, are caused by brief resonant vibrations in the object. Light and other short wavelength electromagnetic radiation is produced by resonance on an atomic scale, such as electrons in atoms. Other examples of resonance: Timekeeping mechanisms of modern clocks and watches, e.g. the balance wheel in a mechanical watch and the quartz crystal in a quartz watch Tidal resonance of the Bay of Fundy Acoustic resonances of musical instruments and the human vocal tract Shattering of a crystal wineglass when exposed to a musical tone of the right pitch Friction idiophones, such as making a glass object vibrate by rubbing around its rim with a fingertip Electrical resonance of tuned circuits in radios and TVs that allow radio frequencies to be selectively received Creation of coherent light by optical resonance in a laser cavity Orbital resonance as exemplified by some moons of the solar system's gas giants Material resonances in atomic scale are the basis of several spectroscopic techniques that are used in condensed matter physics Electron spin resonance Mössbauer effect Nuclear magnetic resonance The visible, rhythmic twisting that resulted in the 1940 collapse of "Galloping Gertie", the original Tacoma Narrows Bridge, is mistakenly characterized as an example of resonance phenomenon in certain textbooks.
The catastrophic vibrations that destroyed the bridge were not due to simple mechanical resonance, but to a more complicated interaction between the bridge and the winds passing through it—a phenomenon known as aeroelastic flutter, a kind of "self-sustaining vibration" as referred to in the nonlinear theory of vibrations. Robert H. Scanlan, father of bridge aerodynamics, has written an article about this misunderstanding; the rocket engines for the International Space Station are controlled by an autopilot. Ordinarily, uploaded parameters for controlling the engine control system for the Zvezda modu