Speed of light
The speed of light in vacuum denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299,792,458 metres per second, it is exact because by international agreement a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1/299792458 second. According to special relativity, c is the maximum speed at which all conventional matter and hence all known forms of information in the universe can travel. Though this speed is most associated with light, it is in fact the speed at which all massless particles and changes of the associated fields travel in vacuum; such particles and waves travel at c regardless of the motion of the source or the inertial reference frame of the observer. In the special and general theories of relativity, c interrelates space and time, appears in the famous equation of mass–energy equivalence E = mc2; the speed at which light propagates through transparent materials, such as glass or air, is less than c.
The ratio between c and the speed v at which light travels in a material is called the refractive index n of the material. For example, for visible light the refractive index of glass is around 1.5, meaning that light in glass travels at c / 1.5 ≈ 200,000 km/s. For many practical purposes and other electromagnetic waves will appear to propagate instantaneously, but for long distances and sensitive measurements, their finite speed has noticeable effects. In communicating with distant space probes, it can take minutes to hours for a message to get from Earth to the spacecraft, or vice versa; the light seen from stars left them many years ago, allowing the study of the history of the universe by looking at distant objects. The finite speed of light limits the theoretical maximum speed of computers, since information must be sent within the computer from chip to chip; the speed of light can be used with time of flight measurements to measure large distances to high precision. Ole Rømer first demonstrated in 1676 that light travels at a finite speed by studying the apparent motion of Jupiter's moon Io.
In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, therefore travelled at the speed c appearing in his theory of electromagnetism. In 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame is a constant and is independent of the motion of the light source, he explored the consequences of that postulate by deriving the theory of relativity and in doing so showed that the parameter c had relevance outside of the context of light and electromagnetism. After centuries of precise measurements, in 1975 the speed of light was known to be 299792458 m/s with a measurement uncertainty of 4 parts per billion. In 1983, the metre was redefined in the International System of Units as the distance travelled by light in vacuum in 1/299792458 of a second; the speed of light in vacuum is denoted by a lowercase c, for "constant" or the Latin celeritas. In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant shown to equal √2 times the speed of light in vacuum.
The symbol V was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865. In 1894, Paul Drude redefined c with its modern meaning. Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c, which by had become the standard symbol for the speed of light. Sometimes c is used for the speed of waves in any material medium, c0 for the speed of light in vacuum; this subscripted notation, endorsed in official SI literature, has the same form as other related constants: namely, μ0 for the vacuum permeability or magnetic constant, ε0 for the vacuum permittivity or electric constant, Z0 for the impedance of free space. This article uses c for the speed of light in vacuum. Since 1983, the metre has been defined in the International System of Units as the distance light travels in vacuum in 1⁄299792458 of a second; this definition fixes the speed of light in vacuum at 299,792,458 m/s. As a dimensional physical constant, the numerical value of c is different for different unit systems.
In branches of physics in which c appears such as in relativity, it is common to use systems of natural units of measurement or the geometrized unit system where c = 1. Using these units, c does not appear explicitly because multiplication or division by 1 does not affect the result; the speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of the observer. This invariance of the speed of light was postulated by Einstein in 1905, after being motivated by Maxwell's theory of electromagnetism and the lack of evidence for the luminiferous aether, it is only possible to verify experimentally that the two-way speed of light is frame-independent, because it is impossible to measure the one-way speed of light without some convention as to how clocks at the source and at the detector should be synchronized. However
General relativity is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present; the relation is specified by the Einstein field equations, a system of partial differential equations. Some predictions of general relativity differ from those of classical physics concerning the passage of time, the geometry of space, the motion of bodies in free fall, the propagation of light. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational redshift of light, the gravitational time delay; the predictions of general relativity in relation to classical physics have been confirmed in all observations and experiments to date.
Although general relativity is not the only relativistic theory of gravity, it is the simplest theory, consistent with experimental data. However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity. Einstein's theory has important astrophysical implications. For example, it implies the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not light, can escape—as an end-state for massive stars. There is ample evidence that the intense radiation emitted by certain kinds of astronomical objects is due to black holes; the bending of light by gravity can lead to the phenomenon of gravitational lensing, in which multiple images of the same distant astronomical object are visible in the sky. General relativity predicts the existence of gravitational waves, which have since been observed directly by the physics collaboration LIGO.
In addition, general relativity is the basis of current cosmological models of a expanding universe. Acknowledged as a theory of extraordinary beauty, general relativity has been described as the most beautiful of all existing physical theories. Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his new relativistic framework. In 1907, beginning with a simple thought experiment involving an observer in free fall, he embarked on what would be an eight-year search for a relativistic theory of gravity. After numerous detours and false starts, his work culminated in the presentation to the Prussian Academy of Science in November 1915 of what are now known as the Einstein field equations; these equations specify how the geometry of space and time is influenced by whatever matter and radiation are present, form the core of Einstein's general theory of relativity. The Einstein field equations are nonlinear and difficult to solve.
Einstein used approximation methods in working out initial predictions of the theory. But as early as 1916, the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the Schwarzschild metric; this solution laid the groundwork for the description of the final stages of gravitational collapse, the objects known today as black holes. In the same year, the first steps towards generalizing Schwarzschild's solution to electrically charged objects were taken, which resulted in the Reissner–Nordström solution, now associated with electrically charged black holes. In 1917, Einstein applied his theory to the universe as a whole, initiating the field of relativistic cosmology. In line with contemporary thinking, he assumed a static universe, adding a new parameter to his original field equations—the cosmological constant—to match that observational presumption. By 1929, the work of Hubble and others had shown that our universe is expanding; this is described by the expanding cosmological solutions found by Friedmann in 1922, which do not require a cosmological constant.
Lemaître used these solutions to formulate the earliest version of the Big Bang models, in which our universe has evolved from an hot and dense earlier state. Einstein declared the cosmological constant the biggest blunder of his life. During that period, general relativity remained something of a curiosity among physical theories, it was superior to Newtonian gravity, being consistent with special relativity and accounting for several effects unexplained by the Newtonian theory. Einstein himself had shown in 1915 how his theory explained the anomalous perihelion advance of the planet Mercury without any arbitrary parameters. A 1919 expedition led by Eddington confirmed general relativity's prediction for the deflection of starlight by the Sun during the total solar eclipse of May 29, 1919, making Einstein famous, yet the theory entered the mainstream of theoretical physics and astrophysics only with the developments between 1960 and 1975, now known as the golden age of general relativity. Physicists began to understand the concept of a black hole, to identify quasars as one of these objects' astrophysical manifestations.
More precise solar system tests confirmed the theory's predictive power, relativistic cosmology, became amenable to direct observational tests. Over the years, general relativity has acqui
Paul Adrien Maurice Dirac was an English theoretical physicist, regarded as one of the most significant physicists of the 20th century. Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. Among other discoveries, he formulated the Dirac equation which describes the behaviour of fermions and predicted the existence of antimatter. Dirac shared the 1933 Nobel Prize in Physics with Erwin Schrödinger "for the discovery of new productive forms of atomic theory", he made significant contributions to the reconciliation of general relativity with quantum mechanics. Dirac was regarded by his colleagues as unusual in character. In a 1926 letter to Paul Ehrenfest, Albert Einstein wrote of Dirac, "This balancing on the dizzying path between genius and madness is awful", he was the Lucasian Professor of Mathematics at the University of Cambridge, a member of the Center for Theoretical Studies, University of Miami, spent the last decade of his life at Florida State University.
Paul Adrien Maurice Dirac was born at his parents' home in Bristol, England, on 8 August 1902, grew up in the Bishopston area of the city. His father, Charles Adrien Ladislas Dirac, was an immigrant from Saint-Maurice, who worked in Bristol as a French teacher, his mother, Florence Hannah Dirac, née Holten, the daughter of a ship's captain, was born in Cornwall and worked as a librarian at the Bristol Central Library. Paul had a younger sister, Béatrice Isabelle Marguerite, known as Betty, an older brother, Reginald Charles Félix, known as Felix, who committed suicide in March 1925. Dirac recalled: "My parents were distressed. I didn't know they cared so much I never knew that parents were supposed to care for their children, but from on I knew."Charles and the children were Swiss nationals until they became naturalised on 22 October 1919. Dirac's father was authoritarian, although he disapproved of corporal punishment. Dirac had a strained relationship with his father, so much so that after his father's death, Dirac wrote, "I feel much freer now, I am my own man."
Charles forced his children to speak to him only in French. When Dirac found that he could not express what he wanted to say in French, he chose to remain silent. Dirac was educated first at Bishop Road Primary School and at the all-boys Merchant Venturers' Technical College, where his father was a French teacher; the school was an institution attached to the University of Bristol. It emphasised technical subjects like bricklaying and metal work, modern languages; this was unusual at a time when secondary education in Britain was still dedicated to the classics, something for which Dirac would express his gratitude. Dirac studied electrical engineering on a City of Bristol University Scholarship at the University of Bristol's engineering faculty, co-located with the Merchant Venturers' Technical College. Shortly before he completed his degree in 1921, he sat the entrance examination for St John's College, Cambridge, he passed and was awarded a £70 scholarship, but this fell short of the amount of money required to live and study at Cambridge.
Despite his having graduated with a first class honours Bachelor of Science degree in engineering, the economic climate of the post-war depression was such that he was unable to find work as an engineer. Instead, he took up an offer to study for a Bachelor of Arts degree in mathematics at the University of Bristol free of charge, he was permitted to skip the first year of the course owing to his engineering degree. In 1923, Dirac graduated, once again with first class honours, received a £140 scholarship from the Department of Scientific and Industrial Research. Along with his £70 scholarship from St John's College, this was enough to live at Cambridge. There, Dirac pursued his interests in the theory of general relativity, an interest he had gained earlier as a student in Bristol, in the nascent field of quantum physics, under the supervision of Ralph Fowler. From 1925 to 1928 he held an 1851 Research Fellowship from the Royal Commission for the Exhibition of 1851, he completed his PhD in June 1926 with the first thesis on quantum mechanics to be submitted anywhere.
He continued his research in Copenhagen and Göttingen. Dirac married Margit Wigner, in 1937, he adopted Margit's two children and Gabriel. Paul and Margit Dirac had two children together, Mary Elizabeth and Florence Monica. Margit, known as Manci, visited her brother in 1934 in Princeton, New Jersey, from her native Hungary and, while at dinner at the Annex Restaurant met the "lonely-looking man at the next table." This account from a Korean physicist, Y. S. Kim, who met and was influenced by Dirac says: "It is quite fortunate for the physics community that Manci took good care of our respected Paul A. M. Dirac. Dirac published eleven papers during the period 1939–46.... Dirac was able to maintain his normal research productivity only because Manci was in charge of everything else." Dirac was known among his colleagues for his taciturn nature. His colleagues in Cambridge jokingly defined a unit called a "dirac", one word per hour; when Niels Bohr complained that he did not know how to finish a sentence in a scientific article he was writing, Dirac replied, "I was taught at school never to start a sentence without knowing the end of it."
He criticised the physicist J. Robert Oppenheimer's interest in poetry: "The aim of science is to make difficult things understandable in a simpler way.
Radiation pressure is the pressure exerted upon any surface due to the exchange of momentum between the object and the electromagnetic field. This includes the momentum of light or electromagnetic radiation of any wavelength, absorbed, reflected, or otherwise emitted by matter on any scale; the forces generated by radiation pressure are too small to be noticed under everyday circumstances. This includes objects in outer space where it is the main force acting on objects besides gravity, where the net effect of a tiny force may have a large cumulative effect over long periods of time. For example, had the effects of the sun's radiation pressure on the spacecraft of the Viking program been ignored, the spacecraft would have missed Mars orbit by about 15,000 km. Radiation pressure from starlight is crucial in a number of astrophysical processes as well; the significance of radiation pressure increases at high temperatures, can sometimes dwarf the usual gas pressure, for instance in stellar interiors and thermonuclear weapons.
Radiation pressure can well be accounted for by considering the momentum of a classical electromagnetic field or in terms of the momenta of photons, particles of light. The interaction of electromagnetic waves or photons with matter may involve an exchange of momentum. Due to the law of conservation of momentum, any change in the total momentum of the waves or photons must involve an equal and opposite change in the momentum of the matter it interacted with, as is illustrated in the accompanying figure for the case of light being reflected by a surface; this transfer of momentum is the general explanation. Johannes Kepler put forward the concept of radiation pressure back in 1619 to explain the observation that a tail of a comet always points away from the Sun; the assertion that light, as electromagnetic radiation, has the property of momentum and thus exerts a pressure upon any surface it is exposed to was published by James Clerk Maxwell in 1862, proven experimentally by Russian physicist Pyotr Lebedev in 1900 and by Ernest Fox Nichols and Gordon Ferrie Hull in 1901.
The pressure is feeble, but can be detected by allowing the radiation to fall upon a delicately poised vane of reflective metal in a Nichols radiometer. Radiation pressure can be viewed as a consequence of the conservation of momentum given the momentum attributed to electromagnetic radiation; that momentum can be well calculated on the basis of electromagnetic theory or from the combined momenta of a stream of photons, giving identical results as is shown below. According to Maxwell's theory of electromagnetism, an electromagnetic wave carries momentum, which will be transferred to an opaque surface it strikes; the energy flux of a plane wave is calculated using the Poynting vector S = E × H, whose magnitude we denote by S. S divided by the speed of light is the density of the linear momentum per unit area of the electromagnetic field. So, the Poynting vector is S===Δx/area, the speed of light, c=Δx/Δt, times pressure, ΔF/area; that pressure is experienced as radiation pressure on the surface: P incident = ⟨ S ⟩ c = I f c where P is pressure, I f is the incident irradiance and c is the speed of light in vacuum.
If the surface is planar at an angle α to the incident wave, the intensity across the surface will be geometrically reduced by the cosine of that angle and the component of the radiation force against the surface will be reduced by the cosine of α, resulting in a pressure: P incident = I f c cos 2 α The momentum from the incident wave is in the same direction of that wave. But only the component of that momentum normal to the surface contributes to the pressure on the surface, as given above; the component of that force tangent to the surface is not called pressure. The above treatment for an incident wave accounts for the radiation pressure experienced by a black body. If the wave is specularly reflected the recoil due to the reflected wave will further contribute to the radiation pressure. In the case of a perfect reflector, this pressure will be identical to the pressure caused by the incident wave: P emitted = I f c thus doubling the net radiation pressure on the surface: P net = P incident + P emitted = 2 I f c For a reflective surface, the second term
In physics, in particular as measured by radiometry, radiant energy is the energy of electromagnetic and gravitational radiation. As energy, its SI unit is the joule; the quantity of radiant energy may be calculated by integrating radiant flux with respect to time. The symbol Qe is used throughout literature to denote radiant energy. In branches of physics other than radiometry, electromagnetic energy is referred to using E or W; the term is used when electromagnetic radiation is emitted by a source into the surrounding environment. This radiation may be invisible to the human eye; the term "radiant energy" is most used in the fields of radiometry, solar energy and lighting, but is sometimes used in other fields. In modern applications involving transmission of power from one location to another, "radiant energy" is sometimes used to refer to the electromagnetic waves themselves, rather than their energy. In the past, the term "electro-radiant energy" has been used; the term "radiant energy" applies to gravitational radiation.
For example, the first gravitational waves observed were produced by a black hole collision that emitted about 5.3×1047 joules of gravitational-wave energy. Because electromagnetic radiation can be conceptualized as a stream of photons, radiant energy can be viewed as photon energy – the energy carried by these photons. Alternatively, EM radiation can be viewed as an electromagnetic wave, which carries energy in its oscillating electric and magnetic fields; these two views are equivalent and are reconciled to one another in quantum field theory. EM radiation can have various frequencies; the bands of frequency present in a given EM signal may be defined, as is seen in atomic spectra, or may be broad, as in blackbody radiation. In the photon picture, the energy carried by each photon is proportional to its frequency. In the wave picture, the energy of a monochromatic wave is proportional to its intensity; this implies that if two EM waves have the same intensity, but different frequencies, the one with the higher frequency "contains" fewer photons, since each photon is more energetic.
When EM waves are absorbed by an object, the energy of the waves is converted to heat. This is a familiar effect, since sunlight warms surfaces that it irradiates; this phenomenon is associated with infrared radiation, but any kind of electromagnetic radiation will warm an object that absorbs it. EM waves can be reflected or scattered, in which case their energy is redirected or redistributed as well. Radiant energy is one of the mechanisms by which energy can leave an open system; such a system can be man-made, such as a solar energy collector, or natural, such as the Earth's atmosphere. In geophysics, most atmospheric gases, including the greenhouse gases, allow the Sun's short-wavelength radiant energy to pass through to the Earth's surface, heating the ground and oceans; the absorbed solar energy is re-emitted as longer wavelength radiation, some of, absorbed by the atmospheric greenhouse gases. Radiant energy is produced in the sun as a result of nuclear fusion. Radiant energy is used for radiant heating.
It can be generated electrically by infrared lamps, or can be absorbed from sunlight and used to heat water. The heat energy is emitted from a warm element and warms people and other objects in rooms rather than directly heating the air; because of this, the air temperature may be lower than in a conventionally heated building though the room appears just as comfortable. Various other applications of radiant energy have been devised; these include treatment and inspection and sorting, medium of control, medium of communication. Many of these applications involve a source of radiant energy and a detector that responds to that radiation and provides a signal representing some characteristic of the radiation. Radiant energy detectors produce responses to incident radiant energy either as an increase or decrease in electric potential or current flow or some other perceivable change, such as exposure of photographic film
Quantum field theory
In theoretical physics, quantum field theory is a theoretical framework that combines classical field theory, special relativity, quantum mechanics and is used to construct physical models of subatomic particles and quasiparticles. QFT treats particles as excited states of their underlying fields, which are—in a sense—more fundamental than the basic particles. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding fields; each interaction can be visually represented by Feynman diagrams, which are formal computational tools, in the process of relativistic perturbation theory. As a successful theoretical framework today, quantum field theory emerged from the work of generations of theoretical physicists spanning much of the 20th century, its development began in the 1920s with the description of interactions between light and electrons, culminating in the first quantum field theory — quantum electrodynamics. A major theoretical obstacle soon followed with the appearance and persistence of various infinities in perturbative calculations, a problem only resolved in the 1950s with the invention of the renormalization procedure.
A second major barrier came with QFT's apparent inability to describe the weak and strong interactions, to the point where some theorists called for the abandonment of the field theoretic approach. The development of gauge theory and the completion of the Standard Model in the 1970s led to a renaissance of quantum field theory. Quantum field theory is the result of the combination of classical field theory, quantum mechanics, special relativity. A brief overview of these theoretical precursors is in order; the earliest successful classical field theory is one that emerged from Newton's law of universal gravitation, despite the complete absence of the concept of fields from his 1687 treatise Philosophiæ Naturalis Principia Mathematica. The force of gravity as described by Newton is an "action at a distance" — its effects on faraway objects are instantaneous, no matter the distance. In an exchange of letters with Richard Bentley, Newton stated that "it is inconceivable that inanimate brute matter should, without the mediation of something else, not material, operate upon and affect other matter without mutual contact."
It was not until the 18th century that mathematical physicists discovered a convenient description of gravity based on fields — a numerical quantity assigned to every point in space indicating the action of gravity on any particle at that point. However, this was considered a mathematical trick. Fields began to take on an existence of their own with the development of electromagnetism in the 19th century. Michael Faraday coined the English term "field" in 1845, he introduced fields as properties of space having physical effects. He argued against "action at a distance", proposed that interactions between objects occur via space-filling "lines of force"; this description of fields remains to this day. The theory of classical electromagnetism was completed in 1862 with Maxwell's equations, which described the relationship between the electric field, the magnetic field, electric current, electric charge. Maxwell's equations implied the existence of electromagnetic waves, a phenomenon whereby electric and magnetic fields propagate from one spatial point to another at a finite speed, which turns out to be the speed of light.
Action-at-a-distance was thus conclusively refuted. Despite the enormous success of classical electromagnetism, it was unable to account for the discrete lines in atomic spectra, nor for the distribution of blackbody radiation in different wavelengths. Max Planck's study of blackbody radiation marked the beginning of quantum mechanics, he treated atoms, which absorb and emit electromagnetic radiation, as tiny oscillators with the crucial property that their energies can only take on a series of discrete, rather than continuous, values. These are known as quantum harmonic oscillators; this process of restricting energies to discrete values is called quantization. Building on this idea, Albert Einstein proposed in 1905 an explanation for the photoelectric effect, that light is composed of individual packets of energy called photons; this implied that the electromagnetic radiation, while being waves in the classical electromagnetic field exists in the form of particles. In 1913, Niels Bohr introduced the Bohr model of atomic structure, wherein electrons within atoms can only take on a series of discrete, rather than continuous, energies.
This is another example of quantization. The Bohr model explained the discrete nature of atomic spectral lines. In 1924, Louis de Broglie proposed the hypothesis of wave-particle duality, that microscopic particles exhibit both wave-like and particle-like properties under different circumstances. Uniting these scattered ideas, a coherent discipline, quantum mechanics, was formulated between 1925 and 1926, with important contributions from de Broglie, Werner Heisenberg, Max Born, Erwin Schrödinger, Paul Dirac, Wolfgang Pauli.:22-23In the same year as his paper on the photoelectric effect, Einstein published his theory of special relativity, built on Maxwell's electromagnetism. New rules, called Lorentz transformation, were given for the way time and space coordinates of an event change under changes in the observer's velocity, the distinction between time and space was blurred.:19 It was proposed that all physical laws must be the same for observers at different velocities, i.e. that physical laws be invariant under Lorentz transformations.
Two difficulties remained. Observationally, the Schrödinger equation underlying q
In physics, special relativity is the 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. Special relativity was proposed by Albert Einstein in a paper published 26 September 1905 titled "On the Electrodynamics of Moving Bodies"; the inconsistency of Newtonian mechanics with Maxwell's equations of electromagnetism and the lack of experimental confirmation for a hypothesized luminiferous aether led to the development of special relativity, which corrects mechanics to handle situations involving all motions and those at a significant fraction of the speed of light. Today, special relativity is the most accurate model of motion at any speed when gravitational effects are negligible. So, the Newtonian mechanics model is still valid as a simple and high accuracy approximation at low velocities relative to the speed of light.
Special relativity implies a wide range of consequences, which have been experimentally verified, including length contraction, time dilation, relativistic mass, mass–energy equivalence, a universal speed limit, the speed of causality and relativity of simultaneity. It has replaced the conventional notion of an absolute universal time with the notion of a time, dependent on reference frame and spatial position. Rather than an invariant time interval between two events, there is an invariant spacetime interval. Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass–energy equivalence formula E = mc2, where c is the speed of light in a vacuum. 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 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. Not until Einstein developed general relativity, introducing a curved spacetime to incorporate gravity, was the phrase "special relativity" employed. A translation, used is "restricted relativity"; the theory is "special" in that it only applies in the special case where the spacetime is flat, i.e. the curvature of spacetime, described by the energy-momentum tensor and causing gravity, is negligible. In order to accommodate gravity, Einstein formulated general relativity in 1915. Special relativity, contrary to some outdated descriptions, is capable of handling accelerations as well as accelerated frames of reference; as Galilean relativity is now accepted to be an approximation of special relativity, valid for low speeds, special relativity is considered an approximation of general relativity, valid for weak gravitational fields, i.e. at a sufficiently small scale and in conditions of free fall. Whereas general relativity incorporates noneuclidean geometry in order to represent gravitational effects as the geometric curvature of spacetime, special relativity is restricted to the flat spacetime known as Minkowski space.
As long as the universe can be modeled as a pseudo-Riemannian manifold, a Lorentz-invariant frame that abides by special relativity can be defined for a sufficiently small neighborhood of each point in this curved spacetime. Galileo Galilei had postulated that there is no absolute and well-defined state of rest, a principle now called Galileo's principle of relativity. Einstein extended this principle so that it accounted for the constant speed of light, a phenomenon, observed in the Michelson–Morley experiment, he postulated that it holds for all the laws of physics, including both the laws of mechanics and of electrodynamics. Einstein discerned two fundamental propositions that seemed to be the most assured, regardless of the exact validity of the known laws of either mechanics or electrodynamics; these propositions were the constancy of the speed of light in a vacuum and the independence of physical laws from the choice of inertial system. In his initial presentation of special relativity in 1905 he expressed these postulates as: The Principle of Relativity – the laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems in uniform translatory motion relative to each other.
The Principle of Invariant Light Speed – "... light is always propagated in empty space with a definite velocity c, independent of the state of motion of the emitting body". That is, light in vacuum propagates with the speed c in at least one system of inertial coordinates, regardless of the state of motion of the light source; the constancy of the speed of light was motivated by Maxwell's theory of electromagnetism and the lack of evidence for the luminiferous ether. There is conflicting evidence on the extent to which Einstein was influenced by the null result of the Michelson–Morley experiment. In any case, the null result of the Michelson–Morley experiment helped the notion of the constancy of the speed of light gain widespread and rapid acce