Albert Einstein 14 March 1879 – 18 April 1955) was a German-born theoretical physicist who is widely held as one of the most influential scientists. Best known for developing the theory of relativity, Einstein also made important contributions to quantum mechanics.[1][6] His mass–energy equivalence formula E = mc2, which arises from special relativity, has been called "the world's most famous equation".[7] He received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect",[8] a pivotal step in the development of quantum theory.
Born in the German Empire, Einstein moved to Switzerland in 1895, forsaking his German citizenship (as a subject of the Kingdom of Württemberg)[note 1] the following year. In 1897, at the age of seventeen, he enrolled in the mathematics and physics teaching diploma program at the Swiss federal polytechnic school in Zürich, graduating in 1900. In 1901, he acquired Swiss citizenship, which he kept for the rest of his life. In 1903, he secured a permanent position at the Swiss Patent Office in Bern. In 1905, he submitted a successful PhD dissertation to the University of Zurich. In 1914, he moved to Berlin in order to join the Prussian Academy of Sciences and the Humboldt University of Berlin. In 1917, he became director of the Kaiser Wilhelm Institute for Physics; he also became a German citizen again, this time as a subject of the Kingdom of Prussia.[note 1] In 1933, while Einstein was visiting the United States, Adolf Hitler came to power in Germany. Horrified by the Nazi war of extermination against his fellow Jews,[9] Einstein decided to remain in the US, and was granted American citizenship in 1940.[10] On the eve of World War II, he endorsed a letter to President Franklin D. Roosevelt alerting him to the potential German nuclear weapons program and recommended that the US begin similar research. Einstein supported the Allies but generally viewed the idea of nuclear weapons with great dismay.[11]
Einstein's work is also known for its influence on the philosophy of science.[12][13] In 1905, he published four groundbreaking papers, sometimes described as his annus mirabilis (miracle year).[14] These papers outlined a theory of the photoelectric effect, explained Brownian motion, introduced his special theory of relativity—a theory which addressed the inability of classical mechanics to account satisfactorily for the behavior of the electromagnetic field—and demonstrated that if the special theory is correct, mass and energy are equivalent to each other. In 1915, he proposed a general theory of relativity that extended his system of mechanics to incorporate gravitation. A cosmological paper that he published the following year laid out the implications of general relativity for the modeling of the structure and evolution of the universe as a whole.[15][16]
In the middle part of his career, Einstein made important contributions to statistical mechanics and quantum theory. Especially notable was his work on the quantum physics of radiation, in which light consists of particles, subsequently called photons. With the Indian physicist Satyendra Nath Bose, he laid the groundwork for Bose-Einstein statistics. For much of the last phase of his academic life, Einstein worked on two endeavors that proved ultimately unsuccessful. First, he advocated against quantum theory's introduction of fundamental randomness into science's picture of the world, objecting that "God does not play dice".[17] Second, he attempted to devise a unified field theory by generalizing his geometric theory of gravitation to include electromagnetism too. As a result, he became increasingly isolated from the mainstream modern physics. His intellectual achievements and originality made Einstein broadly synonymous with genius.[18] In 1999, he was named Time's Person of the Century.[19] In a 1999 poll of 130 leading physicists worldwide by the British journal Physics World, Einstein was ranked the greatest physicist of all time.[20]
Life and career
Childhood, youth and education
See also: Einstein family
A young boy with short hair and a round face, wearing a white collar and large bow, with vest, coat, skirt, and high boots. He is leaning against an ornate chair.
Einstein in 1882, age 3
Albert Einstein was born in Ulm,[21] in the Kingdom of Württemberg in the German Empire, on 14 March 1879.[22][23] His parents, secular Ashkenazi Jews, were Hermann Einstein, a salesman and engineer, and Pauline Koch. In 1880, the family moved to Munich's borough of Ludwigsvorstadt-Isarvorstadt, where Einstein's father and his uncle Jakob founded Elektrotechnische Fabrik J. Einstein & Cie, a company that manufactured electrical equipment based on direct current.[21] He often related a formative event from his youth, when he was sick in bed and his father brought him a compass. This sparked his lifelong fascination with electromagnetism. He realized that "Something deeply hidden had to be behind things."[24]
Albert attended St. Peter‘s Catholic elementary school in Munich from the age of five. When he was eight, he was transferred to the Luitpold Gymnasium, where he received advanced primary and then secondary school education.[25]
In 1894, Hermann and Jakob's company tendered for a contract to install electric lighting in Munich, but without success—they lacked the capital that would have been required to update their technology from direct current to the more efficient, alternating current alternative.[26] The failure of their bid forced them to sell their Munich factory and search for new opportunities elsewhere. The Einstein family moved to Italy, first to Milan and a few months later to Pavia, where they settled in Palazzo Cornazzani.[27] Einstein, then fifteen, stayed behind in Munich in order to finish his schooling. His father wanted him to study electrical engineering, but he was a fractious pupil who found the Gymnasium's regimen and teaching methods far from congenial. He later wrote that the school's policy of strict rote learning was harmful to creativity. At the end of December 1894, a letter from a doctor persuaded the Luitpold's authorities to release him from its care, and he joined his family in Pavia.[28] While in Italy as a teenager, he wrote an essay entitled "On the Investigation of the State of the Ether in a Magnetic Field".[29][30]
Einstein excelled at physics and mathematics from an early age, and soon acquired the mathematical expertise normally only found in a child several years his senior. He began teaching himself algebra, calculus and Euclidean geometry when he was twelve; he made such rapid progress that he discovered an original proof of the Pythagorean theorem before his thirteenth birthday.[31][32][33] A family tutor, Max Talmud, said that only a short time after he had given the twelve year old Einstein a geometry textbook, the boy "had worked through the whole book. He thereupon devoted himself to higher mathematics ... Soon the flight of his mathematical genius was so high I could not follow."[34] Einstein recorded that he had "mastered integral and differential calculus" while still just fourteen.[32] His love of algebra and geometry was so great that at twelve, he was already confident that nature could be understood as a "mathematical structure".[34]
Studio photo of a boy seated in a relaxed posture and wearing a suit, posed in front of a backdrop of scenery.
Einstein in 1893, age 14
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At thirteen, when his range of enthusiasms had broadened to include music and philosophy,[35] Talmud introduced Einstein to Kant's Critique of Pure Reason. Kant became his favorite philosopher; according to Talmud, "At the time he was still a child, only thirteen years old, yet Kant's works, incomprehensible to ordinary mortals, seemed to be clear to him."[34]
Einstein's matriculation certificate at the age of 17. The heading translates as "The Education Committee of the Canton of Aargau". His scores were German 5, French 3, Italian 5, History 6, Geography 4, Algebra 6, Geometry 6, Descriptive Geometry 6, Physics 6, Chemistry 5, Natural History 5, Art Drawing 4, Technical Drawing 4. 6 = very good, 5 = good, 4 = sufficient, 3 = insufficient, 2 = poor, 1 = very poor.
Einstein's Matura certificate, 1896[note 2]
In 1895, at the age of sixteen, Einstein sat the entrance examination for the federal polytechnic school (later the Eidgenössische Technische Hochschule, ETH) in Zürich, Switzerland. He failed to reach the required standard in the general part of the test,[36] but performed with distinction in physics and mathematics.[37] On the advice of the polytechnic's principal, he completed his secondary education at the Argovian cantonal school (a gymnasium) in Aarau, Switzerland, graduating in 1896.[38] While lodging in Aarau with the family of Jost Winteler, he fell in love with Winteler's daughter, Marie. (His sister, Maja, later married Winteler's son Paul.[39])
In January 1896, with his father's approval, Einstein renounced his citizenship of the German Kingdom of Württemberg in order to avoid conscription into military service.[40] The Matura (graduation for the successful completion of higher secondary schooling), awarded to him in September 1896, acknowledged him to have performed well across most of the curriculum, allotting him a top grade of 6 for history, physics, algebra, geometry, and descriptive geometry.[41] At seventeen, he enrolled in the four-year mathematics and physics teaching diploma program at the federal polytechnic school. Marie Winteler, a year older than him, took up a teaching post in Olsberg, Switzerland.[39]
The five other polytechnic school freshmen following the same course as Einstein included just one woman, a twenty year old Serbian, Mileva Marić. Over the next few years, the pair spent many hours discussing their shared interests and learning about topics in physics that the polytechnic school's lectures did not cover. In his letters to Marić, Einstein confessed that exploring science with her by his side was much more enjoyable than reading a textbook in solitude. Eventually the two students became not only friends but also lovers.[42]
Historians of physics are divided on the question of the extent to which Marić contributed to the insights of Einstein's annus mirabilis publications. There is at least some evidence that he was influenced by her scientific ideas,[42][43][44] but there are scholars who doubt whether her impact on his thought was of any great significance at all.[45][46][47][48]
Marriages, relationships and children
Albert Einstein and Mileva Marić Einstein, 1912
Albert Einstein and Elsa Einstein, 1930
Correspondence between Einstein and Marić, discovered and published in 1987, revealed that in early 1902, while Marić was visiting her parents in Novi Sad, she gave birth to a daughter, Lieserl. When Marić returned to Switzerland it was without the child, whose fate is uncertain. A letter of Einstein's that he wrote in September 1903 suggests that the girl was either given up for adoption or died of scarlet fever in infancy.[49][50]
Einstein and Marić married in January 1903. In May 1904, their son Hans Albert was born in Bern, Switzerland. Their son Eduard was born in Zürich in July 1910. In letters that Einstein wrote to Marie Winteler in the months before Eduard's arrival, he described his love for his wife as "misguided" and mourned the "missed life" that he imagined he would have enjoyed if he had married Winteler instead: "I think of you in heartfelt love every spare minute and am so unhappy as only a man can be."[51]
In 1912, Einstein entered into a relationship with Elsa Löwenthal, who was both his first cousin on his mother's side and his second cousin on his father's.[52][53][54] When Marić learned of his infidelity soon after moving to Berlin with him in April 1914, she returned to Zürich, taking Hans Albert and Eduard with her.[42] Einstein and Marić were granted a divorce on 14 February 1919 on the grounds of having lived apart for five years.[55][56] As part of the divorce settlement, Einstein agreed that if he were to win a Nobel Prize, he would give the money that he received to Marić; he won the prize two years later.[57]
Einstein married Löwenthal in 1919.[58][59] In 1923, he began a relationship with a secretary named Betty Neumann, the niece of his close friend Hans Mühsam.[60][61][62][63] Löwenthal nevertheless remained loyal to him, accompanying him when he emigrated to the United States in 1933. In 1935, she was diagnosed with heart and kidney problems. She died in December 1936.[64]
A volume of Einstein's letters released by Hebrew University of Jerusalem in 2006[65] added further names to the catalog of women with whom he was romantically involved. They included Margarete Lebach (a married Austrian),[66] Estella Katzenellenbogen (the rich owner of a florist business), Toni Mendel (a wealthy Jewish widow) and Ethel Michanowski (a Berlin socialite), with whom he spent time and from whom he accepted gifts while married to Löwenthal.[67][68] After being widowed, Einstein was briefly in a relationship with Margarita Konenkova, thought by some to be a Russian spy; her husband, the Russian sculptor Sergei Konenkov, created the bronze bust of Einstein at the Institute for Advanced Study at Princeton.[69][70]
Following an episode of acute mental illness at about the age of twenty, Einstein's son Eduard was diagnosed with schizophrenia.[71] He spent the remainder of his life either in the care of his mother or in temporary confinement in an asylum. After her death, he was committed permanently to Burghölzli, the Psychiatric University Hospital in Zürich.[72]
1902–1909: Assistant at the Swiss Patent Office
Einstein graduated from the federal polytechnic school in 1900, duly certified as competent to teach mathematics and physics.[73] His successful acquisition of Swiss citizenship in February 1901[74] was not followed by the usual sequel of conscription; the Swiss authorities deemed him medically unfit for military service. He found that Swiss schools too appeared to have no use for him, failing to offer him a teaching position despite the almost two years that he spent applying for one. Eventually it was with the help of Marcel Grossmann's father that he secured a post in Bern at the Swiss Patent Office,[75][76] as an assistant examiner – level III.[77][78]
Patent applications that landed on Einstein's desk for his evaluation included ideas for a gravel sorter and an electric typewriter.[78] His employers were pleased enough with his work to make his position permanent in 1903, although they did not think that he should be promoted until he had "fully mastered machine technology".[79] It is conceivable that his labors at the patent office had a bearing on his development of his special theory of relativity. He arrived at his revolutionary ideas about space, time and light through thought experiments about the transmission of signals and the synchronization of clocks, matters which also figured in some of the inventions submitted to him for assessment.[14]
In 1902, Einstein and some friends whom he had met in Bern formed a group that held regular meetings to discuss science and philosophy. Their choice of a name for their club, the Olympia Academy, was an ironic comment upon its far from Olympian status. Sometimes they were joined by Marić, who limited her participation in their proceedings to careful listening.[80] The thinkers whose works they reflected upon included Henri Poincaré, Ernst Mach and David Hume, all of whom significantly influenced Einstein's own subsequent ideas and beliefs.[81]
1900–1905: First scientific papers
Cover image of the PhD dissertation of Albert Einstein
Einstein's 1905 dissertation, Eine neue Bestimmung der Moleküldimensione ("A new determination of molecular dimensions")
Einstein's first paper, "Folgerungen aus den Capillaritätserscheinungen" ("Conclusions drawn from the phenomena of capillarity"), in which he proposed a model of intermolecular attraction that he afterwards disavowed as worthless, was published in the journal Annalen der Physik in 1901.[82][83] His 24-page doctoral dissertation also addressed a topic in molecular physics. Titled "Eine neue Bestimmung der Moleküldimensionen" ("A New Determination of Molecular Dimensions") and dedicated to his friend Marcel Grossman, it was completed on 30 April 1905[84] and approved by Professor Alfred Kleiner of the University of Zurich three months later. (Einstein was formally awarded his PhD on 15 January 1906.)[84][85][86] Four other pieces of work that Einstein completed in 1905—his famous papers on the photoelectric effect, Brownian motion, his special theory of relativity and the equivalence of mass and energy—have led to the year being celebrated as an annus mirabilis for physics akin to 1666 (the year in which Isaac Newton experienced his greatest epiphanies). The publications deeply impressed Einstein's contemporaries.[87]
1908–1933: Early academic career
Einstein's sabbatical as a civil servant approached its end in 1908, when he secured a junior teaching position at the University of Bern. In 1909, a lecture on relativistic electrodynamics that he gave at the University of Zurich, much admired by Alfred Kleiner, led to Zürich's luring him away from Bern with a newly created associate professorship.[88] Promotion to a full professorship followed in April 1911, when he accepted a chair at the German Charles-Ferdinand University in Prague, a move which required him to become an Austrian citizen of the Austro-Hungarian Empire.[89][90] His time in Prague saw him producing eleven research papers.[91]
Head and shoulders shot of a young, moustached man with dark, curly hair wearing a plaid suit and vest, striped shirt, and a dark tie.
Einstein in 1904, age 25
Three young men in suits with high white collars and bow ties, sitting.
Olympia Academy founders: Conrad Habicht, Maurice Solovine, and Einstein
In July 1912, he returned to his alma mater, the ETH Zurich, to take up a chair in theoretical physics. His teaching activities there centred on thermodynamics and analytical mechanics, and his research interests included the molecular theory of heat, continuum mechanics and the development of a relativistic theory of gravitation. In his work on the latter topic, he was assisted by his friend, Marcel Grossmann, whose knowledge of the kind of mathematics required was greater than his own.[92]
In the spring of 1913, two German visitors, Max Planck and Walther Nernst, called upon Einstein in Zürich in the hope of persuading him to relocate to Berlin.[93] They offered him membership of the Prussian Academy of Sciences, the directorship of the planned Kaiser Wilhelm Institute for Physics and a chair at the Humboldt University of Berlin that would allow him to pursue his research supported by a professorial salary but with no teaching duties to burden him.[53] Their invitation was all the more appealing to him because Berlin happened to be the home of his latest girlfriend, Elsa Löwenthal.[93] He duly joined the Academy on 24 July 1913,[94] and moved into an apartment in the Berlin district of Dahlem on 1 April 1914.[53] He was installed in his Humboldt University position shortly thereafter.[94]
The outEinstein had been sympathetic toward vegetarianism for a long time. In a letter in 1930 to Hermann Huth, vice-president of the German Vegetarian Federation (Deutsche Vegetarier-Bund), he wrote:
Although I have been prevented by outward circumstances from observing a strictly vegetarian diet, I have long been an adherent to the cause in principle. Besides agreeing with the aims of vegetarianism for aesthetic and moral reasons, it is my view that a vegetarian manner of living by its purely physical effect on the human temperament would most beneficially influence the lot of mankind.[201]
He became a vegetarian himself only during the last part of his life. In March 1954 he wrote in a letter: "So I am living without fats, without meat, without fish, but am feeling quite well this way. It almost seems to me that man was not born to be a carnivore."[202]
Love of music
Einstein playing the violin (image published in 1927)
Einstein developed an appreciation for music at an early age. In his late journals he wrote:
If I were not a physicist, I would probably be a musician. I often think in music. I live my daydreams in music. I see my life in terms of music ... I get most joy in life out of music.[203][204]
His mother played the piano reasonably well and wanted her son to learn the violin, not only to instill in him a love of music but also to help him assimilate into German culture. According to conductor Leon Botstein, Einstein began playing when he was 5. However, he did not enjoy it at that age.[205]
When he turned 13, he discovered the violin sonatas of Mozart, whereupon he became enamored of Mozart's compositions and studied music more willingly. Einstein taught himself to play without "ever practicing systematically". He said that "love is a better teacher than a sense of duty".[205] At the age of 17, he was heard by a school examiner in Aarau while playing Beethoven's violin sonatas. The examiner stated afterward that his playing was "remarkable and revealing of 'great insight'". What struck the examiner, writes Botstein, was that Einstein "displayed a deep love of the music, a quality that was and remains in short supply. Music possessed an unusual meaning for this student."[205]
Music took on a pivotal and permanent role in Einstein's life from that period on. Although the idea of becoming a professional musician himself was not on his mind at any time, among those with whom Einstein played chamber music were a few professionals, including Kurt Appelbaum, and he performed for private audiences and friends. Chamber music had also become a regular part of his social life while living in Bern, Zürich, and Berlin, where he played with Max Planck and his son, among others. He is sometimes erroneously credited as the editor of the 1937 edition of the Köchel catalog of Mozart's work; that edition was prepared by Alfred Einstein, who may have been a distant relation.[206][207]
In 1931, while engaged in research at the California Institute of Technology, he visited the Zoellner family conservatory in Los Angeles, where he played some of Beethoven and Mozart's works with members of the Zoellner Quartet.[208][209] Near the end of his life, when the young Juilliard Quartet visited him in Princeton, he played his violin with them, and the quartet was "impressed by Einstein's level of coordination and intonation".[205]
Death
On 17 April 1955, Einstein experienced internal bleeding caused by the rupture of an abdominal aortic aneurysm, which had previously been reinforced surgically by Rudolph Nissen in 1948.[210] He took the draft of a speech he was preparing for a television appearance commemorating the state of Israel's seventh anniversary with him to the hospital, but he did not live to complete it.[211]
Einstein refused surgery, saying, "I want to go when I want. It is tasteless to prolong life artificially. I have done my share; it is time to go. I will do it elegantly."[212] He died in the Princeton Hospital early the next morning at the age of 76, having continued to work until near the end.[213]
During the autopsy, the pathologist Thomas Stoltz Harvey removed Einstein's brain for preservation without the permission of his family, in the hope that the neuroscience of the future would be able to discover what made Einstein so intelligent.[214] Einstein's remains were cremated in Trenton, New Jersey,[215] and his ashes were scattered at an undisclosed location.[216][217]
In a memorial lecture delivered on 13 December 1965 at UNESCO headquarters, nuclear physicist J. Robert Oppenheimer summarized his impression of Einstein as a person: "He was almost wholly without sophistication and wholly without worldliness ... There was always with him a wonderful purity at once childlike and profoundly stubborn."[218]
Einstein bequeathed his personal archives, library, and intellectual assets to the Hebrew University of Jerusalem in Israel.[219]
Scientific career
Throughout his life, Einstein published hundreds of books and articles.[21][220] He published more than 300 scientific papers and 150 non-scientific ones.[15][220] On 5 December 2014, universities and archives announced the release of Einstein's papers, comprising more than 30,000 unique documents.[221][222] 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.[223][224]
Statistical mechanics
Thermodynamic fluctuations and statistical physics
Main articles: Statistical mechanics, thermal fluctuations, and statistical physics
Einstein's first paper[82][225] 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 atomic 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.[225]
Theory of critical opalescence
Main article: 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.[226] 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 are four articles pertaining to the photoelectric effect (which gave rise to quantum theory), Brownian motion, the special theory of relativity, and E = mc2 that Einstein published in the Annalen der Physik scientific journal in 1905. These four works contributed substantially to the foundation of modern physics and changed views on space, time, and matter. The four papers are:
Title (translated) Area of focus Received Published Significance
"On a Heuristic Viewpoint Concerning the Production and Transformation of Light"[227] Photoelectric effect 18 March 9 June Resolved an unsolved puzzle by suggesting that energy is exchanged only in discrete amounts (quanta).[228] This idea was pivotal to the early development of quantum theory.[229]
"On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat"[230] 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"[231] Special relativity 30 June 26 September Reconciled 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.[232][specify] Discredited the concept of a "luminiferous ether".[233]
"Does the Inertia of a Body Depend Upon Its Energy Content?"[234] Matter–energy equivalence 27 September 21 November Equivalence of matter and energy, E = mc2, the existence of "rest energy", and the basis of nuclear energy.
Special relativity
Main article: History of special relativity
Einstein's "Zur Elektrodynamik bewegter Körper"[231] ("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.[235] 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 slow down, and the body itself would 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.[note 4]
In his paper on mass–energy equivalence, Einstein produced E = mc2 as a consequence of his special relativity equations.[236] Einstein's 1905 work on relativity remained controversial for many years, but was accepted by leading physicists, starting with Max Planck.[note 5][237]
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.[238]
General relativity
General relativity and the equivalence principle
Main article: History of general relativity
See also: Theory of relativity and Einstein field equations
Black circle covering the sun, rays visible around it, in a dark sky.
Eddington's photograph 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.[239]
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.[240] 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.[241][242]
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.[243]
Gravitational waves
In 1916, Einstein predicted gravitational waves,[244][245] ripples in the curvature of spacetime which propagate as waves, 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 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.[246] The explanation for the decay in their orbital period was that they were emitting gravitational waves.[246][247] Einstein's prediction was confirmed on 11 February 2016, when researchers at LIGO published the first observation of gravitational waves,[248] detected on Earth on 14 September 2015, nearly one hundred years after the prediction.[246][249][250][251][252]
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.[253]
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[254] and abandoned the theory in November 1915.
Physical cosmology
Main article: Physical cosmology
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.[255] 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.[256][257]
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[258][259] and the Einstein–de Sitter universe of 1932.[260][261] In each of these models, Einstein discarded the cosmological constant, claiming that it was "in any case theoretically unsatisfactory".[258][259][262]
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.[263]
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.[264][265] 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.[266][267] As he stated in the paper, "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.[268][269] However, Einstein's steady-state model contained a fundamental flaw and he quickly abandoned the idea.[266][267][270]
Energy momentum pseudotensor
Main article: 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 with translation invariance, but general covariance makes translation invariance into something of a gauge symmetry. The energy and momentum derived within general relativity by Noether's prescriptions do not make a real tensor for this reason.[271]
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.[272]
Wormholes
In 1935, Einstein collaborated with Nathan Rosen to produce a model of a wormhole, often called Einstein–Rosen bridges.[273][274] 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 holes 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.[275]
Einstein–Cartan theory
Main article: Einstein–Cartan theory
Einstein, sitting at a table, looks up from the papers he is reading and into the camera.
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. This modification was made by Einstein and Cartan in the 1920s.
Equations of motion
Main article: 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: "Spacetime tells matter how to move; matter tells spacetime how to curve.