Editing Albert Einstein (section)

=== General relativity ===
==== General relativity and the equivalence principle ====
{{Main|History of general relativity}}
{{See also|Theory of relativity|Einstein field equations}}
[[File:1919 eclipse positive.jpg|alt=Black circle covering the sun, rays visible around it, in a dark sky.|thumb|upright|[[Arthur Stanley Eddington|Eddington]]'s photo of a [[solar eclipse]]]]
[[General relativity]] (GR) is a [[theory of gravitation]] that was developed by Einstein between 1907 and 1915. According to it, the observed gravitational attraction between masses results from the warping of [[spacetime]] 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 so strong that not even light can escape.<ref>{{Cite book |last=Fraknoi |first=Andrew |url=https://openstax.org/details/books/astronomy-2e |title=Astronomy 2e |date=2022 |display-authors=etal |publisher=OpenStax |isbn=978-1-951693-50-3 |edition=2e |oclc=1322188620 |pages=800–815}}</ref>

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.<ref>Einstein (1923).</ref> 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 for a free-falling observer the rules of special relativity must apply. This argument is called the [[equivalence principle]]. In the same article, Einstein also predicted the phenomena of [[gravitational time dilation]], [[gravitational redshift]] and [[gravitational lensing]].{{Sfnp|Pais|1982|pp=179–183}}<ref>Stachel, et al (2008). Vol. 2: The Swiss Years—Writings, 1900–1909, pp. 273–274.</ref>

In 1911, Einstein published another article "On the Influence of Gravitation on the Propagation of Light" expanding on the 1907 article, in which he estimated the amount of deflection of light by massive bodies. Thus, the theoretical prediction of general relativity could for the first time be tested experimentally.{{Sfnp|Pais|1982|pp=194–195}}

==== Gravitational waves ====
In 1916, Einstein predicted [[gravitational wave]]s,<ref>Einstein (1916).</ref><ref>Einstein (1918).</ref> ripples in the [[curvature]] of spacetime which propagate as [[wave]]s, traveling outward from the source, transporting energy as gravitational radiation. The existence of gravitational waves is possible under general relativity due to its [[Lorentz invariance]] which brings the concept of a finite speed of propagation of the physical interactions of gravity with it. By contrast, gravitational waves cannot exist in the [[Newton's law of universal gravitation|Newtonian theory of gravitation]], which postulates that the physical interactions of gravity propagate at infinite speed.

The first, indirect, detection of gravitational waves came in the 1970s through observation of a pair of closely orbiting [[neutron stars]], [[PSR B1913+16]].<ref name="natgeo"/> The explanation for the decay in their orbital period was that they were emitting gravitational waves.<ref name="natgeo"/><ref name="Tf1T0"/> Einstein's prediction was confirmed on 11 February 2016, when researchers at [[LIGO]] published the [[first observation of gravitational waves]],<ref name="PRL-20160211"/> detected on Earth on 14 September 2015, nearly one hundred years after the prediction.<ref name="natgeo"/><ref name="CO6kH"/><ref name="oSmHb"/><ref name="hkKSp"/><ref name="38Msx"/>

==== Hole argument and Entwurf theory ====
While developing general relativity, Einstein became confused about the [[gauge invariance]] in the theory. He formulated an argument that led him to conclude that a general relativistic field theory is impossible. He gave up looking for fully generally covariant tensor equations and searched for equations that would be invariant under general linear transformations only.<ref>{{Cite journal |last=Norton |first=John |author-link=John D. Norton |date=1984 |title=How Einstein Found His Field Equations: 1912–1915 |url=https://www.jstor.org/stable/27757535 |journal=Historical Studies in the Physical Sciences |volume=14 |issue=2 |pages=253–316 |doi=10.2307/27757535 |jstor=27757535 |issn=0073-2672}}</ref>

In June 1913, the Entwurf ('draft') theory was the result of these investigations. As its name suggests, it was a sketch of a theory, less elegant and more difficult than general relativity, with the equations of motion supplemented by additional gauge fixing conditions. After more than two years of intensive work, Einstein realized that the [[hole argument]] was mistaken<ref name="sOA9t"/> and abandoned the theory in November 1915.

==== Physical cosmology ====
{{Main|Physical cosmology}}
[[File:MillikanLemaitreEinstein.jpg|thumb|right|[[Robert Andrews Millikan|Robert A. Millikan]], [[Georges Lemaître]] and Einstein at the [[California Institute of Technology]] in January 1933]]
In 1917, Einstein applied the general theory of relativity to the structure of the universe as a whole.<ref>Einstein (1917a).</ref> He discovered that the general field equations predicted a universe that was dynamic, either contracting or expanding. As observational evidence for a dynamic universe was lacking at the time, Einstein introduced a new term, the [[cosmological constant]], into the field equations, in order to allow the theory to predict a static universe. The modified field equations predicted a static universe of closed curvature, in accordance with Einstein's understanding of [[Mach's principle]] in these years. This model became known as the Einstein World or [[Einstein's static universe]].{{Sfnp|Pais|1994|pp=285–286}}<ref name="iJwuX"/>

Following the discovery of the recession of the galaxies by [[Edwin Hubble]] in 1929, Einstein abandoned his static model of the universe, and proposed two dynamic models of the cosmos, the [[Friedmann–Einstein universe]] of 1931<ref name=E1931>Einstein (1931).</ref><ref name="cor-2013"/> and the [[Einstein–de Sitter universe]] of 1932.<ref>Einstein & de Sitter (1932).</ref><ref name="J9Tqu"/> In each of these models, Einstein discarded the cosmological constant, claiming that it was "in any case theoretically unsatisfactory".<ref name=E1931/><ref name="cor-2013"/><ref name="sxfvo"/>

In many Einstein biographies, it is claimed that Einstein referred to the cosmological constant in later years as his "biggest blunder", based on a letter [[George Gamow]] claimed to have received from him. The astrophysicist [[Mario Livio]] has cast doubt on this claim.<ref name="qmmVf"/>

In late 2013, a team led by the Irish physicist [[Cormac O'Raifeartaigh]] discovered evidence that, shortly after learning of Hubble's observations of the recession of the galaxies, Einstein considered a [[steady-state model]] of the universe.<ref name="Tq53z"/><ref name="8pfEk"/> In a hitherto overlooked manuscript, apparently written in early 1931, Einstein explored a model of the expanding universe in which the density of matter remains constant due to a continuous creation of matter, a process that he associated with the cosmological constant.<ref name="cor-steady-state" /><ref name="Einstein's aborted model"/> As he stated in the paper, {{qi|In what follows, I would like to draw attention to a solution to equation (1) that can account for Hubbel's {{sic}} facts, and in which the density is constant over time [...] If one considers a physically bounded volume, particles of matter will be continually leaving it. For the density to remain constant, new particles of matter must be continually formed in the volume from space.}}

It thus appears that Einstein considered a [[steady-state model]] of the expanding universe many years before Hoyle, Bondi and Gold.<ref name="ILjYQ"/><ref name="ThZb0"/> However, Einstein's steady-state model contained a fundamental flaw and he quickly abandoned the idea.<ref name="cor-steady-state"/><ref name="Einstein's aborted model"/><ref name="7ShC9"/>

==== Energy momentum pseudotensor ====
{{Main|Stress–energy–momentum pseudotensor}}
General relativity includes a dynamical spacetime, so it is difficult to see how to identify the conserved energy and momentum. [[Noether's theorem]] allows these quantities to be determined from a [[Lagrangian (field theory)|Lagrangian]] with [[translation invariance]], but [[general covariance]] makes translation invariance into something of a [[gauge symmetry]]. The energy and momentum derived within general relativity by [[Emmy Noether|Noether]]'s prescriptions do not make a real tensor for this reason.<ref>{{cite arXiv|first=Nina |last=Byers |author-link=Nina Byers |title=E. Noether's Discovery of the Deep Connection Between Symmetries and Conservation Laws |eprint=physics/9807044 |date=23 September 1998}}</ref>

Einstein argued that this is true for a fundamental reason: the gravitational field could be made to vanish by a choice of coordinates. He maintained that the non-covariant energy momentum pseudotensor was, in fact, the best description of the energy momentum distribution in a gravitational field. While the use of non-covariant objects like pseudotensors was criticized by [[Erwin Schrödinger]] and others, Einstein's approach has been echoed by physicists including [[Lev Landau]] and [[Evgeny Lifshitz]].<ref>{{cite journal|doi=10.1103/PhysRev.111.315 |first=J. N. |last=Goldberg |title=Conservation laws in general relativity |year=1958 |journal=Physical Review |volume=111 |number=1 |pages=315–320|bibcode=1958PhRv..111..315G }}</ref>

==== Wormholes ====
In 1935, Einstein collaborated with [[Nathan Rosen]] to produce a model of a [[wormhole]], often called [[Einstein–Rosen bridges]].<ref>Einstein & Rosen (1935).</ref><ref name="QNjpt"/> His motivation was to model elementary particles with charge as a solution of gravitational field equations, in line with the program outlined in the paper "Do Gravitational Fields play an Important Role in the Constitution of the Elementary Particles?". These solutions cut and pasted [[Schwarzschild black hole]]s to make a bridge between two patches. Because these solutions included spacetime curvature without the presence of a physical body, Einstein and Rosen suggested that they could provide the beginnings of a theory that avoided the notion of point particles. However, it was later found that Einstein–Rosen bridges are not stable.<ref name="ja7FY"/>

==== Einstein–Cartan theory ====
{{Main|Einstein–Cartan theory}}
[[File:Albert Einstein photo 1920.jpg|alt=Einstein, sitting at a table, looks up from the papers he is reading and into the camera.|thumb|upright|Einstein at his office, [[University of Berlin]], 1920]]In order to incorporate spinning point particles into general relativity, the affine connection needed to be generalized to include an antisymmetric part, called the [[Torsion tensor|torsion]]. This modification was made by Einstein and Cartan in the 1920s.

==== Equations of motion ====
{{Main|Einstein–Infeld–Hoffmann equations}}
In general relativity, gravitational force is reimagined as curvature of [[spacetime]]. A curved path like an orbit is not the result of a force deflecting a body from an ideal straight-line path, but rather the body's attempt to fall freely through a background that is itself curved by the presence of other masses. A remark by [[John Archibald Wheeler]] that has become proverbial among physicists summarizes the theory: {{qi|Spacetime tells matter how to move; matter tells spacetime how to curve.}}<ref name="Wheeler">{{Cite book|last=Wheeler|first=John Archibald|url={{GBurl|id=zGFkK2tTXPsC|p=235}}|title=Geons, Black Holes, and Quantum Foam: A Life in Physics|date=18 June 2010|publisher=W. W. Norton & Company|isbn=978-0-393-07948-7|language=en|author-link=John Archibald Wheeler}}</ref><ref>{{Cite journal|last=Kersting|first=Magdalena|date=May 2019|title=Free fall in curved spacetime—how to visualise gravity in general relativity|journal=[[Physics Education]] |volume=54|issue=3|pages=035008|doi=10.1088/1361-6552/ab08f5|bibcode=2019PhyEd..54c5008K |s2cid=127471222 |issn=0031-9120|doi-access=free|hdl=10852/74677|hdl-access=free}}</ref> The [[Einstein field equations]] cover the latter aspect of the theory, relating the curvature of spacetime to the distribution of matter and energy. The [[geodesic equation]] covers the former aspect, stating that freely falling bodies follow [[Geodesics in general relativity|lines that are as straight as possible in a curved spacetime]]. Einstein regarded this as an "independent fundamental assumption" that had to be postulated in addition to the field equations in order to complete the theory. Believing this to be a shortcoming in how general relativity was originally presented, he wished to derive it from the field equations themselves. Since the equations of general relativity are non-linear, a lump of energy made out of pure gravitational fields, like a black hole, would move on a trajectory which is determined by the Einstein field equations themselves, not by a new law. Accordingly, Einstein proposed that the field equations would determine the path of a singular solution, like a black hole, to be a geodesic. Both physicists and philosophers have often repeated the assertion that the geodesic equation can be obtained from applying the field equations to the motion of a [[gravitational singularity]], but this claim remains disputed.<ref>{{cite journal|last=Tamir |first=M |url=http://philsci-archive.pitt.edu/9158/1/Tamir_-_Proving_the_Principle.pdf |title=Proving the principle: Taking geodesic dynamics too seriously in Einstein's theory |journal=Studies in History and Philosophy of Modern Physics |volume=43 |number=2 |pages=137–154 |year=2012 |doi=10.1016/j.shpsb.2011.12.002|bibcode=2012SHPMP..43..137T }}</ref><ref>{{cite book|last=Malament |first=David |chapter=A Remark About the "Geodesic Principle" in General Relativity |author-link=David Malament |chapter-url=http://philsci-archive.pitt.edu/5072/1/GeodesicLaw.pdf |title=Analysis and Interpretation in the Exact Sciences |pages=245–252 |series=The Western Ontario Series in Philosophy of Science |volume=78 |publisher=Springer |year=2012 |editor-last1=Frappier |editor-first1=M. |editor-last2=Brown |editor-first2=D. |editor-last3=DiSalle |editor-first3=R. |doi=10.1007/978-94-007-2582-9_14 |isbn=978-94-007-2581-2 |quote=Though the geodesic principle can be recovered as theorem in general relativity, it is not a consequence of Einstein's equation (or the conservation principle) alone. Other assumptions are needed to derive the theorems in question.}}</ref>