when was einstein's theory of general relativity published
Relativity priority dispute


, and "Einstein and Minkowski" on the other side. Whittaker (1954) stated that David Hilbert had derived the theory of General Relativity from an elegant variational principle "almost simultaneously" with Einstein's discovery of the theory. From Fölsing's 1993 (English translation 1998) Einstein biography " Hilbert, like all his other colleagues, acknowledged Einstein as the sole creator of relativity theory." In 1997, Cory, Renn and Stachel published a 3-page article in "Science" entitled "Belated Decision in the Hilbert-Einstein
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Marcel Grossmann


differential calculus, started by Christoffel and fully developed by Ricci-Curbastro and Levi-Civita. Grossmann facilitated Einstein's unique synthesis of mathematical and theoretical physics in what is still today considered the most elegant and powerful theory of gravity: the general theory of relativity. The collaboration of Einstein and Grossmann led to a ground-breaking paper: "Outline of a Generalized Theory of Relativity and of a Theory of Gravitation", which was published in 1913 and was one of the two fundamental papers which established Einstein's theory of gravity
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General relativity


General relativity (GR, also known as the general theory of relativity or GTR) 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 refines 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 "" is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field
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Special relativity


In physics, special relativity (also known as the special theory of relativity) is the generally accepted and experimentally confirmed physical theory regarding the relationship between space and time. In Albert Einstein's original pedagogical treatment, it is based on two postulates: Some of the work of Albert Einstein in special relativity is built on the earlier work by Hendrik Lorentz. Special relativity was originally proposed by Albert Einstein in a paper published on 26 September 1905 titled "On the Electrodynamics of Moving Bodies". The inconsistency of Newtonian mechanics with Maxwell
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Moshe Carmeli


theory called cosmological general relativity. He took Einstein's theory of general relativity and extended it into five dimensions, adding the radial velocity of galaxies expanding in the Hubble flow as the fifth dimension. This fifth dimension is known as "space-velocity". He published his initial special relativistic version of the theory in 1997 in his book "Cosmological Special Relativity: The Large-Scale Structure of Space, Time, and Velocity". He then developed the complete general relativistic theory called cosmological general relativity, publishing several papers on
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Criticism of the theory of relativity


had earlier published several of the core elements of Einstein's 1905 relativity paper, including a generalized relativity principle that was intended by Poincaré to apply to all physics. Some examples: Some contemporary historians of science have revived the question as to whether Einstein was possibly influenced by the ideas of Poincaré, who first stated the relativity principle and applied it to electrodynamics, developing interpretations and modifications of Lorentz's electron theory that appear to have anticipated what is now called special relativity. Another discussion concerns a possible mutual influence between Einstein and David
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Peter Bergmann


published the first textbook on general relativity, "Introduction to the Theory of Relativity", with a foreword by Einstein. The second edition of this book was published by Dover Publications in 1976. His other textbooks were: He also co-wrote "Albert Einstein: His Influence on Physics, Philosophy and Politics", together with Peter C. Aichelburg and Roman Ulrich Sexl (Vieweg, 1979). When Edward P. Tryon came out in 1973 with a paper in "Nature" titled "Is the Universe a Vacuum Fluctuation?
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Einstein–Cartan theory


In theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory, is a classical theory of gravitation similar to general relativity. The theory was first proposed by Élie Cartan in 1922 and expounded in the following few years. Einstein-Cartan theory differs from general relativity in two ways: (1) it is formulated within the framework of Riemann-Cartan geometry, which possesses a locally gauged Lorentz symmetry, while general relativity is formulated within the framework of Riemannian geometry, which
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Physical cosmology


particle physics experiments and theory, theoretical and observational astrophysics, general relativity, quantum mechanics, and plasma physics. Modern cosmology developed along tandem tracks of theory and observation. In 1916, Albert Einstein published his theory of general relativity, which provided a unified description of gravity as a geometric property of space and time. At the time, Einstein believed in a static universe, but found that his original formulation of the theory did not permit it. This is because masses distributed throughout the universe gravitationally attract, and move toward each
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John D. Norton


Einstein and the philosophy of science. He has published on general relativity, special relativity, the relationship between thermodynamics and information processing, quantum physics, and the genesis of scientific theories. He is well-known for his analysis of Einstein's "Zurich Notebook," a small, brown notebook which contains Einstein's private day-to-day calculations during a critical period (1912–1913) in his development of general relativity. The trio of Einstein scholars, John Norton, John Stachel, and John Earman, have sometimes been
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Introduction to the mathematics of general relativity


, just as mass density is the source of such a field in Newtonian gravity. The Einstein field equations (EFE) or Einstein's equations are a set of 10 equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy. First published by Einstein in 1915 as a tensor equation, the EFE equate local spacetime curvature (expressed by the Einstein tensor) with the local energy and momentum within that spacetime (expressed by the stress–energy
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Theory of everything


quantum) electrical forces, justifying Dirac's boast that "the underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known". After 1915, when Albert Einstein published the theory of gravity (general relativity), the search for a unified field theory combining gravity with electromagnetism began with a renewed interest. In Einstein's day, the strong and the weak forces had not yet been discovered, yet, he found the potential existence of two other distinct forces -gravity
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Relativity: The Special and the General Theory


Relativity: The Special and the General Theory began as a short paper and was eventually published as a book written by Albert Einstein with the aim of giving: It was first published in German in 1916 and later translated into English in 1920. It is divided into 3 parts, the first dealing with special relativity, the second dealing with general relativity and the third dealing with considerations on the universe as a whole. There have been many versions published since the original in 1916, the latest in December, 2011. The work
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Theory of relativity


and others did subsequent work. Einstein developed general relativity between 1907 and 1915, with contributions by many others after 1915. The final form of general relativity was published in 1916. The term "theory of relativity" was based on the expression "relative theory" () used in 1906 by Planck, who emphasized how the theory uses the principle of relativity. In the discussion section of the same paper, Alfred Bucherer used for the first time the expression "theory of relativity" (). By the 1920s, the
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Numerical relativity


differential equations, and geometry among other mathematical areas of specialization. Albert Einstein published his theory of general relativity in 1915. It, like his earlier theory of special relativity, described space and time as a unified spacetime subject to what are now known as the Einstein field equations. These form a set of coupled nonlinear partial differential equations (PDEs). After more than 100 years since the first publication of the theory, relatively few closed-form solutions are known for the field equations, and, of those, most are
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Walk of Ideas


the most well-known equation in physics: E=mc². It belongs to the revolutionizing papers of Albert Einstein concerning the Theory of Relativity. In 1905, his paper "Zur Elektrodynamik bewegter Körper" ("The electrodynamics of objects in motion") established the Special Theory of Relativity, which revolutionized the understanding of space and time. In 1915, he published the General Theory of Relativity, in which the curvature of spacetime brings about gravity. Nowadays, Albert Einstein is seen by many as the epitome of a scientist
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Einstein–Cartan–Evans theory


't Hooft, published an editorial note effectively retracting the journal's support for the hypothesis. Earlier versions of the theory were called "O(3) electrodynamics". Evans claims that he is able to derive a generally covariant field equation for electromagnetism and gravity, similar to that derived by Mendel Sachs. Evans argues that Einstein's theory of general relativity does not take into account torsion, which is included in the Einstein–Cartan theory. In 1998 Evans founded the Alpha Institute for Advanced Studies (AIAS) to keep developing his
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History of special relativity


frames of reference can still be formulated. So contrary to those "scalar theories", Einstein (1911–1915) developed a "tensor theory" (i.e. general relativity), which fulfills both the equivalence principle and general covariance. As a consequence, the notion of a complete "special relativistic" theory of gravitation had to be given up, as in general relativity the constancy of light speed (and Lorentz covariance) is only locally valid. The decision between those models was brought about by Einstein, when he was able to
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History of special relativity


He described Einstein's theory as a "generalization" of Lorentz's theory and, to this "Lorentz-Einstein-Theory", he gave the name "relative theory"; while Alfred Bucherer changed Planck's nomenclature into the now common "theory of relativity" (""Einsteinsche Relativitätstheorie""). On the other hand, Einstein himself and many others continued to refer simply to the new method as the "relativity principle". And in an important overview article on the relativity principle (1908a), Einstein
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The Einstein Theory of Relativity


The Einstein Theory of Relativity (1923) is a silent short film directed by Dave Fleischer and released by Fleischer Studios. In August 1922, "Scientific American" published an article explaining their position that a silent film would be unsuccessful in presenting the theory of relativity to the general public, arguing that only as part of a broader educational package including lecture and text would such film be successful. "Scientific American" then went on to review frames from an unnamed German film reported to be financially successful. Six months later,
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Albert Einstein


Minkowski reinterpreted special relativity in geometric terms as a theory of spacetime. Einstein adopted Minkowski's formalism in his 1915 general theory of relativity. General relativity (GR) is a theory of gravitation that was developed by Einstein between 1907 and 1915. According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses. General relativity has developed into an essential tool in modern astrophysics. It provides the foundation for the current understanding of black holes, regions of space where gravitational attraction is
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Tests of general relativity


times as massive as the sun. Einstein's theory suggested that large objects bend the space around them, causing other objects to diverge from the straight lines they would otherwise follow. Although previous studies have validated Einstein's theory, this was the first time his theory had been tested on such a gigantic object. The findings were published in "The Astrophysical Journal". Astronomers using the Hubble Space Telescope and the Very Large Telescope has made the precise test of general relativity on galactic scale. The nearby galaxy ESO 325-G004 acts as
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Cosmological constant


cosmological constant. However, soon after Einstein developed his static theory, observations by Edwin Hubble indicated that the universe appears to be expanding; this was consistent with a cosmological solution to the "original" general relativity equations that had been found by the mathematician Friedmann, working on the Einstein equations of general relativity. Einstein reportedly referred to his failure to accept the validation of his equations—when they had predicted the expansion of the universe in theory, before it was demonstrated in observation of the cosmological redshift—as his "biggest
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Variational methods in general relativity


Variational methods in general relativity refers to various mathematical techniques that employ the use of variational calculus in Einstein's theory of general relativity. The most commonly used tools are Lagrangians and Hamiltonians and are used to derive the Einstein field equations. The equations of motion in physical theories can often be derived from an object called the Lagrangian. In classical mechanics, this object is usually of the form, 'kinetic energy − potential energy'. In general, the Lagrangian is that function which when integrated over produces the Action functional. David
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Alfred Bucherer


Bucherer (1906) was the first who used — during some critical remarks on Einstein's theory — the expression "Einsteinian relativity theory / theory of relativity" ("Einsteinsche Relativitätstheorie"). This was based on Max Planck's term "relative theory" for the Lorentz-Einstein theory. And in 1908 Bucherer himself rejected his own version of the relativity principle, and accepted the "Lorentz-Einstein theory". Later (1923, 1924), Bucherer criticized general relativity in some papers. However, this criticism was
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Negative mass


proposed a "dark fluid" theory, related, in part, to notions of gravitationally repulsive negative masses, presented earlier by Albert Einstein, that may help better understand, in a testable manner, the considerable amounts of unknown dark matter and dark energy in the cosmos. First some background. When Einstein published his general theory of relativity in 1916, it immediately piqued the interest of the German physicist, Karl Schwarzschild. He studied the mathematics and soon discovered the first exact solution of the equations other than the trivial one of
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Anti-gravity


Astronomie and Zur allgemeinen Relativitätstheorie, both published 1915. Einstein, both independently, and with Walther Mayer, attempted to unify Einstein's theory of gravity, the general theory of relativity, with electromagnetism, using the work of Theodor Kaluza (published 1921 ), and James Clerk Maxwell, in an attempt to include gravity with quantum field theory. Theoretical quantum physicists have postulated the existence of a quantum gravity particle, the graviton. Various theoretical explanations of the reality of quantum gravity include the Superstring theory (Gabriele Veneziano 1968, et
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Tests of general relativity


in the cities of Sobral, Ceará, Brazil and in São Tomé and Príncipe on the west coast of Africa. The result was considered spectacular news and made the front page of most major newspapers. It made Einstein and his theory of general relativity world-famous. When asked by his assistant what his reaction would have been if general relativity had not been confirmed by Eddington and Dyson in 1919, Einstein famously made the quip: "Then I would feel sorry for the dear Lord. The theory is correct anyway."
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History of loop quantum gravity


The history of loop quantum gravity spans more than three decades of intense research. General relativity is the theory of gravitation published by Albert Einstein in 1915. According to it, the force of gravity is a manifestation of the local geometry of spacetime. Mathematically, the theory is modelled after Bernhard Riemann's metric geometry, but the Lorentz group of spacetime symmetries (an essential ingredient of Einstein's own theory of special relativity) replaces the group of rotational symmetries of space. (Later, loop quantum gravity inherited this geometric interpretation of
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Age of the universe


, then everything inside would be at the same temperature, and thus there would be no stars and no life. No scientific explanation for this contradiction was put forth at the time. In 1915 Albert Einstein published the theory of general relativity and in 1917 constructed the first cosmological model based on his theory. In order to remain consistent with a steady state universe, Einstein added what was later called a cosmological constant to his equations. However, already in 1922, also using Einstein's theory, Alexander Friedmann, and independently five
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Classical field theory


gravitation was found to be inconsistent with special relativity, Albert Einstein formulated a new theory of gravitation called general relativity. This treats gravitation as a geometric phenomenon ('curved spacetime') caused by masses and represents the gravitational field mathematically by a tensor field called the metric tensor. The Einstein field equations describe how this curvature is produced. Newtonian gravitation is now superseded by Einstein's theory of general relativity, in which gravitation is thought of as being due to a curved spacetime, caused by masses. The Einstein field equation describes
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Gravitational lens


passing close to the Sun was slightly bent, so that stars appeared slightly out of position. The result was considered spectacular news and made the front page of most major newspapers. It made Einstein and his theory of general relativity world-famous. When asked by his assistant what his reaction would have been if general relativity had not been confirmed by Eddington and Dyson in 1919, Einstein said "Then I would feel sorry for the dear Lord. The theory is correct anyway." In 1912, Einstein had speculated that an
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Introduction to general relativity


were observed, and these were accounted for in the general theory of relativity. Similarly, the predictions of general relativity must also be checked with experiment, and Einstein himself devised three tests now known as the classical tests of the theory: Of these tests, only the perihelion advance of Mercury was known prior to Einstein's final publication of general relativity in 1916. The subsequent experimental confirmation of his other predictions, especially the first measurements of the deflection of light by the sun in 1919, catapulted Einstein to international stardom. These
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Lorentz ether theory


a theory of gravitation were superseded by Einstein's theory of general relativity. This theory is based on principles like the equivalence principle, the general principle of relativity, the principle of general covariance, geodesic motion, local Lorentz covariance (the laws of special relativity apply locally for all inertial observers), and that spacetime curvature is created by stress-energy within the spacetime. In 1920 Einstein compared Lorentz's ether with the "gravitational ether" of general relativity. He said that immobility is the only mechanical property of which the
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General Relativity (book)


General Relativity is a textbook on Einstein's general theory of relativity written by the gravitational physicist Robert Wald. Published by the University of Chicago in 1984, the book, a tome of almost 500 pages, covers many aspects of the general theory of relativity. It is divided into two parts. Part I covers the fundamentals of the subject and Part II the more advanced topics such as causal structure, and quantum effects. It is aimed at beginning graduate students. The book uses the abstract index notation for tensors. It treats
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Einstein aether theory


In physics the Einstein æther theory, also called æ-theory, is a generally covariant modification of general relativity which describes a spacetime endowed with both a metric and a unit timelike vector field named the æther. The theory has a preferred reference frame and hence violates Lorentz invariance. Einstein-æther theories were popularized by Maurizio Gasperini in a series of papers, such as "Singularity Prevention and Broken Lorentz Symmetry" in the 1980s. In addition to the metric of general relativity these theories also included a scalar field which intuitively corresponded
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General relativity


collaboration LIGO. In addition, general relativity is the basis of current cosmological models of a consistently expanding universe. Widely acknowledged as a theory of extraordinary beauty, general relativity has often 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
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Initial value formulation (general relativity)


The initial value formulation of general relativity is a reformulation of Albert Einstein's theory of general relativity that describes a universe evolving over time. Each solution of the Einstein field equations encompasses the whole history of a universe – it is not just some snapshot of how things are, but a whole spacetime: a statement encompassing the state of matter and geometry everywhere and at every moment in that particular universe. By this token, Einstein's theory appears to be different from most other physical theories, which specify evolution equations for physical systems
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Philipp Lenard


's constant, "h". This was shown to be the case some years later. The photo-electric quantum theory was the work cited when Einstein was awarded the Nobel Prize in Physics. Suspicious of the general adulation of Einstein, Lenard became a prominent skeptic of relativity and of Einstein's theories generally; he did not, however, dispute Einstein's explanation of the photoelectric effect. Lenard received the 1905 Nobel Prize for Physics in recognition of this work. Lenard was the first person to study what has been termed
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Gravitational redshift


a simple consequence of Einstein's equivalence principle ("all bodies fall with the same acceleration, independent of their composition") and was found by Einstein eight years before the full theory of relativity. Observing the gravitational redshift in the solar system is one of the classical tests of general relativity. Gravitational redshifts are an important effect in satellite-based navigation systems such as GPS. If the effects of general relativity were not taken into account, such systems would not work at all. Einstein's theory of general relativity incorporates the
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Albert Einstein


gravitational waves came in the 1970s through observation of a pair of closely orbiting neutron stars, PSR B1913+16. The explanation of the decay in their orbital period was that they were emitting gravitational waves. Einstein's prediction was confirmed on 11 February 2016, when researchers at LIGO published the first observation of gravitational waves, detected on Earth on 14 September 2015, exactly one hundred years after the prediction. While developing general relativity, Einstein became confused about the gauge invariance in the theory. He formulated an argument that led him
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Ernst Mach


Mach are attributed a number of principles that distill his ideal of physical theorisation—what is now called "Machian physics": The last is singled out, particularly by Albert Einstein, as "the" Mach's principle. Einstein cited it as one of the three principles underlying general relativity. In 1930, he stated that "it is justified to consider Mach as the precursor of the general theory of relativity", though Mach, before his death, would apparently reject Einstein's theory. Einstein was aware that his theories
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Classical unified field theories


with Einstein and Einstein's aide Grommer it was determined that this theory did not admit a non-singular, static, spherically symmetric solution. This theory did have some influence on Einstein's later work and was further developed later by Klein in an attempt to incorporate relativity into quantum theory, in what is now known as Kaluza–Klein theory. Sir Arthur Stanley Eddington was a noted astronomer who became an enthusiastic and influential promoter of Einstein's general theory of relativity. He was among the first to propose an extension of the
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Lovelock theory of gravity


In theoretical physics, Lovelock's theory of gravity (often referred to as Lovelock gravity) is a generalization of Einstein's theory of general relativity introduced by David Lovelock in 1971. It is the most general metric theory of gravity yielding conserved second order equations of motion in arbitrary number of spacetime dimensions "D". In this sense, Lovelock's theory is the natural generalization of Einstein's General Relativity to higher dimensions. In three and four dimensions ("D" = 3, 4), Lovelock's theory coincides with
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Einstein field equations


The Einstein field equations (EFE; also known as Einstein's equations) comprise the set of 10 equations in Albert Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy. First published by Einstein in 1915 as a tensor equation, the EFE relate local "" (expressed by the Einstein tensor) with the local energy and momentum within that spacetime (expressed by the stress–energy tensor). Similar to the way that electromagnetic fields are determined using
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Gunnar Nordström


of the era, including Niels Bohr and Albert Einstein. For example, it was Bohr's contributions that helped Nordström to circumvent the Russian censorship of German post to Finland, Finland was at the time a grand duchy of the Russian empire. The theory for which Nordström was arguably most famous in his own lifetime, his theory of gravitation, was for a long time considered as a competitor to Einstein's theory of general relativity which was published in 1915, after Nordström's theory. In 1914 Nordström introduced an additional space dimension
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Friedwardt Winterberg


pointed out shortcomings of Einstein's general theory of relativity due to its inability to be reconciled with quantum mechanics at the Physical Interpretations of Relativity Theory conference and published his findings in "Physics Essays". Winterberg has published a series of articles on quantum gravity on viXra between 2011 and 2018. In a 1955 paper Winterberg proposed a test of general relativity using accurate atomic clocks placed in orbit in artificial satellites. At that time atomic clocks were not yet of the required accuracy and artificial satellites did not exist. Werner Heisenberg wrote a
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General relativity


to different field equations. Examples are Whitehead's theory, Brans–Dicke theory, teleparallelism, "f"("R") gravity and Einstein–Cartan theory. The derivation outlined in the previous section contains all the information needed to define general relativity, describe its key properties, and address a question of crucial importance in physics, namely how the theory can be used for model-building. General relativity is a metric theory of gravitation. At its core are Einstein's equations, which describe the relation between the geometry of a four
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Alternatives to general relativity


Newtonian limit and satisfies the weak equivalence principle. This theory is Einstein's first treatment of gravitation in which general covariance is strictly obeyed. Writing: they relate Einstein–Grossmann (1913) to Nordström (1913). They also state: That is, the trace of the stress energy tensor is proportional to the curvature of space. This theory is what we now call "general relativity" (included here for comparison). Discarding the Minkowski metric entirely, Einstein gets: which can also be written Five days before Einstein
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Relativity priority dispute


Einstein. At issue is the extent to which Einstein and various other individuals should be credited for the formulation of these theories, based on priority considerations. The general history of the development of these theories, including the contributions made by many other scientists, is found at History of special relativity and History of general relativity. Concerning special relativity, the most important names that are mentioned in discussions about the distribution of credit are Albert Einstein, Hendrik Lorentz, Henri Poincaré, and Hermann Minkowski. Consideration is also given to numerous other
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Mechanics


traveling at speeds close to the speed of light, Newton's laws were superseded by Albert Einstein’s theory of relativity. [A sentence illustrating the computational complication of Einstein's theory of relativity.] For atomic and subatomic particles, Newton's laws were superseded by quantum theory. For everyday phenomena, however, Newton's three laws of motion remain the cornerstone of dynamics, which is the study of what causes motion. In analogy to the distinction between quantum and classical mechanics, Einstein's general and special theories of relativity have
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Einstein–Cartan–Evans theory


Einstein–Cartan–Evans theory or ECE theory was an attempted unified theory of physics proposed by the Welsh chemist and physicist Myron Wyn Evans (May 26, 1950 – May 2, 2019), which claimed to unify general relativity, quantum mechanics and electromagnetism. The hypothesis was largely published in the journal "Foundations of Physics Letters" between 2003 and 2005. Several of Evans' central claims were later shown to be mathematically incorrect and, in 2008, the new editor of "Foundations of Physics", Nobel laureate Gerard
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Experimentum crucis


Island in Africa in 1919 to record the positions of stars around the Sun during a solar eclipse (see Eddington experiment). The observation of star positions confirmed predictions of gravitational lensing made by Albert Einstein in the general theory of relativity published in 1915. Eddington's observations were considered to be the first solid evidence in favor of Einstein's theory. In some cases, a proposed theory can account for existing anomalous experimental results for which no other existing theory can furnish an explanation. An example would be the ability of the quantum
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Criticism of the theory of relativity


theoretical situation had changed. Alfred Bucherer and Paul Langevin (1904) developed another model, in which the electron is contracted in the line of motion, and dilated in the transverse direction, so that the volume remains constant. While Kaufmann was still evaluating his experiments, Einstein published his theory of special relativity. Eventually, Kaufmann published his results in December 1905 and argued that they are in agreement with Abraham's theory and require rejection of the "basic assumption of Lorentz and Einstein" (the relativity principle). Lorentz reacted
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Banesh Hoffmann


he remained till the late 1970s. He retired in the 1960s but continued to teach one course a semester — in the fall a course on classical and quantum mechanics and in the spring one on the special and general theories of relativity. He died on 5 August 1986. One of the Queens College mathematics department's honors for graduating seniors is named in his honor. Hoffmann became Einstein’s biographer in 1972 when he co-authored "" with Einstein's secretary, Helen Dukas. An eBook version of the biography was published
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Albert Einstein


so strong that not even light can escape. As Einstein later said, the reason for the development of general relativity was that the preference of inertial motions within special relativity was unsatisfactory, while a theory which from the outset prefers no state of motion (even accelerated ones) should appear more satisfactory. Consequently, in 1907 he published an article on acceleration under special relativity. In that article titled "On the Relativity Principle and the Conclusions Drawn from It", he argued that free fall is really inertial motion, and that
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Emmy Noether


her expertise in invariant theory to help them in understanding general relativity, a geometrical theory of gravitation developed mainly by Albert Einstein. Hilbert had observed that the conservation of energy seemed to be violated in general relativity, because gravitational energy could itself gravitate. Noether provided the resolution of this paradox, and a fundamental tool of modern theoretical physics, with Noether's first theorem, which she proved in 1915, but did not publish until 1918. She not only solved the problem for general relativity, but also determined the conserved quantities for
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Introduction to general relativity


the experimental data. Nevertheless, a number of open questions remain, the most fundamental of which is how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity. In September 1905, Albert Einstein published his theory of special relativity, which reconciles Newton's laws of motion with electrodynamics (the interaction between objects with electric charge). Special relativity introduced a new framework for all of physics by proposing new concepts of space and time. Some then-accepted physical
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Inertia


Einstein's concept of inertia remained unchanged from Newton's original meaning. However, this resulted in a limitation inherent in special relativity: the principle of relativity could only apply to inertial reference frames. To address this limitation, Einstein developed his general theory of relativity ("The Foundation of the General Theory of Relativity," 1916), which provided a theory including "noninertial" (accelerated) reference frames. Another form of inertia is "rotational inertia" (→ moment of inertia), the property that a rotating rigid
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General covariance


fields. The classical (non-quantum) theory of electrodynamics is one theory that has such a formulation. Albert Einstein proposed this principle for his special theory of relativity; however, that theory was limited to space-time coordinate systems related to each other by uniform "inertial" motion. Einstein recognized that the general principle of relativity should also apply to accelerated relative motions, and he used the newly developed tool of tensor calculus to extend the special theory's global Lorentz covariance (applying only to inertial frames) to the
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Deductive-nomological model


. General philosophers of science commonly believe that aether, rather, is fictitious, "relegated to the dustbin of scientific history ever since" 1905 brought special relativity. Einstein was noncommittal to aether's nonexistence, simply said it superfluous. Abolishing Newtonian motion for electrodynamic primacy, however, Einstein inadvertently reinforced aether, and to explain motion was led back to aether in general relativity. Yet resistance to relativity theory became associated with earlier theories of aether, whose word and concept became taboo. Einstein explained special relativity's compatibility with an aether
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Tests of general relativity


/sec, with more accurate measurements by the Hubble Space Telescope showing 80.4±4.8 km/sec. The general theory of relativity incorporates Einstein's special theory of relativity, and hence test of special relativity are also testing aspects of general relativity. As a consequence of the equivalence principle, Lorentz invariance holds locally in non-rotating, freely falling reference frames. Experiments related to Lorentz invariance special relativity (that is, when gravitational effects can be neglected) are described in tests of special relativity. The modern era of testing general relativity
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Criticism of the theory of relativity


. However, as pointed out by Einstein, there is one fundamental difference between this concept and absolute space of Newton: the inertio-gravitational field of general relativity is determined by matter, thus it is not absolute. In the "Bad Nauheim Debate" (1920) between Einstein and (among others) Philipp Lenard, the latter stated the following objections: He criticized the lack of "illustrativeness" of Einstein's version of relativity, a condition that he suggested could only be met by an aether theory. Einstein responded
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Criticism of the theory of relativity


Hilbert as regards completing the field equations of general relativity (see Relativity priority dispute). A collection of various criticisms can be found in the book "Hundert Autoren gegen Einstein" ("A Hundred Authors Against Einstein"), published in 1931. It contains very short texts from 28 authors, and excerpts from the publications of another 19 authors. The rest consists of a list that also includes people who only for some time were opposed to relativity. Besides philosophic objections (mostly based on Kantianism), also some alleged
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History of general relativity


gravitation was explained as a geometric phenomenon. At the urging of Tullio Levi-Civita, Einstein began by exploring the use of general covariance (which is essentially the use of curvature tensors) to create a gravitational theory. However, in 1913 Einstein abandoned that approach, arguing that it is inconsistent based on the "hole argument". In 1914 and much of 1915, Einstein was trying to create field equations based on another approach. When that approach was proven to be inconsistent, Einstein revisited the concept of general covariance and
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Unified field theory


1864, Maxwell published his famous paper on a dynamical theory of the electromagnetic field. This was the first example of a theory that was able to encompass previously separate field theories (namely electricity and magnetism) to provide a unifying theory of electromagnetism. By 1905, Albert Einstein had used the constancy of the speed of light in Maxwell's theory to unify our notions of space and time into an entity we now call spacetime and in 1915 he expanded this theory of special relativity to a description of gravity, general relativity, using
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Higher-dimensional Einstein gravity


Higher-dimensional Einstein gravity is any of various physical theories that attempt to generalise to higher dimensions various results of the well established theory of standard (four-dimensional) Einstein gravity, that is, general relativity. This attempt at generalisation has been strongly influenced in recent decades by string theory. At present, this work can probably be most fairly described as extended theoretical speculation. Currently, it has no "direct" observational and experimental support, in contrast to four-dimensional general relativity. However, this theoretical work has
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Criticism of the theory of relativity


meaning. Einstein responded that, based on Mach's principle, one can think of these gravitational fields as induced by the distant masses. In this respect the criticism of Lenard and Mie has been vindicated, since according to the modern consensus, in agreement with Einstein's own mature views, Mach's principle as originally conceived by Einstein is not actually supported by general relativity, as already mentioned above. Ludwik Silberstein, who initially was a supporter of the special theory, objected at different occasions against general relativity. In 1920 he
5558644
History of general relativity


equations before Hilbert amended his own work to include them. This suggests that Einstein developed the correct field equations first, though Hilbert may have reached them later independently (or even learned of them afterwards through his correspondence with Einstein). However, others have criticized those assertions. In the early years after Einstein's theory was published, Sir Arthur Eddington lent his considerable prestige in the British scientific establishment in an effort to champion the work of this German scientist. Because the theory was so complex and abstruse (even today it is
15580556
Differential equation


equations (EFE; also known as "Einstein's equations") are a set of ten partial differential equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy. First published by Einstein in 1915 as a tensor equation, the EFE equate local spacetime curvature (expressed by the Einstein tensor) with the local energy and momentum within that spacetime (expressed by the stress–energy tensor). In quantum mechanics, the analogue of Newton's
2359519
David Hilbert


8 years with a confounding problem of putting the theory into final form. By early summer 1915, Hilbert's interest in physics had focused on general relativity, and he invited Einstein to Göttingen to deliver a week of lectures on the subject. Einstein received an enthusiastic reception at Göttingen. Over the summer Einstein learned that Hilbert was also working on the field equations and redoubled his own efforts. During November 1915 Einstein published several papers culminating in "The Field Equations of Gravitation" (see Einstein field equations). Nearly simultaneously David
8320657
Antony Garrett Lisi


particle physics with Albert Einstein's general relativistic description of gravitation, using the largest simple exceptional Lie algebra, E. In a paper posted to the physics arXiv on November 6, 2007, and in a popular article published in Scientific American in December, 2010, Lisi describes his proposal that gravity, the standard model bosons and fermions can be unified as parts of an E superconnection. This unified field theory attempts to describe all fundamental interactions observed in nature, as a possible theory of everything, unifying Albert Einstein's general relativity with
9244852
Moshe Carmeli


publishing 128 refereed research papers in various journals and forums, plus assorted other publications (146 in all). He is most notable for his work on gauge theory and his development of the theory of cosmological general relativity, which extends Einstein's theory of general relativity from a four-dimensional spacetime to a five-dimensional space-velocity framework. Carmeli was born in Baghdad, Iraq in 1933. However, he spent the majority of his life and career in Israel and the United States of America. In 1960, he
16884929
Schwarzschild metric


1916, a little more than a month after the publication of Einstein's theory of general relativity. It was the first exact solution of the Einstein field equations other than the trivial flat space solution. Schwarzschild died shortly after his paper was published, as a result of a disease he contracted while serving in the German army during World War I. Johannes Droste in 1916 independently produced the same solution as Schwarzschild, using a simpler, more direct derivation. In the early years of general relativity there was a lot of confusion about the
19022982
Introduction to general relativity


theories were inconsistent with that framework; a key example was Newton's theory of gravity, which describes the mutual attraction experienced by bodies due to their mass. Several physicists, including Einstein, searched for a theory that would reconcile Newton's law of gravity and special relativity. Only Einstein's theory proved to be consistent with experiments and observations. To understand the theory's basic ideas, it is instructive to follow Einstein's thinking between 1907 and 1915, from his simple thought experiment involving an observer in free fall to his fully
775454
History of special relativity


in his famous lecture (1908) he mentioned Voigt, Lorentz and Einstein. Minkowski himself considered Einstein's theory as a generalization of Lorentz's and credited Einstein for completely stating the relativity of time, but he criticized his predecessors for not fully developing the relativity of space. However, modern historians of science argue that Minkowski's claim for priority was unjustified, because Minkowski (like Wien or Abraham) adhered to the electromagnetic world-picture and apparently didn't fully understand the difference between Lorentz's electron theory and Einstein's kinematics
21352218
Gravitational wave


in 1893 by Oliver Heaviside using the analogy between the inverse-square law in gravitation and electricity. In 1905, Henri Poincaré proposed gravitational waves, emanating from a body and propagating at the speed of light, as being required by the Lorentz transformations and suggested that, in analogy to an accelerating electrical charge producing electromagnetic waves, accelerated masses in a relativistic field theory of gravity should produce gravitational waves. When Einstein published his general theory of relativity in 1915, he was skeptical of Poincaré's idea since the theory implied there were
1246086
Eddington experiment


was one of the tests proposed for his 1915 theory of General Relativity. Following the return of the expeditions, the results were presented by Eddington to the Royal Society of London, and, after some deliberation, were accepted. Widespread newspaper coverage of the results led to worldwide fame for Einstein and his theories. One of the first considerations of gravitational deflection of light was published in 1801, when Johann Georg von Soldner pointed out that Newtonian gravity predicts that starlight will be deflected when it passes near a massive object. Initially,
15299349
General relativity


theory. Einstein himself had shown in 1915 how his theory explained the anomalous perihelion advance of the planet Mercury without any arbitrary parameters ("fudge factors"). Similarly, 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 instantly famous. Yet the theory entered the mainstream of theoretical physics and astrophysics only with the developments between approximately 1960 and 1975, now known as the golden age of general relativity. Physicists
11619187
Flatland


Einstein's general theory of relativity was published, which brought to prominence the concept of a fourth dimension. "Flatland" was mentioned in a letter entitled "Euclid, Newton and Einstein" published in "Nature" on 12 February 1920. In this letter Abbott is depicted, in a sense, as a prophet due to his intuition of the importance of "time" to explain certain phenomena: The "Oxford Dictionary of National Biography" now contains a reference to "Flatland". Numerous imitations or sequels to "Flatland
332929
Einstein–Cartan theory


spin tensor associated with the matter source, which entails that the torsion generally be non-zero inside matter. A consequence of the linearity is that outside of matter there is zero torsion, so that the exterior geometry remains the same as what would be described in general relativity. The differences between Einstein-Cartan theory and general relativity (formulated either in terms of the Einstein-Hilbert action on Riemannian geometry or the Palatini action on Riemann-Cartan geometry) rest solely on what happens to the geometry inside matter sources. That
20222147
Ultimate fate of the universe


, of the cosmic microwave background radiation, a fact that is a straightforward prediction of the Big Bang theory, and one that the original Steady State theory could not account for. As a result, the Big Bang theory quickly became the most widely held view of the origin of the universe. When Einstein formulated general relativity, he and his contemporaries believed in a static universe. When Einstein found that his equations could easily be solved in such a way as to allow the universe to be expanding now, and to contract in
18124249
Einstein–Cartan theory


. It is derived by rewriting the Einstein-Hilbert action in terms of the affine connection and then separately posing a constraint that forces both the torsion and contorsion to be zero, which thus forces the affine connection to be equal to the Levi-Civita connection. Because it is a direct translation of the action and field equations of general relativity, expressed in terms of the Levi-Civita connection, this may be regarded as the theory of general relativity, itself, transposed into the framework of Riemann-Cartan geometry. Einstein
20222144
Theory of relativity


equations of electromagnetism). General relativity is a theory of gravitation developed by Einstein in the years 1907–1915. The development of general relativity began with the equivalence principle, under which the states of accelerated motion and being at rest in a gravitational field (for example, when standing on the surface of the Earth) are physically identical. The upshot of this is that free fall is inertial motion: an object in free fall is falling because that is how objects move when there is no force being exerted on them, instead of
10558648
William Kingdon Clifford


Frankland quoted the "Space-Theory of Matter" in his book on parallelism. He wrote: Years later, after general relativity had been advanced by Albert Einstein, various authors noted that Clifford had anticipated Einstein: In 1923 Hermann Weyl mentioned Clifford as one of those who, like Bernhard Riemann, anticipated the geometric ideas of relativity. In 1940 Eric Temple Bell published his "The Development of Mathematics". There on pages 359 and 360 he discusses the prescience of Clifford on relativity: Also in 1960, at Stanford University
14045708
Theory of relativity


relativity is a theory of gravitation whose defining feature is its use of the Einstein field equations. The solutions of the field equations are metric tensors which define the topology of the spacetime and how objects move inertially. Einstein stated that the theory of relativity belongs to a class of "principle-theories". As such, it employs an analytic method, which means that the elements of this theory are not based on hypothesis but on empirical discovery. By observing natural processes, we understand their general characteristics, devise mathematical models to
10558650
Einstein–Cartan theory


does not; (2) an additional set of equations are posed that relate torsion to spin. This difference can be factored into general relativity (Einstein-Hilbert) → general relativity (Palatini) → Einstein-Cartan by first reformulating general relativity onto a Riemann-Cartan geometry, replacing the Einstein-Hilbert action over Riemannian geometry by the Palatini action over Riemann-Cartan geometry; and second, removing the zero torsion constraint from the Palatini action, which results in the additional set of equations for spin and torsion, as
20222140
Einstein Tower


". In 1911 Einstein published the initial version of his innovative General Theory of Relativity. One of the predicted effects according to the theory was a slight shift of spectral lines in the sun’s gravitation field, now known as the red shift. The solar observatory in Potsdam was designed and constructed primarily to verify this phenomenon. The Mount Wilson Observatory in California, the first tower telescope worldwide, was the model for the facility designed by Freundlich. In tower telescopes a coelostat (a system with two deflecting mirrors, pronounced "
11724971
Hans Reichenbach


In the same year, he published his first book on the philosophical implications of the theory of relativity, "The Theory of Relativity and A Priori Knowledge", which criticized the Kantian notion of synthetic "a priori". He subsequently published "Axiomatization of the Theory of Relativity" (1924), "From Copernicus to Einstein" (1927) and "The Philosophy of Space and Time" (1928), the last stating the logical positivist view on the theory of relativity. In 1926, with the help of
14803496
Albert Einstein


a paper on general relativity in 1916 with his theory of gravitation. He continued to deal with problems of statistical mechanics and quantum theory, which led to his explanations of particle theory and the motion of molecules. He also investigated the thermal properties of light which laid the foundation of the photon theory of light. In 1917, he applied the general theory of relativity to model the structure of the universe. Except for one year in Prague, Einstein lived in Switzerland between 1895 and 1914, during which time he renounced his German
72918
Yilmaz theory of gravitation


very difficult to construct a theory of quantum gravity which goes over to general relativity in an appropriate limit. However Yilmaz has claimed that his theory is 'compatible with quantum mechanics'. He suggests that it might be an alternative to superstring theory. In his theory, Yilmaz wishes to retain the left hand side of the Einstein field equation (namely the Einstein tensor, which is well-defined for any Lorentzian manifold, independent of general relativity) but to modify the right hand side, the stress–energy tensor, by
948750
Black hole cosmology


close match a coincidence. In the version as originally proposed by Pathria and Good, and studied more recently by, among others, Nikodem Popławski, According to general relativity, the gravitational collapse of a sufficiently compact mass forms a singular Schwarzschild black hole. In the Einstein–Cartan–Sciama–Kibble theory of gravity, however, it forms a regular "Einstein–Rosen bridge", or wormhole. Schwarzschild wormholes and Schwarzschild black holes are different mathematical solutions of general relativity and the "Einstein–Cartan theory". Yet
18278914
Robert Andrews Millikan


20th century developments in physics, as in the case of the photon theory. Another example is that his textbook, as late as the 1927 version, unambiguously states the existence of the ether, and mentions Einstein's theory of relativity only in a noncommittal note at the end of the caption under Einstein's portrait, stating as the last in a list of accomplishments that he was "author of the special theory of relativity in 1905 and of the general theory of relativity in 1914, both of which have had great success in
4548103
Erich Kretschmann


of the argument was more topological while Einstein's use involved physical measurements. Kretschmann is most famous for his 1917 claim that Einstein's use of the principle of covariance in General Relativity is vacuous. Kretschmann claimed that the demand that a theory be put in generally covariant form does not limit or restrict the range of acceptable theories, but is simply a challenge to the mathematician's ingenuity. According to Kretschmann, any theory can be put in generally covariant form. Einstein responded that even if general covariance is not a purely formal limitation
11451825
History of physics


and blackbody radiation, Einstein received the Nobel Prize in 1921. The gradual acceptance of Einstein's theories of relativity and the quantized nature of light transmission, and of Niels Bohr's model of the atom created as many problems as they solved, leading to a full-scale effort to reestablish physics on new fundamental principles. Expanding relativity to cases of accelerating reference frames (the "general theory of relativity") in the 1910s, Einstein posited an equivalence between the inertial force of acceleration and the force of gravity, leading to
13701131
History of general relativity


, the ETH. Once back in Zurich, he immediately visited his old ETH classmate Marcel Grossmann, now a professor of mathematics, who introduced him to Riemannian geometry and, more generally, to differential geometry. On the recommendation of Italian mathematician Tullio Levi-Civita, Einstein began exploring the usefulness of general covariance (essentially the use of tensors) for his gravitational theory. For a while Einstein thought that there were problems with the approach, but he later returned to it and, by late 1915, had published his general
15580547
Criticism of the theory of relativity


the rotation, and consequently the speed of light is not constant in accelerated frames. As was shown by Einstein, the only form of accelerated motion that cannot be described is the one due to gravitation, since special relativity is not compatible with the Equivalence principle. Einstein was also unsatisfied with the fact that inertial frames are preferred over accelerated frames. Thus over the course of several years (1908–1915), Einstein developed general relativity. This theory includes the replacement of Euclidean geometry by non-Euclidean geometry, and the resultant
5558622
Principle of locality


Quantum Mechanics, which Einstein himself had helped to create. Locality is a key axiom of Einstein's relativistic quantum field theory, where it is essential to causality that effects do not propagate faster than the speed of light. Einstein's quantum theory (currently termed the "old quantum theory") is said to be "relativistic" because it does "not" violate either his general or special theory of relativity: speed of light is a limiting factor. In Einstein's theory, two observable objects are localised, each within
1832222
Kaluza–Klein theory


above, and then departed into Klein's quantum interpretation. Klein solved a Schroedinger-like wave equation using an expansion in terms of fifth-dimensional waves resonating in the closed, compact fifth dimension. A splitting of five-dimensional spacetime into the Einstein equations and Maxwell equations in four dimensions was first discovered by Gunnar Nordström in 1914, in the context of his theory of gravity, but subsequently forgotten. Kaluza published his derivation in 1921 as an attempt to unify electromagnetism with Einstein's general relativity. In 1926, Oskar Klein
17412156
Introduction to the mathematics of general relativity


tensor). The Einstein Field Equations can be written as where is the Einstein tensor and is the stress–energy tensor. This implies that the curvature of space (represented by the Einstein tensor) is directly connected to the presence of matter and energy (represented by the stress–energy tensor). In Einstein's theory of general relativity, the Schwarzschild metric (also Schwarzschild vacuum or Schwarzschild solution), is a solution to the Einstein field equations which describes the gravitational field outside a spherical mass, on the assumption that
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