Editing Albert Einstein (section)

== Scientific career ==
Throughout his life, Einstein published hundreds of books and articles.<ref name="Bio"/><ref name="Paul Arthur Schilpp, editor 1951 730–746"/> He published more than 300 scientific papers and 150 non-scientific ones.<ref name="Nobel"/><ref name="Paul Arthur Schilpp, editor 1951 730–746"/> On 5 December 2014, universities and archives announced the release of Einstein's papers, comprising more than 30,000 unique documents.<ref>Stachel et al (2008).</ref><ref name="NYT-20141204-DB"/> In addition to the work he did by himself he also collaborated with other scientists on additional projects including the [[Bose–Einstein statistics]], the [[Einstein refrigerator]] and others.<ref name="Instituut-Lorentz"/><ref name="e5xd8"/>

=== Statistical mechanics ===
==== Thermodynamic fluctuations and statistical physics ====
{{Main|Statistical mechanics|thermal fluctuations|statistical physics}}
Einstein's first paper<ref>Einstein (1901).</ref><ref name="PubList"/> submitted in 1900 to ''[[Annalen der Physik]]'' was on [[capillary attraction]]. It was published in 1901 with the title "Folgerungen aus den Capillaritätserscheinungen", which translates as "Conclusions from the capillarity phenomena". Two papers he published in 1902–1903 (thermodynamics) attempted to interpret [[atom]]ic phenomena from a statistical point of view. These papers were the foundation for the 1905 paper on Brownian motion, which showed that Brownian movement can be construed as firm evidence that molecules exist. His research in 1903 and 1904 was mainly concerned with the effect of finite atomic size on diffusion phenomena.<ref name="PubList"/>

==== Theory of critical opalescence ====
{{Main|Critical opalescence}}
Einstein returned to the problem of thermodynamic fluctuations, giving a treatment of the density variations in a fluid at its critical point. Ordinarily the density fluctuations are controlled by the second derivative of the free energy with respect to the density. At the critical point, this derivative is zero, leading to large fluctuations. The effect of density fluctuations is that light of all wavelengths is scattered, making the fluid look milky white. Einstein relates this to [[Rayleigh scattering]], which is what happens when the fluctuation size is much smaller than the wavelength, and which explains why the sky is blue.<ref name="L2N73"/> Einstein quantitatively derived critical opalescence from a treatment of density fluctuations, and demonstrated how both the effect and Rayleigh scattering originate from the atomistic constitution of matter.

=== 1905 – ''Annus Mirabilis'' papers ===
The [[Annus mirabilis papers|''Annus Mirabilis'' papers]] are four articles pertaining to the photoelectric effect (which gave rise to [[quantum mechanics|quantum theory]]), [[Brownian motion]], the [[special theory of relativity]], and [[Mass–energy equivalence|''E''{{nbs}}={{nbs}}''mc''<sup>2</sup>]] that Einstein published in the ''Annalen der Physik'' scientific journal in 1905. These four works contributed substantially to the foundation of [[History of physics#Modern physics|modern physics]] and changed views on [[space]], time, and [[matter]]. The four papers are:

{| class=wikitable
|-
! Title <small>(translated)</small> !!<small>Area of focus</small> !! Received !! Published !! Significance
|-
| "On a Heuristic Viewpoint Concerning the Production and Transformation of Light"<ref name=1905a>Einstein (1905a).</ref> || Photoelectric effect || 18 March || 9 June || Resolved an unsolved puzzle by suggesting that energy is exchanged only in discrete amounts ([[quantum|quanta]]).<ref name="1Jhcb"/> This idea was pivotal to the early development of quantum theory.<ref name="oJBvd"/>
|-
| "On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat"<ref>Einstein (1905c).</ref> || [[Brownian motion]] || 11 May || 18 July || Explained empirical evidence for the [[atomic theory]], supporting the application of [[statistical physics]].
|-
| "On the Electrodynamics of Moving Bodies"<ref name=1905d>Einstein (1905d).</ref> || [[Special relativity]] || 30 June || 26{{nbs}}September || Reconciled [[James Clerk Maxwell|Maxwell]]'s equations for electricity and magnetism with the laws of mechanics by introducing changes to mechanics, resulting from analysis based on empirical evidence that the speed of light is independent of the motion of the observer.<ref name="RhZ8x"/>{{specify|reason=reliable sources claim that he was unaware of those empirical data and was motivated by the transormation properties of Maxwell's Equations.|date=August 2024}} Discredited the concept of a "[[luminiferous ether]]".<ref name="lhfJ9"/>
|-
| "Does the Inertia of a Body Depend Upon Its Energy Content?"<ref>Einstein (1905e).</ref> || [[Mass–energy equivalence|{{nowrap|Matter–energy}} equivalence]] || 27{{nbs}}September || 21 November || Equivalence of matter and energy, ''E''{{nbs}}={{nbs}}''mc''<sup>2</sup>, the existence of "[[rest energy]]", and the basis of nuclear energy.
|}

=== Special relativity ===
{{Main|History of special relativity}}
Einstein's "{{lang|de|Zur Elektrodynamik bewegter Körper}}"<ref name=1905d/> ("On the Electrodynamics of Moving Bodies") was received on 30 June 1905 and published 26 September of that same year. It reconciled conflicts between [[Maxwell's equations]] (the laws of electricity and magnetism) and the laws of Newtonian mechanics by introducing changes to the laws of mechanics.{{Sfnp|Fölsing|1997|pp=178–198}} Observationally, the effects of these changes are most apparent at high speeds (where objects are moving at speeds close to the [[speed of light]]). The theory developed in this paper later became known as Einstein's special theory of relativity.

This paper predicted that, when measured in the frame of a relatively moving observer, a clock carried by a moving body would appear to [[Time dilation|slow down]], and the body itself would [[Length contraction|contract]] in its direction of motion. This paper also argued that the idea of a [[luminiferous aether]]—one of the leading theoretical entities in physics at the time—was superfluous.<ref group=note name="aBfxO"/>

In his paper on [[mass–energy equivalence]], Einstein produced ''E''{{nbs}}={{nbs}}''mc''<sup>2</sup> as a consequence of his special relativity equations.{{Sfnp|Stachel|2002|pp=vi, 15, 90, 131, [{{GBurl|id=OAsQ_hFjhrAC|p=215}} 215]}} Einstein's 1905 work on relativity remained controversial for many years, but was accepted by leading physicists, starting with [[Max Planck]].<ref group=note name="sBl2q"/>{{Sfnp|Pais|1982|pp=382–386}}

Einstein originally framed special relativity in terms of [[kinematics]] (the study of moving bodies). In 1908, [[Hermann Minkowski]] reinterpreted special relativity in geometric terms as a theory of [[spacetime]]. Einstein adopted Minkowski's formalism in his 1915 [[general theory of relativity]].{{Sfnp|Pais|1982|pp=151–152}}

=== 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>

=== Old quantum theory ===
{{Main|Old quantum theory}}

==== Photons and energy quanta ====
[[File:Photoelectric effect in a solid - diagram.svg|alt=|thumb|The photoelectric effect. Incoming photons on the left strike a metal plate (bottom), and eject electrons, depicted as flying off to the right.]]
In a 1905 paper,<ref name=1905a/> Einstein postulated that light itself consists of localized particles (''[[quantum|quanta]]''). Einstein's light quanta were nearly universally rejected by all physicists, including Max Planck and Niels Bohr. This idea only became universally accepted in 1919, with [[Robert Millikan]]'s detailed experiments on the photoelectric effect, and with the measurement of [[Compton scattering]].

Einstein concluded that each wave of frequency ''f'' is associated with a collection of photons with energy ''hf'' each, where ''h'' is the [[Planck constant]]. He did not say much more, because he was not sure how the particles were related to the wave. But he did suggest that this idea would explain certain experimental results, notably the [[photoelectric effect]].<ref name=1905a/> Light quanta were dubbed ''[[photons]]'' by [[Gilbert N. Lewis]] in 1926.{{sfnp|Isaacson|2007|p=576}}

==== Quantized atomic vibrations ====
{{Main|Einstein solid}}
In 1907, Einstein proposed a model of matter where each atom in a lattice structure is an independent harmonic oscillator. In the Einstein model, each atom oscillates independently—a series of equally spaced quantized states for each oscillator. Einstein was aware that getting the frequency of the actual oscillations would be difficult, but he nevertheless proposed this theory because it was a particularly clear demonstration that quantum mechanics could solve the specific heat problem in classical mechanics. [[Peter Debye]] refined this model.<ref name="ixm32"/>

==== Bose–Einstein statistics ====
{{Main|Bose–Einstein statistics}}
In 1924, Einstein received a description of a [[statistical mechanics|statistical]] model from Indian physicist [[Satyendra Nath Bose]], based on a counting method that assumed that light could be understood as a gas of indistinguishable particles. Einstein noted that Bose's statistics applied to some atoms as well as to the proposed light particles, and submitted his translation of Bose's paper to the ''[[Zeitschrift für Physik]]''. Einstein also published his own articles describing the model and its implications, among them the [[Bose–Einstein condensate]] phenomenon that some particulates should appear at very low temperatures.<ref>Einstein (1924).</ref> It was not until 1995 that the first such condensate was produced experimentally by [[Eric Allin Cornell]] and [[Carl Wieman]] using [[ultracold atom|ultra-cooling]] equipment built at the [[NIST]]–[[JILA]] laboratory at the [[University of Colorado at Boulder]].<ref name="nlagl"/> Bose–Einstein statistics are now used to describe the behaviors of any assembly of [[boson]]s. Einstein's sketches for this project may be seen in the Einstein Archive in the library of the Leiden University.<ref name="Instituut-Lorentz"/>

==== Wave–particle duality ====
[[File:Albert Einstein 1921 (re-cropped).jpg|thumb|upright|Einstein in 1921, by [[Harris & Ewing]] studio]]
Although the patent office promoted Einstein to Technical Examiner Second Class in 1906, he had not given up on academia. In 1908, he became a ''[[Privatdozent]]'' at the University of Bern.{{Sfnp|Pais|1982|p=522}} In "''Über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung''" ("[[s:Translation:The Development of Our Views on the Composition and Essence of Radiation|The Development of our Views on the Composition and Essence of Radiation]]"), on the [[quantization (physics)|quantization]] of light, and in an earlier 1909 paper, Einstein showed that Max Planck's energy quanta must have well-defined [[momentum|momenta]] and act in some respects as independent, [[point particle|point-like particles]]. This paper introduced the ''photon'' concept and inspired the notion of [[wave–particle duality]] in quantum mechanics. Einstein saw this wave–particle duality in radiation as concrete evidence for his conviction that physics needed a new, unified foundation.

==== Zero-point energy ====
In a series of works completed from 1911 to 1913, Planck reformulated his 1900 quantum theory and introduced the idea of [[zero-point energy]] in his "second quantum theory". Soon, this idea attracted the attention of Einstein and his assistant [[Otto Stern]]. Assuming the energy of rotating diatomic molecules contains zero-point energy, they then compared the theoretical specific heat of hydrogen gas with the experimental data. The numbers matched nicely. However, after publishing the findings, they promptly withdrew their support, because they no longer had confidence in the correctness of the idea of zero-point energy.<ref>Stachel et al (2008) Vol. 4: The Swiss Years—Writings, 1912–1914, pp. 270 ff.</ref>

==== Stimulated emission ====
In 1917, at the height of his work on relativity, Einstein published an article in ''Physikalische Zeitschrift'' that proposed the possibility of [[stimulated emission]], the physical process that makes possible the [[maser]] and the [[laser]].<ref>Einstein (1917b).</ref>
This article showed that the statistics of absorption and emission of light would only be consistent with Planck's distribution law if the emission of light into a mode with n photons would be enhanced statistically compared to the emission of light into an empty mode. This paper was enormously influential in the later development of quantum mechanics, because it was the first paper to show that the statistics of atomic transitions had simple laws.<ref>{{Cite book |last1=Duncan |first1=Anthony |url=https://www.worldcat.org/oclc/1119627546 |title=Constructing quantum mechanics. Volume 1, The scaffold : 1900–1923 |last2=Janssen |first2=Michel |date=2019 |publisher=[[Oxford University Press]] |isbn=978-0-19-258422-9 |edition=1st |location=Oxford |pages=133–142 |oclc=1119627546}}</ref>

==== Matter waves ====
Einstein discovered [[Louis de Broglie]]'s work and supported his ideas, which were received skeptically at first. In another major paper from this era, Einstein observed that [[de Broglie waves]] could explain the [[Bohr-Sommerfeld quantization|quantization rules of Bohr and Sommerfeld]]. This paper would inspire Schrödinger's work of 1926.<ref>{{Cite journal |last=Hanle |first=Paul A. |date=July 1979 |title=The Schrödinger-Einstein correspondence and the sources of wave mechanics |url=https://pubs.aip.org/aapt/ajp/article/47/7/644-648/1051199 |journal=American Journal of Physics |language=en |volume=47 |issue=7 |pages=644–648 |doi=10.1119/1.11950 |bibcode=1979AmJPh..47..644H |issn=0002-9505}}</ref><ref>{{Cite journal |last1=Raman |first1=V. V. |last2=Forman |first2=Paul |date=1969 |title=Why Was It Schrödinger Who Developed de Broglie's Ideas? |url=https://www.jstor.org/stable/27757299 |journal=Historical Studies in the Physical Sciences |volume=1 |pages=291–314 |doi=10.2307/27757299 |jstor=27757299 |issn=0073-2672}}</ref>

=== Quantum mechanics ===
==== Einstein's objections to quantum mechanics ====
[[File:NYT May 4, 1935.jpg|thumb|upright|Newspaper headline on 4 May 1935]]
Einstein played a major role in developing quantum theory, beginning with his 1905 paper on the photoelectric effect. However, he became displeased with modern quantum mechanics as it had evolved after 1925, despite its acceptance by other physicists. He was skeptical that the randomness of quantum mechanics was fundamental rather than the result of determinism, stating that God "is not playing at dice".<ref name="zZ2hS"/> Until the end of his life, he continued to maintain that quantum mechanics was incomplete.<ref name="yzZtL"/>

==== Bohr versus Einstein ====
{{Main|Bohr–Einstein debates}}
[[File:Niels Bohr Albert Einstein4 by Ehrenfest cr.jpg|upright|alt=Two men sitting, looking relaxed. A dark-haired Bohr is talking while Einstein looks skeptical.|thumb|Einstein and [[Niels Bohr]], 1925]] The Bohr–Einstein debates were a series of public disputes about quantum mechanics between Einstein and [[Niels Bohr]], who were two of its founders. Their debates are remembered because of their importance to the [[philosophy of science]].<ref name="Bohr1949" /><ref>Einstein (1969).</ref><ref>{{Cite journal |last1=Schlosshauer |first1=Maximilian |last2=Kofler |first2=Johannes |last3=Zeilinger |first3=Anton |date=1 August 2013 |title=A snapshot of foundational attitudes toward quantum mechanics |journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics |volume=44 |issue=3 |pages=222–230 |arxiv=1301.1069 |bibcode=2013SHPMP..44..222S |doi=10.1016/j.shpsb.2013.04.004 |issn=1355-2198 |s2cid=55537196}}</ref> Their debates would influence later [[interpretations of quantum mechanics]].

==== Einstein–Podolsky–Rosen paradox ====
{{Main|EPR paradox}}
Einstein never fully accepted quantum mechanics. While he recognized that it made correct predictions, he believed a more fundamental description of nature must be possible. Over the years he presented multiple arguments to this effect, but the one he preferred most dated to a debate with Bohr in 1930. Einstein suggested a [[Einstein's thought experiments|thought experiment]] in which two objects are allowed to interact and then moved apart a great distance from each other. The quantum-mechanical description of the two objects is a mathematical entity known as a [[wavefunction]]. If the wavefunction that describes the two objects before their interaction is given, then the [[Schrödinger equation]] provides the wavefunction that describes them after their interaction. But because of what would later be called [[quantum entanglement]], measuring one object would lead to an instantaneous change of the wavefunction describing the other object, no matter how far away it is. Moreover, the choice of which measurement to perform upon the first object would affect what wavefunction could result for the second object. Einstein reasoned that no influence could propagate from the first object to the second instantaneously fast. Indeed, he argued, physics depends on being able to tell one thing apart from another, and such instantaneous influences would call that into question. Because the true "physical condition" of the second object could not be immediately altered by an action done to the first, Einstein concluded, the wavefunction could not be that true physical condition, only an incomplete description of it.{{sfnp|Howard|1990}}{{sfnp|Harrigan|Spekkens|2010}}

A more famous version of this argument came in 1935, when Einstein published a paper with [[Boris Podolsky]] and [[Nathan Rosen]] that laid out what would become known as the [[EPR paradox]].<ref>Einstein, Podolsky & Rosen (1935).</ref> In this thought experiment, two particles interact in such a way that the wavefunction describing them is entangled. Then, no matter how far the two particles were separated, a precise position measurement on one particle would imply the ability to predict, perfectly, the result of measuring the position of the other particle. Likewise, a precise momentum measurement of one particle would result in an equally precise prediction for of the momentum of the other particle, without needing to disturb the other particle in any way. They argued that no action taken on the first particle could instantaneously affect the other, since this would involve information being transmitted faster than light, which is forbidden by the [[theory of relativity]]. They invoked a principle, later known as the "EPR criterion of reality", positing that: {{qi|If, without in any way disturbing a system, we can predict with certainty (i.e., with [[probability]] equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.}} From this, they inferred that the second particle must have a definite value of both position and of momentum prior to either quantity being measured. But quantum mechanics considers these two observables [[Observable#Incompatibility of observables in quantum mechanics|incompatible]] and thus does not associate simultaneous values for both to any system. Einstein, Podolsky, and Rosen therefore concluded that quantum theory does not provide a complete description of reality.{{sfnp|Peres|2002}}

In 1964, [[John Stewart Bell]] carried the analysis of quantum entanglement much further. He deduced that if measurements are performed independently on the two separated particles of an entangled pair, then the assumption that the outcomes depend upon hidden variables within each half implies a mathematical constraint on how the outcomes on the two measurements are correlated. This constraint would later be called a [[Bell inequality]]. Bell then showed that quantum physics predicts correlations that violate this inequality. Consequently, the only way that hidden variables could explain the predictions of quantum physics is if they are "nonlocal", which is to say that somehow the two particles are able to interact instantaneously no matter how widely they ever become separated.{{sfnp|Mermin|1993}}{{sfnp|Penrose|2007}} Bell argued that because an explanation of quantum phenomena in terms of hidden variables would require nonlocality, the EPR paradox {{qi|is resolved in the way which Einstein would have liked least}}.{{sfnp|Bell|1966}}

Despite this, and although Einstein personally found the argument in the EPR paper overly complicated,{{sfnp|Howard|1990}}{{sfnp|Harrigan|Spekkens|2010}} that paper became among the most influential papers published in ''[[Physical Review]]''. It is considered a centerpiece of the development of [[quantum information theory]].{{Sfnp|Fine|2017}}

=== Unified field theory ===
{{Main|Classical unified field theories}}
Encouraged by his success with general relativity, Einstein sought an even more ambitious geometrical theory that would treat gravitation and electromagnetism as aspects of a single entity. In 1950, he described his [[unified field theory]] in a ''[[Scientific American]]'' article titled "On the Generalized Theory of Gravitation".<ref>Einstein (1950).</ref> His attempt to find the most fundamental laws of nature won him praise but not success: a particularly conspicuous blemish of his model was that it did not accommodate the [[strong nuclear force|strong]] and [[weak nuclear force]]s, neither of which was well understood until many years after his death. Although most researchers now believe that Einstein's approach to unifying physics was mistaken, his goal of a [[theory of everything]] is one to which his successors still aspire.<ref>{{Cite journal |last=Goenner |first=Hubert F. M. |date=1 December 2004 |title=On the History of Unified Field Theories |journal=Living Reviews in Relativity |language=en |volume=7 |issue=1 |pages=2 |doi=10.12942/lrr-2004-2 |doi-access=free |issn=1433-8351 |pmc=5256024 |pmid=28179864|bibcode=2004LRR.....7....2G }}</ref>

=== Other investigations ===
{{Main|Einstein's unsuccessful investigations}}
Einstein conducted other investigations that were unsuccessful and abandoned. These pertain to [[force]], [[superconductivity]], and other research.

=== Collaboration with other scientists ===
[[File:Solvay conference 1927.jpg|thumb|The 1927 [[Solvay Conference]] in Brussels, a gathering of the world's top physicists. Einstein is in the center.]]
In addition to longtime collaborators [[Leopold Infeld]], [[Nathan Rosen]], [[Peter Bergmann]] and others, Einstein also had some one-shot collaborations with various scientists.

==== Einstein–de Haas experiment ====
{{Main|Einstein–de Haas effect}}
In 1908, [[Owen Willans Richardson]] predicted that a change in the [[magnetic moment]] of a free body will cause this body to rotate. This effect is a consequence of the [[conservation of angular momentum]] and is strong enough to be observable in [[ferromagnetic materials]].<ref name="Richardson-1908">
{{cite journal
 |last1=Richardson |first1=O. W.
 |year=1908
 |journal=Physical Review
 |title=A Mechanical Effect Accompanying Magnetization
 |url=https://zenodo.org/record/1997325
 |series=Series I
 |volume=26 |issue=3 |pages=248–253
 |bibcode=1908PhRvI..26..248R
 |doi=10.1103/PhysRevSeriesI.26.248
}}</ref> Einstein and [[Wander Johannes de Haas]] published two papers in 1915 claiming the first experimental observation of the effect.<ref name="EdH-1-1915">
{{cite journal
 |last1=Einstein |first1=A.
 |last2=de Haas |first2=W. J.
 |year=1915
 |title=Experimenteller Nachweis der Ampereschen Molekularströme
 |trans-title=Experimental Proof of Ampère's Molecular Currents
 |language=German
 |journal=Deutsche Physikalische Gesellschaft, Verhandlungen
 |volume=17 |pages=152–170
|bibcode=1915DPhyG..17..152E
 }}</ref><ref name="EdH-2-1915">
{{cite journal
 |last1=Einstein |first1=A.
 |last2=de Haas |first2=W. J.
 |year=1915
 |title=Experimental proof of the existence of Ampère's molecular currents
 |journal=Koninklijke Akademie van Wetenschappen te Amsterdam, Proceedings
 |volume=18 |pages=696–711
 |bibcode=1915KNAB...18..696E
 |url=http://www.dwc.knaw.nl/DL/publications/PU00012546.pdf
}}</ref> Measurements of this kind demonstrate that the phenomenon of [[magnetization]] is caused by the alignment ([[Spin polarization|polarization]]) of the [[angular momenta]] of the [[electron]]s in the material along the axis of magnetization. These measurements also allow the separation of the two contributions to the magnetization: that which is associated with the [[Spin (physics)|spin]] and with the orbital motion of the electrons. The Einstein-de Haas experiment is the only experiment concived, realized and published by Albert Einstein himself.

A complete original version of the Einstein-de Haas experimental equipment was donated by [[Geertruida de Haas-Lorentz]], wife of de Haas and daughter of Lorentz, to the [[Ampère Museum]] in Lyon France in 1961 where it is currently on display. It was lost among the museum's holdings and was rediscovered in 2023.<ref>{{Cite journal |last1=San Miguel |first1=Alfonso |last2=Pallandre |first2=Bernard |date=13 March 2024 |title=Revisiting the Einstein-de Haas experiment: the Ampère Museum's hidden treasure |url=https://www.europhysicsnews.org/images/stories/news/epn_Einstein-de_Haas.pdf |journal=Europhysics News |volume=55 |issue=4 |pages=12–14|doi=10.1051/epn/2024409 |bibcode=2024ENews..55...28S }}</ref><ref>{{Cite web |last=Johnston |first=Hamish |date=17 March 2024 |title=Einstein's only experiment is found in French museum |url=https://physicsworld.com/einsteins-only-experiment-is-found-in-french-museum/ |access-date=24 March 2024 |website=Physics World |language=en-GB}}</ref>

==== Einstein as an inventor ====
In 1926, Einstein and his former student [[Leó Szilárd]] co-invented (and in 1930, patented) the [[Einstein refrigerator]]. This [[absorption refrigerator]] was then revolutionary for having no moving parts and using only heat as an input.<ref name="Goettling"/> On 11 November 1930, {{US patent|1781541}} was awarded to Einstein and Leó Szilárd for the refrigerator. Their invention was not immediately put into commercial production, but the most promising of their patents were acquired by the Swedish company [[Electrolux]].{{refn |group=note |In September 2008 it was reported that Malcolm McCulloch of [[Oxford University]] was heading a three-year project to develop more robust appliances that could be used in locales lacking electricity, and that his team had completed a prototype Einstein refrigerator. He was quoted as saying that improving the design and changing the types of gases used might allow the design's efficiency to be quadrupled.<ref>{{Cite news |last=Alok |first=Jha |title=Einstein fridge design can help global cooling |work=The Guardian |date=21 September 2008 |access-date=22 February 2011 |url= https://www.theguardian.com/science/2008/sep/21/scienceofclimatechange.climatechange |archive-url= https://web.archive.org/web/20110124172925/http://www.guardian.co.uk/science/2008/sep/21/scienceofclimatechange.climatechange |archive-date=24 January 2011 |url-status=live}}</ref>}}

Einstein also invented an electromagnetic pump,<ref name="patents.google.com">{{cite web | url=https://patents.google.com/patent/GB303065A/en?oq=GB303065 | title=Electrodynamic movement of fluid metals particularly for refrigerating machines }}</ref> sound reproduction device,<ref>{{cite web | url=https://patents.google.com/patent/DE590783C/en | title=Device, in particular for sound reproduction devices, in which changes in electrical current through magnetostriction cause movements of a magnetic body }}</ref> and several other household devices.<ref>Albert Einstein's patents. 2006. World Pat Inf. 28/2, 159–65. M. Trainer. doi: 10.1016/j.wpi.2005.10.012</ref>