Albert Einstein (1879-1955)

Letter from Albert Einstein to commemorate Tesla’s 75th birthday, 1931
Letter from Albert Einstein to commemorate Tesla’s 75th birthday, 1931


Dear Mr. Tesla, I am pleased to hear that you are celebrating your 75th birthday and that you as a successful pioneer in the field if high-frequency currents, the wonderful development of this area of technology have allowed to experience. I congratulate you on the great success of your life's work.


Albert Einstein


Albert Einstein (/ˈælbərt ˈaɪnstaɪn/; German: [ˈalbɐt ˈaɪnʃtaɪn] ( listen); 14 March 1879 – 18 April 1955) was a German-born theoretical physicist. He developed the general theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).[2][3] He is best known for his mass–energy equivalence formula E = mc2 (which has been dubbed "the world's most famous equation").[4] 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".[5] The latter was pivotal in establishing quantum theory.


Near the beginning of his career, Einstein thought that Newtonian mechanics was no longer enough to reconcile the laws of classical mechanics with the laws of the electromagnetic field. This led to the development of his special theory of relativity. He realized, however, that the principle of relativity could also be extended to gravitational fields, and with his subsequent theory of gravitation in 1916, he published a paper on the general theory of relativity. He continued to deal with problems of statistical mechanics and quantum theory, which led to his explanations of particle theory and the motion of molecules. He also investigated the thermal properties of light which laid the foundation of the photon theory of light. In 1917, Einstein applied the general theory of relativity to model the large-scale structure of the universe.[6]


He was visiting the United States when Adolf Hitler came to power in 1933 and did not go back to Germany, where he had been a professor at the Berlin Academy of Sciences. He settled in the U.S., becoming an American citizen in 1940.[7] On the eve of World War II, he endorsed a letter to President Franklin D. Roosevelt alerting him to the potential development of "extremely powerful bombs of a new type" and recommending that the U.S. begin similar research. This eventually led to what would become the Manhattan Project. Einstein supported defending the Allied forces, but largely denounced the idea of using the newly discovered nuclear fission as a weapon. Later, with the British philosopher Bertrand Russell, Einstein signed the Russell–Einstein Manifesto, which highlighted the danger of nuclear weapons. Einstein was affiliated with the Institute for Advanced Study in Princeton, New Jersey, until his death in 1955.


Einstein published more than 300 scientific papers along with over 150 non-scientific works.[6][8] His great intellectual achievements and originality have made the word "Einstein" synonymous with genius.[9]




Early life and education


Albert Einstein was born in Ulm, in the Kingdom of Württemberg in the German Empire on 14 March 1879.[10] His father was Hermann Einstein, a salesman and engineer. His mother was Pauline Einstein (née Koch). In 1880, the family moved to Munich, where his father and his uncle founded Elektrotechnische Fabrik J. Einstein & Cie, a company that manufactured electrical equipment based on direct current.[10]


The Einsteins were non-observant Ashkenazi Jews. Albert attended a Catholic elementary school from the age of five for three years. At the age of eight, he was transferred to the Luitpold Gymnasium (now known as the Albert Einstein Gymnasium), where he received advanced primary and secondary school education until he left Germany seven years later.[11] Contrary to popular suggestions that he had struggled with early speech difficulties, the Albert Einstein Archives indicate he excelled at the first school that he attended.[12] He was right-handed;[12][13] there appears to be no evidence for the widespread popular belief[14] that he was left-handed.


His father once showed him a pocket compass; Einstein realized that there must be something causing the needle to move, despite the apparent "empty space".[15] As he grew, Einstein built models and mechanical devices for fun and began to show a talent for mathematics.[10] When Einstein was ten years old, Max Talmud (later changed to Max Talmey), a poor Jewish medical student from Poland, was introduced to the Einstein family by his brother. During weekly visits over the next five years, he gave the boy popular books on science, mathematical texts and philosophical writings. These included Immanuel Kant's Critique of Pure Reason, and Euclid's Elements (which Einstein called the "holy little geometry book").[16][17][fn 1]


In 1894, his father's company failed: direct current (DC) lost the War of Currents to alternating current (AC). In search of business, the Einstein family moved to Italy, first to Milan and then, a few months later, to Pavia. When the family moved to Pavia, Einstein stayed in Munich to finish his studies at the Luitpold Gymnasium. His father intended for him to pursue electrical engineering, but Einstein clashed with authorities and resented the school's regimen and teaching method. He later wrote that the spirit of learning and creative thought were lost in strict rote learning. At the end of December 1894, he travelled to Italy to join his family in Pavia, convincing the school to let him go by using a doctor's note.[19] It was during his time in Italy that he wrote a short essay with the title "On the Investigation of the State of the Ether in a Magnetic Field."[20][21]


In 1895, at the age of sixteen, Einstein sat the entrance examinations for the Swiss Federal Polytechnic in Zürich (later the Eidgenössische Technische Hochschule ETH). He failed to reach the required standard in the general part of the examination,[22] but obtained exceptional grades in physics and mathematics.[23] On the advice of the Principal of the Polytechnic, he attended the Aargau Cantonal School in Aarau, Switzerland, in 1895–96 to complete his secondary schooling. While lodging with the family of Professor Jost Winteler, he fell in love with Winteler's daughter, Marie. (Albert's sister Maja later married Wintelers' son Paul.)[24] In January 1896, with his father's approval, he renounced his citizenship in the German Kingdom of Württemberg to avoid military service.[25] In September 1896, he passed the Swiss Matura with mostly good grades, including a top grade of 6 in physics and mathematical subjects, on a scale of 1-6,[26] and, though only seventeen, enrolled in the four-year mathematics and physics teaching diploma program at the Zürich Polytechnic. Marie Winteler moved to Olsberg, Switzerland for a teaching post.


Einstein's future wife, Mileva Marić, also enrolled at the Polytechnic that same year, the only woman among the six students in the mathematics and physics section of the teaching diploma course. Over the next few years, Einstein and Marić's friendship developed into romance, and they read books together on extra-curricular physics in which Einstein was taking an increasing interest. In 1900, Einstein was awarded the Zürich Polytechnic teaching diploma, but Marić failed the examination with a poor grade in the mathematics component, theory of functions.[27] There have been claims that Marić collaborated with Einstein on his celebrated 1905 papers,[28][29] but historians of physics who have studied the issue find no evidence that she made any substantive contributions.[30][31][32][33]



Marriages and children


With the discovery and publication in 1987 of an early correspondence between Einstein and Marić it became known that they had a daughter they called "Lieserl" in their letters, born in early 1902 in Novi Sad where Marić was staying with her parents. Marić returned to Switzerland without the child, whose real name and fate are unknown. Einstein probably never saw his daughter, and the contents of a letter he wrote to Marić in September 1903 suggest that she was either adopted or died of scarlet fever in infancy.[34][35]


Einstein and Marić married in January 1903. In May 1904, the couple's first son, Hans Albert Einstein, was born in Bern, Switzerland. Their second son, Eduard, was born in Zurich in July 1910. In 1914, Einstein moved to Berlin, while his wife remained in Zurich with their sons. They divorced on 14 February 1919, having lived apart for five years.


Einstein married Elsa Löwenthal on 2 June 1919, after having had a relationship with her since 1912. She was his first cousin maternally and his second cousin paternally. In 1933, they emigrated to the United States. In 1935, Elsa Einstein was diagnosed with heart and kidney problems and died in December 1936.[36]



Patent office


After graduating, Einstein spent almost two frustrating years searching for a teaching post. He acquired Swiss citizenship in February 1901,[37] but was not conscripted for medical reasons. With the help of Marcel Grossmann's father Einstein secured a job in Bern at the Federal Office for Intellectual Property, the patent office,[38] as an assistant examiner.[39] He evaluated patent applications for electromagnetic devices. In 1903, Einstein's position at the Swiss Patent Office became permanent, although he was passed over for promotion until he "fully mastered machine technology".[40]


Much of his work at the patent office related to questions about transmission of electric signals and electrical-mechanical synchronization of time, two technical problems that show up conspicuously in the thought experiments that eventually led Einstein to his radical conclusions about the nature of light and the fundamental connection between space and time.[41]


With a few friends he had met in Bern, Einstein started a small discussion group, self-mockingly named "The Olympia Academy", which met regularly to discuss science and philosophy. Their readings included the works of Henri Poincaré, Ernst Mach, and David Hume, which influenced his scientific and philosophical outlook.



Academic career


In 1901, his paper "Folgerungen aus den Capillaritätserscheinungen" ("Conclusions from the Capillarity Phenomena") was published in the prestigious Annalen der Physik.[42][43] On 30 April 1905, Einstein completed his thesis, with Alfred Kleiner, Professor of Experimental Physics, serving as pro-forma advisor. Einstein was awarded a PhD by the University of Zürich. His dissertation was entitled "A New Determination of Molecular Dimensions."[44][45] This paper included Einstein's initial estimates of Avogadro constant as 2.2×1023 based on diffusion coefficients and viscosities of sugar solutions in water.[46] That same year, which has been called Einstein's annus mirabilis (miracle year), he published four groundbreaking papers, on the photoelectric effect, Brownian motion, special relativity, and the equivalence of mass and energy, which were to bring him to the notice of the academic world.


By 1908, he was recognized as a leading scientist, and he was appointed lecturer at the University of Bern. The following year, he quit the patent office and the lectureship to take the position of physics docent[47] at the University of Zürich. He became a full professor at Charles-Ferdinand University in Prague in 1911. Also in 1911, corrections of algebraic errors in his thesis brought Einstein's Avogadro constant estimate to 6.6×1023. In 1914, he returned to Germany after being appointed director of the Kaiser Wilhelm Institute for Physics (1914–1932)[48] and a professor at the Humboldt University of Berlin, with a special clause in his contract that freed him from most teaching obligations. He became a member of the Prussian Academy of Sciences. In 1916, Einstein was appointed president of the German Physical Society (1916–1918).[49][50]


During 1911, he had calculated that, based on his new theory of general relativity, light from another star would be bent by the Sun's gravity. That prediction was claimed confirmed by observations made by a British expedition led by Sir Arthur Eddington during the solar eclipse of 29 May 1919. International media reports of this made Einstein world famous. On 7 November 1919, the leading British newspaper The Times printed a banner headline that read: "Revolution in Science – New Theory of the Universe – Newtonian Ideas Overthrown".[51] Much later, questions were raised whether the measurements had been accurate enough to support Einstein's theory. In 1980 historians John Earman and Clark Glymour published an analysis suggesting that Eddington had suppressed unfavorable results.[52] The two reviewers found possible flaws in Eddington's selection of data, but their doubts, although widely quoted and, indeed, now with a "mythical" status almost equivalent to the status of the original observations, have not been confirmed.[53][54] Eddington's selection from the data seems valid and his team indeed made astronomical measurements verifying the theory.[55]


In 1921, Einstein was awarded the Nobel Prize in Physics for his explanation of the photoelectric effect, as relativity was considered still somewhat controversial. He also received the Copley Medal from the Royal Society in 1925.[2]



Travels abroad


Einstein visited New York City for the first time on 2 April 1921, where he received an official welcome by Mayor John Francis Hylan, followed by three weeks of lectures and receptions. He went on to deliver several lectures at Columbia University and Princeton University, and in Washington he accompanied representatives of the National Academy of Science on a visit to the White House. On his return to Europe he was the guest of the British statesman and philosopher Viscount Haldane in London, where he met several renowned scientific, intellectual and political figures, and delivered a lecture at King's College.[56]


In 1922, he traveled throughout Asia and later to Palestine, as part of a six-month excursion and speaking tour. His travels included Singapore, Ceylon, and Japan, where he gave a series of lectures to thousands of Japanese. His first lecture in Tokyo lasted four hours, after which he met the emperor and empress at the Imperial Palace where thousands came to watch. Einstein later gave his impressions of the Japanese in a letter to his sons:[57]:307 "Of all the people I have met, I like the Japanese most, as they are modest, intelligent, considerate, and have a feel for art."[57]:308


On his return voyage, he also visited Palestine for 12 days in what would become his only visit to that region. "He was greeted with great British pomp, as if he were a head of state rather than a theoretical physicist", writes Isaacson. This included a cannon salute upon his arrival at the residence of the British high commissioner, Sir Herbert Samuel. During one reception given to him, the building was "stormed by throngs who wanted to hear him". In Einstein's talk to the audience, he expressed his happiness over the event:


"I consider this the greatest day of my life. Before, I have always found something to regret in the Jewish soul, and that is the forgetfulness of its own people. Today, I have been made happy by the sight of the Jewish people learning to recognize themselves and to make themselves recognized as a force in the world".[58]:308



Emigration to U.S. in 1933


In February 1933 while on a visit to the United States, Einstein decided not to return to Germany due to the rise to power of the Nazis under Germany's new chancellor, Adolf Hitler.[59][60] He visited American universities in early 1933 where he undertook his third two-month visiting professorship at the California Institute of Technology in Pasadena. He and his wife Elsa returned by ship to Belgium at the end of March. During the voyage they were informed that their cottage was raided by the Nazis and his personal sailboat had been confiscated. Upon landing in Antwerp on 28 March, he immediately went to the German consulate where he turned in his passport and formally renounced his German citizenship.[58] A few years later, the Nazis sold his boat and turned his cottage into an Aryan youth camp.[61]


In early April 1933, he learned that the new German government had passed laws barring Jews from holding any official positions, including teaching at universities.[58] A month later, Einstein's works were among those targeted by Nazi book burnings, and Nazi propaganda minister Joseph Goebbels proclaimed, "Jewish intellectualism is dead."[58] Einstein also learned that his name was on a list of assassination targets, with a "$5,000 bounty on his head."[58] One German magazine included him in a list of enemies of the German regime with the phrase, "not yet hanged".[58]


He resided in Belgium for some months, before temporarily living in England.[62][63] In a letter to his friend, physicist Max Born, who also emigrated from Germany and lived in England, Einstein wrote, "... I must confess that the degree of their brutality and cowardice came as something of a surprise."[58]


In October 1933 he returned to the U.S. and took up a position at the Institute for Advanced Study (in Princeton, New Jersey), that required his presence for six months each year.[64][65] He was still undecided on his future (he had offers from European universities, including Oxford), but in 1935 he arrived at the decision to remain permanently in the United States and apply for citizenship.[66][67]


His affiliation with the Institute for Advanced Study would last until his death in 1955.[68] He was one of the four first selected (two of the others being John von Neumann and Kurt Gödel) at the new Institute, where he soon developed a close friendship with Gödel. The two would take long walks together discussing their work. His last assistant was Bruria Kaufman, who later became a physicist. During this period, Einstein tried to develop a unified field theory and to refute the accepted interpretation of quantum physics, both unsuccessfully.


Other scientists also fled to America. Among them were Nobel laureates and professors of theoretical physics. With so many other Jewish scientists now forced by circumstances to live in America, often working side by side, Einstein wrote to a friend, "For me the most beautiful thing is to be in contact with a few fine Jews—a few millennia of a civilized past do mean something after all." In another letter he writes, "In my whole life I have never felt so Jewish as now."[58]



World War II and the Manhattan Project


In 1939, a group of Hungarian scientists that included émigré physicist Leó Szilárd attempted to alert Washington of ongoing Nazi atomic bomb research. The group's warnings were discounted.[69] Einstein and Szilárd, along with other refugees such as Edward Teller and Eugene Wigner, "regarded it as their responsibility to alert Americans to the possibility that German scientists might win the race to build an atomic bomb, and to warn that Hitler would be more than willing to resort to such a weapon."[57]:630[70] On July 12, 1939, a few months before the beginning of World War II in Europe, Szilárd and Wigner visited Einstein[71] and they explained the possibility of atomic bombs, to which pacifist Einstein replied: Daran habe ich gar nicht gedacht ("I had not thought of that at all").[72] Einstein was persuaded to lend his prestige by writing a letter with Szilárd to President Franklin D. Roosevelt to alert him of the possibility. The letter also recommended that the U.S. government pay attention to and become directly involved in uranium research and associated chain reaction research.


The letter is believed to be "arguably the key stimulus for the U.S. adoption of serious investigations into nuclear weapons on the eve of the U.S. entry into World War II".[73] In addition to the letter, Einstein used his connections with the Belgian Royal Family[74] and the Belgian queen mother[69] to get access with a personal envoy to the White House's Oval Office.[69] President Roosevelt could not take the risk of allowing Hitler to possess atomic bombs first. As a result of Einstein's letter and his meetings with Roosevelt, the U.S. entered the "race" to develop the bomb, drawing on its "immense material, financial, and scientific resources" to initiate the Manhattan Project. It became the only country to successfully develop an atomic bomb during World War II.


For Einstein, "war was a disease ... [and] he called for resistance to war." By signing the letter to Roosevelt he went against his pacifist principles.[75] In 1954, a year before his death, Einstein said to his old friend, Linus Pauling, "I made one great mistake in my life—when I signed the letter to President Roosevelt recommending that atom bombs be made; but there was some justification—the danger that the Germans would make them ..."[76]



US citizenship


Einstein became an American citizen in 1940. Not long after settling into his career at the Institute for Advanced Study (in Princeton, New Jersey), he expressed his appreciation of the "meritocracy" in American culture when compared to Europe. According to Isaacson, he recognized the "right of individuals to say and think what they pleased", without social barriers, and as a result, the individual was "encouraged" to be more creative, a trait he valued from his own early education. Einstein wrote:[58]:432


What makes the new arrival devoted to this country is the democratic trait among the people. No one humbles himself before another person or class ... American youth has the good fortune not to have its outlook troubled by outworn traditions.


Einstein worked in 1943 and 1944 as a $25-per-day consultant to the Research and Development Division of the U.S. Navy's Division of Ordnance. He wrote to Stephen Brunauer, the research chemist who recruited him, that he hoped to avoid visits to Washington, D.C., "knowing that I would be very much molested by snobbish people".[77]


As a member of the National Association for the Advancement of Colored People (NAACP) in Princeton who campaigned for the civil rights of African Americans, Einstein corresponded with civil rights activist W. E. B. Du Bois, and in 1946 Einstein called racism America's "worst disease".[78] He later stated, "Race prejudice has unfortunately become an American tradition which is uncritically handed down from one generation to the next. The only remedies are enlightenment and education".[79]


During the final stage of his life, Einstein transitioned to a vegetarian lifestyle,[80] arguing that "the vegetarian manner of living by its purely physical effect on the human temperament would most beneficially influence the lot of mankind".[81]


After the death of Israel's first president, Chaim Weizmann, in November 1952, Prime Minister David Ben-Gurion offered Einstein the position of President of Israel, a mostly ceremonial post.[82] The offer was presented by Israel's ambassador in Washington, Abba Eban, who explained that the offer "embodies the deepest respect which the Jewish people can repose in any of its sons".[57]:522 However, Einstein declined, and wrote in his response that he was "deeply moved", and "at once saddened and ashamed" that he could not accept it:


"All my life I have dealt with objective matters, hence I lack both the natural aptitude and the experience to deal properly with people and to exercise official function. I am the more distressed over these circumstances because my relationship with the Jewish people became my strongest human tie once I achieved complete clarity about our precarious position among the nations of the world".[57]:522[82][83]





On 17 April 1955, Albert Einstein experienced internal bleeding caused by the rupture of an abdominal aortic aneurysm, which had previously been reinforced surgically by Dr. Rudolph Nissen in 1948.[84] 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 long enough to complete it.[85]


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."[86] He died in Princeton Hospital early the next morning at the age of 76, having continued to work until near the end.


During the autopsy, the pathologist of Princeton Hospital, 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.[87] Einstein's remains were cremated and his ashes were scattered at an undisclosed location.[88][89]


In his lecture at Einstein's memorial, nuclear physicist Robert Oppenheimer summarized his impression of him 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."[90]



Scientific career


Throughout his life, Einstein published hundreds of books and articles.[8][10] 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.[91]



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 Albert 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




On a Heuristic Viewpoint Concerning the Production and Transformation of Light

Photoelectric effect

18 March

9 June

Resolved an unsolved puzzle by suggesting that energy is exchanged only in discrete amounts (quanta).[92] This idea was pivotal to the early development of quantum theory.[93]

On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat

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

Special relativity

30 June

26 September

Reconciled Maxwell's equations for electricity and magnetism with the laws of mechanics by introducing major changes to mechanics close to the speed of light, resulting from analysis based on empirical evidence that the speed of light is independent of the motion of the observer.[94] Discredited the concept of a "luminiferous ether."[95]

Does the Inertia of a Body Depend Upon Its Energy Content?

Matter–energy equivalence

27 September

21 November

Equivalence of matter and energy, E = mc2 (and by implication, the ability of gravity to "bend" light), the existence of "rest energy", and the basis of nuclear energy.

Thermodynamic fluctuations and statistical physics


Albert Einstein's first paper[96] 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.[96]



General principles


He articulated the principle of relativity. This was understood by Hermann Minkowski to be a generalization of rotational invariance from space to space-time. Other principles postulated by Einstein and later vindicated are the principle of equivalence and the principle of adiabatic invariance of the quantum number.



Theory of relativity and E = mc²


Einstein's "Zur Elektrodynamik bewegter Körper" ("On the Electrodynamics of Moving Bodies") was received on 30 June 1905 and published 26 September of that same year. It reconciles Maxwell's equations for electricity and magnetism with the laws of mechanics, by introducing major changes to mechanics close to the speed of light. This later became known as Einstein's special theory of relativity.


Consequences of this include the time-space frame of a moving body appearing to slow down and contract (in the direction of motion) when measured in the frame of the observer. This paper also argued that the idea of a luminiferous aether—one of the leading theoretical entities in physics at the time—was superfluous.[97]


In his paper on mass–energy equivalence, Einstein produced E = mc2 from his special relativity equations.[98] Einstein's 1905 work on relativity remained controversial for many years, but was accepted by leading physicists, starting with Max Planck.[99][100]



Photons and energy quanta


In a 1905 paper,[101] Einstein postulated that light itself consists of localized particles (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 Planck's constant. He does not say much more, because he is not sure how the particles are related to the wave. But he does suggest that this idea would explain certain experimental results, notably the photoelectric effect.[102]



Quantized atomic vibrations


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 different, 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.[103]



Adiabatic principle and action-angle variables


Throughout the 1910s, quantum mechanics expanded in scope to cover many different systems. After Ernest Rutherford discovered the nucleus and proposed that electrons orbit like planets, Niels Bohr was able to show that the same quantum mechanical postulates introduced by Planck and developed by Einstein would explain the discrete motion of electrons in atoms, and the periodic table of the elements.


Einstein contributed to these developments by linking them with the 1898 arguments Wilhelm Wien had made. Wien had shown that the hypothesis of adiabatic invariance of a thermal equilibrium state allows all the blackbody curves at different temperature to be derived from one another by a simple shifting process. Einstein noted in 1911 that the same adiabatic principle shows that the quantity which is quantized in any mechanical motion must be an adiabatic invariant. Arnold Sommerfeld identified this adiabatic invariant as the action variable of classical mechanics.



Wave–particle duality


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.[104] In "über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung" ("The Development of our Views on the Composition and Essence of Radiation"), on the quantization of light, and in an earlier 1909 paper, Einstein showed that Max Planck's energy quanta must have well-defined momenta and act in some respects as independent, point-like particles. This paper introduced the photon concept (although the name photon was introduced later by Gilbert N. Lewis in 1926) 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.



Theory of 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.[105] 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.



Zero-point energy


Einstein's physical intuition led him to note that Planck's oscillator energies had an incorrect zero point. He modified Planck's hypothesis by stating that the lowest energy state of an oscillator is equal to 1⁄2hf, to half the energy spacing between levels. This argument, which was made in 1913 in collaboration with Otto Stern, was based on the thermodynamics of a diatomic molecule which can split apart into two free atoms.



General relativity and the equivalence principle


General relativity (GR) is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915. According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses. General relativity has developed into an essential tool in modern astrophysics. It provides the foundation for the current understanding of black holes, regions of space where gravitational attraction is so strong that not even light can escape.


As Albert 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.[106] Consequently, in 1908 he published an article on acceleration under special relativity. In that article, he argued that free fall is really inertial motion, and that for a freefalling observer the rules of special relativity must apply. This argument is called the Equivalence principle. In the same article, Einstein also predicted the phenomenon of gravitational time dilation. In 1911, Einstein published another article expanding on the 1907 article, in which additional effects such as the deflection of light by massive bodies were predicted.



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.


In June 1913, the Entwurf ("draft") theory was the result of these investigations. As its name suggests, it was a sketch of a theory, with the equations of motion supplemented by additional gauge fixing conditions. Simultaneously less elegant and more difficult than general relativity, after more than two years of intensive work Einstein abandoned the theory in November 1915 after realizing that the hole argument was mistaken.[107]





In 1917, Einstein applied the General theory of relativity to model the structure of the universe as a whole. He apprehended that his equations predicted the universe to be either contracting or expanding. He wanted the universe to be eternal and unchanging, but this type of universe is not consistent with relativity. To fix this, Einstein modified the general theory by introducing a new notion, the cosmological constant, which he called ''Lambda''.[108] The purpose of Lambda was to rectify the effects of gravity and allow the whole system to stay balanced. With a positive cosmological constant, the universe could be an eternal static sphere. However, in 1929, Edwin Hubble confirmed that the universe is expanding, Einstein exclaimed after his Mount Wilson visit with Hubble: "If there is no quasi-static world, then away with the cosmological term!"[109][110] and Einstein supposedly discarded the cosmological constant.


Einstein believed a spherical static universe is philosophically preferred, because it would obey Mach's principle. He had shown that general relativity incorporates Mach's principle to a certain extent in frame dragging by gravitomagnetic fields, but he knew that Mach's idea would not work if space goes on forever. In a closed universe, he believed that Mach's principle would hold. Mach's principle has generated much controversy over the years.


In many of Einstein biographies, writers claim that he called the creation of Lambda his "biggest blunder". Recently, astrophysicist Mario Livio showed that Einstein possibly never said that.[111] Instead of discarding Lambda, Einstein was continually experimenting with it.[112]


In late 2013, Irish physicist Cormac O'Raifeartaigh, happened to discover a handwritten manuscript by Einstein which was since then overlooked by other scientists. The research paper was titled ''"Zum kosmologischen Problem"'' ("About the Cosmological Problem").[113][114] And Einstein proposed a revision of his model, still with a cosmological constant, but now the constant was responsible for the creation of new matter as the universe expanded. Thus, the average density of the system never changed. 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." And: "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."''


This is consistent with the now-obsolete Steady State model of cosmology, proposed later in 1949, and with today's modern understanding of dark energy.[115]



Modern quantum theory


Einstein was displeased with quantum theory and mechanics (the very theory he helped create), despite its acceptance by other physicists, stating that God "is not playing at dice."[116] Einstein continued to maintain his disbelief in the theory, and attempted unsuccessfully to disprove it until he died at the age of 76.[117] 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.[118] 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. 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 gave a wave equation for de Broglie waves, which Einstein suggested was the Hamilton–Jacobi equation of mechanics. This paper would inspire Schrödinger's work of 1926.



Bose–Einstein statistics


In 1924, Einstein received a description of a 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.[119] It was not until 1995 that the first such condensate was produced experimentally by Eric Allin Cornell and Carl Wieman using ultra-cooling equipment built at the NIST–JILA laboratory at the University of Colorado at Boulder.[120] Bose–Einstein statistics are now used to describe the behaviors of any assembly of bosons. Einstein's sketches for this project may be seen in the Einstein Archive in the library of the Leiden University.[91]



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 presecriptions do not make a real tensor for this reason.


Einstein argued that this is true for fundamental reasons, because 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. This approach has been echoed by Lev Landau and Evgeny Lifshitz, and others, and has become standard.


The use of non-covariant objects like pseudotensors was heavily criticized in 1917 by Erwin Schrödinger and others.



Unified field theory


Following his research on general relativity, Einstein entered into a series of attempts to generalize his geometric theory of gravitation to include electromagnetism as another aspect of a single entity. In 1950, he described his "unified field theory" in a Scientific American article entitled "On the Generalized Theory of Gravitation".[121] Although he continued to be lauded for his work, Einstein became increasingly isolated in his research, and his efforts were ultimately unsuccessful. In his pursuit of a unification of the fundamental forces, Einstein ignored some mainstream developments in physics, most notably the strong and weak nuclear forces, which were not well understood until many years after his death. Mainstream physics, in turn, largely ignored Einstein's approaches to unification. Einstein's dream of unifying other laws of physics with gravity motivates modern quests for a theory of everything and in particular string theory, where geometrical fields emerge in a unified quantum-mechanical setting.





Einstein collaborated with others to produce a model of a wormhole. 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.


If one end of a wormhole was positively charged, the other end would be negatively charged. These properties led Einstein to believe that pairs of particles and antiparticles could be described in this way.



Einstein–Cartan theory


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


The theory of general relativity has a fundamental law—the Einstein equations which describe how space curves, the geodesic equation which describes how particles move may be derived from the Einstein equations.


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 equations themselves, not by a new law. So Einstein proposed that the path of a singular solution, like a black hole, would be determined to be a geodesic from general relativity itself.


This was established by Einstein, Infeld, and Hoffmann for pointlike objects without angular momentum, and by Roy Kerr for spinning objects.



Other investigations


Einstein conducted other investigations that were unsuccessful and abandoned. These pertain to force, superconductivity, gravitational waves, and other research.



Collaboration with other scientists


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


Einstein and De Haas demonstrated that magnetization is due to the motion of electrons, nowadays known to be the spin. In order to show this, they reversed the magnetization in an iron bar suspended on a torsion pendulum. They confirmed that this leads the bar to rotate, because the electron's angular momentum changes as the magnetization changes. This experiment needed to be sensitive, because the angular momentum associated with electrons is small, but it definitively established that electron motion of some kind is responsible for magnetization.



Schrödinger gas model


Einstein suggested to Erwin Schrödinger that he might be able to reproduce the statistics of a Bose–Einstein gas by considering a box. Then to each possible quantum motion of a particle in a box associate an independent harmonic oscillator. Quantizing these oscillators, each level will have an integer occupation number, which will be the number of particles in it.


This formulation is a form of second quantization, but it predates modern quantum mechanics. Erwin Schrödinger applied this to derive the thermodynamic properties of a semiclassical ideal gas. Schrödinger urged Einstein to add his name as co-author, although Einstein declined the invitation.[122]



Einstein refrigerator


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.[123] On 11 November 1930, U.S. Patent 1,781,541 was awarded to Albert Einstein and Leó Szilárd for the refrigerator. Their invention was not immediately put into commercial production, as the most promising of their patents were quickly bought up by the Swedish company Electrolux to protect its refrigeration technology from competition.[124]



Bohr versus Einstein


The Bohr–Einstein debates were a series of public disputes about quantum mechanics between Albert Einstein and Niels Bohr who were two of its founders. Their debates are remembered because of their importance to the philosophy of science.[125][126][127]



Einstein–Podolsky–Rosen paradox


In 1935, Einstein returned to the question of quantum mechanics. He considered how a measurement on one of two entangled particles would affect the other. He noted, along with his collaborators, that by performing different measurements on the distant particle, either of position or momentum, different properties of the entangled partner could be discovered without disturbing it in any way.


He then used a hypothesis of local realism to conclude that the other particle had these properties already determined. The principle he proposed is that if it is possible to determine what the answer to a position or momentum measurement would be, without in any way disturbing the particle, then the particle actually has values of position or momentum.


This principle distilled the essence of Einstein's objection to quantum mechanics. As a physical principle, it was shown to be incorrect when the Aspect experiment of 1982 confirmed Bell's theorem, which had been promulgated in 1964.



Political and religious views


Einstein's political view was in favor of socialism and critical of capitalism, which he detailed in his essays such as "Why Socialism?".[128][129] Einstein offered to and was called on to give judgments and opinions on matters often unrelated to theoretical physics or mathematics.[130]


Einstein's views about religious belief have been collected from interviews and original writings.


He called himself an agnostic, while disassociating himself from the label atheist.[131] He said he believed in the "pantheistic" God of Baruch Spinoza, but not in a personal god, a belief he criticized.[132][133]



Love of music


Einstein developed an appreciation of music at an early age. 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 German culture. According to conductor Leon Botstein, Einstein is said to have begun playing when he was five, but did not enjoy it at that age.[136]


When he turned thirteen he discovered the violin sonatas of Mozart. "Einstein fell in love" with Mozart's music, notes Botstein, and learned to play music more willingly. According to Einstein, he taught himself to play without "ever practicing systematically", adding that "Love is a better teacher than a sense of duty."[136] At age seventeen, he was heard by a school examiner in Aarau as he played Beethoven's violin sonatas, the examiner stating 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."[136]


Botstein notes that music assumed a pivotal and permanent role in Einstein's life from that period on. Although the idea of becoming a professional himself was not on his mind at any time, among those with whom Einstein played chamber music were a few professionals, and he performed for private audiences and friends. Chamber music also became 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. In 1931, while engaged in research at the California Institute of Technology, he visited the Zoellner family conservatory in Los Angeles and played some of Beethoven and Mozart's works with members of the Zoellner Quartet, recently retired from two decades of acclaimed touring all across the United States; Einstein later presented the family patriarch with an autographed photograph as a memento.[137][138] Near the end of his life, when the young Juilliard Quartet visited him in Princeton, he played his violin with them; although they slowed the tempo to accommodate his lesser technical abilities, Botstein notes the quartet was "impressed by Einstein's level of coordination and intonation."[136]



Non-scientific legacy


While traveling, Einstein wrote daily to his wife Elsa and adopted stepdaughters Margot and Ilse. The letters were included in the papers bequeathed to The Hebrew University. Margot Einstein permitted the personal letters to be made available to the public, but requested that it not be done until twenty years after her death (she died in 1986[139]). Barbara Wolff, of The Hebrew University's Albert Einstein Archives, told the BBC that there are about 3,500 pages of private correspondence written between 1912 and 1955.[140]


Corbis, successor to The Roger Richman Agency, licenses the use of his name and associated imagery, as agent for the university.[141]



In popular culture


In the period before World War II, the New York Times published a vignette in their "The Talk of the Town" feature saying that Einstein was so well known in America that he would be stopped on the street by people wanting him to explain "that theory". He finally figured out a way to handle the incessant inquiries. He told his inquirers "Pardon me, sorry! Always I am mistaken for Professor Einstein."[142]


Einstein has been the subject of or inspiration for many novels, films, plays, and works of music.[143] He is a favorite model for depictions of mad scientists and absent-minded professors; his expressive face and distinctive hairstyle have been widely copied and exaggerated. Time magazine's Frederic Golden wrote that Einstein was "a cartoonist's dream come true".[144]



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