**Hand color tinted photo of the father of Modern Physics, Albert Einstein**

**Albert Einstein** (pronounced /ˈælbərt ˈaɪnstaɪn/; German: [ˈalbɐt ˈaɪ̯nʃtaɪ̯n] ; 14 March 1879 – 18 April 1955) was an ethnically Jewish, German-born theoretical physicist. He is best known for his theories of special relativity and general relativity. Einstein 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.”. He is often regarded as the father of Modern Physics and the greatest scientist of the 20th Century.

Einstein’s many contributions to physics include:

The special theory of relativity, which reconciled mechanics with electromagnetism.

The general theory of relativity, a new theory of gravitation obeying the equivalence principle.

Founding of relativistic cosmology with a cosmological constant

The first post-Newtonian expansion, explaining the perihelion advance of Mercury

Prediction of the deflection of light by gravity and gravitational lensing

The first fluctuation dissipation theorem which explained the Brownian movement of molecules

The theory of density fluctuations in gasses and liquids, giving a criterion for critical opalescence

The photon theory and wave-particle duality derived from the thermodynamic properties of light

The quantum theory of atomic motion in solids

Zero-point energy

The semiclassical version of the Schrödinger equation

Relations for atomic transition probabilities which predicted stimulated emission

The quantum theory of a monatomic gas which predicted Bose-Einstein condensation

The EPR paradox

A program for a unified field theory

The geometrization of fundamental physics.

Einstein published more than 300 scientific works and more than 150 non-scientific works. In 1999 Time magazine named him the Person of the Century beating contenders like Mahatma Gandhi and Franklin Roosevelt, and in the words of a biographer, “to the scientifically literate and the public at large, Einstein is synonymous with genius.”

Early life and education

Albert Einstein was born in Ulm, in the Kingdom of Württemberg in the German Empire on March 14, 1879. 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.

The Einsteins, although of Jewish ancestry, did not observe Jewish religious practices, and their son attended a Catholic elementary school. Although Einstein had early speech difficulties, he was a top student in elementary school. As he grew, Einstein built models and mechanical devices for fun, and began to show a talent for mathematics. In 1889, a family friend Max Talmud introduced the ten year old Einstein to key texts in science, mathematics and philosophy, including Kant’s Critique of Pure Reason and Euclid’s Elements (which Einstein called the “holy little geometry book”)

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. In the spring of 1895, he withdrew to join his family in Pavia, convincing the school to let him go by using a doctor’s note. During this time, Einstein wrote his first scientific work, “The Investigation of the State of Aether in Magnetic Fields”.

Einstein applied directly to the Eidgenössische Polytechnische Schule (later Eidgenössische Technische Hochschule (ETH)) in Zürich, Switzerland. Lacking the requisite gymnasium certificate, he took an entrance examination, which he failed, although he got exceptional marks in mathematics and physics. The Einsteins sent Albert to Aarau, in northern Switzerland to finish secondary school. While lodging with the family of Professor Jost Winteler, he fell in love with the family’s daughter, Marie. (His sister Maja later married the Winteler son, Paul.) In Aarau, Einstein studied Maxwell’s electromagnetic theory. At age 17, he graduated, and, with his father’s approval, renounced his citizenship in the German Kingdom of Württemberg to avoid military service, and enrolled in 1896 in the mathematics and physics program at the Polytechnic in Zurich. Marie Winteler moved to Olsberg, Switzerland for a teaching post.

In the same year, Einstein’s future wife, Mileva Marić, also entered the Polytechnic to study mathematics and physics, the only woman in the academic cohort. Over the next few years, Einstein and Marić’s friendship developed into romance. In a letter to her, Einstein called Marić “a creature who is my equal and who is as strong and independent as I am.” Einstein graduated in 1900 from the Polytechnic with a diploma in mathematics and physics; Although historians have debated whether Marić influenced Einstein’s work, the overwhelming consensus amongst academic historians of science is that she did not.

Marriages and children

In early 1902, Einstein and Mileva Marić had a daughter they called Lieserl, born in Novi Sad where the parents of Mileva lived. Her fate is uncertain after 1903. Einstein and Marić married in 1903, and in 1904 the couple’s first son, Hans Albert Einstein, was born in Bern, Switzerland. Their second son, Eduard, was born in Zurich in 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 (née Einstein) in 1923. She was his first cousin maternally and his second cousin paternally. In autumn 1935 they moved to a house they purchased in Princeton, New Jersey; shortly afterward, Elsa Einstein was diagnosed with heart and kidney problems and died in December, 1936.

Patent office

After graduating, Einstein spent almost two frustrating years searching for a teaching post, but a former classmate’s father helped him secure a job in Bern, at the Federal Office for Intellectual Property, the patent office, as an assistant examiner. 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”.

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.

With friends he met in Bern, Einstein formed a weekly discussion club on science and philosophy, which he jokingly named “The Olympia Academy.” Their readings included Henri Poincaré, Ernst Mach, and David Hume, who influenced Einstein’s scientific and philosophical outlook. The next year, Einstein published a paper in the prestigious Annalen der Physik on the capillary forces of a straw.

Scientific career

Throughout his life, Einstein published hundreds of books and articles. Most were about physics, but a few expressed leftist political opinions about pacifism, socialism, and zionism. 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.

Physics in 1900

Einstein’s early papers all come from attempts to demonstrate that atoms exist, and have a finite nonzero size. At the time of his first paper in 1902, it was not yet completely accepted by physicists that atoms were real, even though chemists had good evidence ever since Antoine Lavoisier’s work a century earlier. The reason physicists were skeptical was because no 19th century theory could fully explain the properties of matter from the properties of atoms.

Ludwig Boltzmann was a leading 19th century atomist physicist, who had struggled for years to gain acceptance for atoms. Boltzmann had given an interpretation of the laws of thermodynamics, suggesting that the law of entropy increase is statistical. In Boltzmann’s way of thinking, the entropy is the logarithm of the number of ways a system could be configured inside. The reason the entropy goes up is only because it is more likely for a system to go from a special state with only a few possible internal configurations to a more generic state with many. While Boltzmann’s statistical interpretation of entropy is universally accepted today, and Einstein believed it, at the turn of the 20th century it was a minority position.

The statistical idea was most successful in explaining the properties of gases. James Clerk Maxwell, another leading atomist, had found the distribution of velocities of atoms in a gas, and derived the surprising result that the viscosity of a gas should be independent of density. Intuitively, the friction in a gas would seem to go to zero as the density goes to zero, but this is not so, because the mean free path of atoms becomes large at low densities. A subsequent experiment by Maxwell and his wife confirmed this surprising prediction. Other experiments on gases and vacuum, using a rotating slitted drum, showed that atoms in a gas had velocities distributed according to Maxwell’s distribution law.

In addition to these successes, there were also inconsistencies. Maxwell noted that at cold temperatures, atomic theory predicted specific heats that are too large. In classical statistical mechanics, every spring-like motion has thermal energy kBT on average at temperature T, so that the specific heat of every spring is Boltzmann’s constant kB. A monatomic solid with N atoms can be thought of as N little balls representing N atoms attached to each other in a box grid with 3N springs, so the specific heat of every solid is 3NkB, a result which became known as the Dulong–Petit law. This law is true at room temperature, but not for colder temperatures. At temperatures near zero, the specific heat goes to zero.

Similarly, a gas made up of two atoms can be thought of as two balls on a spring. This spring has energy kBT at high temperatures, and should contribute an extra kB to the specific heat. It does at room temperature, but at low temperature, this contribution disappears. At zero temperature, all other contributions to the specific heat from rotations and vibrations also disappear. This behavior was inconsistent with classical physics.

The most glaring inconsistency was in the theory of light waves. Continuous waves in a box can be thought of as infinitely many spring-like motions, one for each possible standing wave. Each standing wave has a specific heat of kB, so the total specific heat of a continuous wave like light should be infinite in classical mechanics. This is obviously wrong, because it would mean that all energy in the universe would be instantly sucked up into light waves, and everything would slow down and stop.

These inconsistencies led some people to say that atoms were not physical, but mathematical. Notable among the skeptics was Ernst Mach, whose logical positivist philosophy led him to demand that if atoms are real, it should be possible to see them directly. Mach believed that atoms were a useful fiction, that in reality they could be assumed to be infinitesimally small, that Avogadro’s number was infinite, or so large that it might as well be infinite, and kB was infinitesimally small. Certain experiments could then be explained by atomic theory, but other experiments could not, and this is the way it will always be.

Einstein opposed this position. Throughout his career, he was a realist. He believed that a single consistent theory should explain all observation, and that this theory would be a description what was really going on, underneath it all. So he set out to show that the atomic point of view was correct. This led him first to thermodynamics, then to statistical physics, and to the theory of specific heats of solids.

In 1905, while he was working in the patent office, the leading German language physics journal, Annalen der Physik published four of Einstein’s papers. The four papers eventually were recognized as revolutionary, and 1905 became known as Einstein’s “Miracle Year”, and the papers, as the Annus Mirabilis Papers.

Thermodynamic fluctuations and statistical physics

Einstein’s earliest papers were concerned with thermodynamics. He wrote a paper establishing a thermodynamic identity in 1902, and a few other papers which attempted to interpret phenomena from a statistical atomic point of view.

His research in 1903 and 1904 was mainly concerned with the effect of finite atomic size on diffusion phenomena. As in Maxwell’s work, the finite nonzero size of atoms leads to effects which can be observed. This research, and the thermodynamic identity, were well within the mainstream of physics in his time. They would eventually form the content of his PhD thesis.

His first major result in this field was the theory of thermodynamic fluctuations. When in equilibrium, a system has a maximum entropy. According to the statistical interpretation, the entropy can fluctuate a little bit. Einstein pointed out that the statistical fluctuations of a macroscopic object, like a mirror suspended on spring, would be completely determined by the second derivative of the entropy with respect to the position of the mirror. This makes a connection between microscopic and macroscopic objects.

Searching for ways to test this relation, his great breakthrough came in 1905. The theory of fluctuations, he realized, would have a visible effect for an object which could move around freely. Such an object would have a velocity which is random, and would move around randomly, just like an individual atom. The average kinetic energy of the object would be kT, and the time decay of the fluctuations would be entirely determined by the law of friction.

The law of friction for a small ball in a viscous fluid like water was discovered by George Stokes. He showed that for small velocities, the friction force would be proportional to the velocity, and to the radius of the particle (see Stokes’ law). This relation could be used to calculate how far a small ball in water would travel due to its random thermal motion, and Einstein noted that such a ball, of size about a micron, would travel about a few microns per second. This motion could be easily observed with a microscope. Such a motion had already been observed with a microscope by a Botanist named Brown, and had been called Brownian motion. Einstein was able to identify this motion with the motion predicted by his theory. Since the fluctuations which give rise to Brownian motion are just the same as the fluctuations of the velocities of atoms, measuring the precise amount of Brownian motion using Einstein’s theory would show that Boltzmann’s constant is nonzero. It would measure Avogadro’s number.

These experiments were carried out a few years later, and gave a rough estimate of Avogadro’s number consistent with the more accurate estimates due to Max Planck’s theory of blackbody light, and Robert Millikan’s measurement of the charge of the electron. Unlike the other methods, Einstein’s required very few theoretical assumptions or new physics, since it was directly measuring atomic motion on visible grains.

Einstein’s theory of Brownian motion was the first paper in the field of statistical physics. It established that thermodynamic fluctuations were related to dissipation. This was shown by Einstein to be true for time-independent fluctuations, but in the Brownian motion paper he showed that dynamical relaxation rates calculated from classical mechanics could be used as statistical relaxation rates to derive dynamical diffusion laws. These relations are known as Einstein relations.

The theory of Brownian motion was the least revolutionary of Einstein’s Annus mirabilis papers, but it had an important role in securing the acceptance of the atomic theory by physicists.

Special relativity

His 1905 paper on the electrodynamics of moving bodies introduced the radical theory of special relativity, which showed that the observed independence of the speed of light on the observer’s state of motion required fundamental changes to the notion of simultaneity. Consequences of this include the time-space frame of a moving body slowing down and contracting (in the direction of motion) relative to 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. In his paper on mass–energy equivalence, which had previously considered to be distinct concepts, Einstein deduced from his equations of special relativity what has been called the twentieth century’s best-known equation: E = mc2. This equation suggests that tiny amounts of mass could be converted into huge amounts of energy and presaged the development of nuclear power. Einstein’s 1905 work on relativity remained controversial for many years, but was accepted by leading physicists, starting with Max Planck.

Photons

In a 1905 paper, 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’s paper on the light particles was almost entirely motivated by thermodynamic considerations. He was not at all motivated by the detailed experiments on the photoelectric effect, which did not confirm his theory until fifteen years later. Einstein considers the entropy of light at temperature T, and decomposes it into a low-frequency part and a high-frequency part. The high-frequency part, where the light is described by Wien’s law, has an entropy which looks exactly the same as the entropy of a gas of classical particles.

Since the entropy is the logarithm of the number of possible states, Einstein concludes that the number of states of short wavelength light waves in a box with volume V is equal to the number of states of a group of localizable particles in the same box. Since unlike others, he was comfortable of the statistical interpretation, he confidently postulates that the light itself is made up out of localized particles, since this is the only reasonable interpretation of the entropy.

This leads him to conclude 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.

Quantized atomic vibrations

Einstein continued his work on quantum mechanics in 1906, by explaining the specific heat anomaly in solids. This was the first application of quantum theory to a mechanical system. Since Planck’s distribution for light oscillators had no problem with infinite specific heats, the same idea could be applied to solids to fix the specific heat problem there. Einstein showed in a simple model that the hypothesis that solid motion is quantized explains why the specific heat of a solid goes to zero at zero temperature.

Einstein’s model treats each atom as connected to a single spring. Instead of connecting all the atoms to each other, which leads to standing waves with all sorts of different frequencies, Einstein imagined that each atom was attached to a fixed point in space by a spring. This is not physically correct, but it still predicts that the specific heat is 3NkB, since the number of independent oscillations stays the same.

Einstein then assumes that the motion in this model are quantized, according to the Planck law, so that each independent spring motion has energy which is an integer multiple of hf, where f is the frequency of oscillation. With this assumption, he applied Boltzmann’s statistical method to calculate the average energy of the spring. The result was the same as the one that Planck had derived for light: for temperatures where kBT is much smaller than hf, the motion is frozen, and the specific heat goes to zero.

So Einstein concluded that quantum mechanics would solve the main problem of classical physics, the specific heat anomaly. The particles of sound implied by this formulation are now called phonons. Because all of Einstein’s springs have the same stiffness, they all freeze out at the same temperature, and this leads to a prediction that the specific heat should go to zero exponentially fast when the temperature is low. The solution to this problem is to solve for the independent normal modes individually, and to quantize those. Then each normal mode has a different frequency, and long wavelength vibration modes freeze out at colder temperatures than short wavelength ones. This was done by Debye, and after this modification, Einstein’s quantization method reproduced quantitatively the behavior of the specific heats of solids at low temperatures. This work was the foundation of condensed matter physics.

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. The law that the action variable is quantized was the basic principle of the quantum theory as it was known between 1900 and 1925.

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. 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.

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 Raleigh scattering, which is what happens when the fluctuation size is much smaller than the wavelength, and which explains why the sky is blue.

Einstein at the Solvay conference in 1911. That year he became an associate professor at the University of Zurich and shortly afterward, he accepted a full professorship at the German Charles-Ferdinand University in Prague.

Zero-point energy

Einstein’s unerring 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.

Principle of equivalence

In 1907, while still working at the patent office, Einstein had what he would call his “happiest thought”. He realized that the principle of relativity could be extended to gravitational fields. He thought about the case of a uniformly accelerated box not in a gravitational field, and noted that it would be indistinguishable from a box sitting still in an unchanging gravitational field. He used special relativity to see that the rate of clocks at the top of a box accelerating upward would be faster than the rate of clocks at the bottom. He concludes that the rates of clocks depend on their position in a gravitational field, and that the difference in rate is proportional to the gravitational potential to first approximation.

Although this approximation is crude, it allowed him to calculate the deflection of light by gravity, and show that it is nonzero. This gave him confidence that the scalar theory of gravity proposed by Gunnar Nordstrom was incorrect. But the actual value for the deflection that he calculated was too small by a factor of two, because the approximation he used doesn’t work well for things moving at near the speed of light. When Einstein finished the full theory of General Relativity, he would rectify this error, and predict the correct amount of light deflection by the sun.

From Prague, Einstein published a paper about the effects of gravity on light, specifically the gravitational redshift and the gravitational deflection of light. The paper challenged astronomers to detect the deflection during a solar eclipse. German astronomer Erwin Finlay-Freundlich publicized Einstein’s challenge to scientists around the world. Einstein thought about the nature of the gravitational field in the years 1909-1912, studying its properties by means of simple thought experiments. A notable one is the rotating disk. Einstein imagined an observer making experiments on a rotating turntable. He noted that such an observer would find a different value for the mathematical constant pi than the one predicted by Euclidean geometry. The reason is that the radius of a circle would be measured with an uncontracted ruler, but according to special relativity, the circumference would seem to be longer, because the ruler would be contracted. Since Einstein believed that the laws of physics were local, described by local fields, he concluded from this that spacetime could be locally curved. This led him to study Riemannian geometry, and to formulate General relativity in this language.

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. The Entwurf theory was the result of these investigations. As it 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, Einstein abandoned the theory after realizing that the hole argument was mistaken.

General relativity

In 1912, Einstein returned to Switzerland to accept a professorship at his alma mater, the ETH. There he met mathematician Marcel Grossmann who introduced him to Riemannian geometry and, more generally, to differential geometry. On the recommendation of Italian mathematician Tullio Levi-Civita, Einstein began exploring the usefulness of general covariance (essentially the use of tensors) for his gravitational theory. For a while Einstein thought that there were problems with the approach, but he later returned to it and, by late 1915, had published his general theory of relativity in the form in which it is used today. This theory explains gravitation as distortion of the structure of spacetime by matter, affecting the inertial motion of other matter. During World War I, the work of Central Powers scientists was available only to Central Powers academics, for national security reasons. Some of Einstein’s work did reach the United Kingdom and the United States through the efforts of the Austrian Paul Ehrenfest and physicists in the Netherlands, especially 1902 Nobel Prize-winner Hendrik Lorentz and Willem de Sitter of Leiden University. After the war ended, Einstein maintained his relationship with Leiden University, accepting a contract as an Extraordinary Professor; for ten years, from 1920 to 1930, he travelled to Holland regularly to lecture. In 1917, several astronomers accepted Einstein ‘s 1911 challenge from Prague. The Mount Wilson Observatory in California, U.S., published a solar spectroscopic analysis that showed no gravitational redshift. In 1918, the Lick Observatory, also in California, announced that it too had disproved Einstein’s prediction, although its findings were not published.

One of the 1919 eclipse photographs taken during Arthur Stanley Eddington’s expedition, which confirmed Einstein’s However, in May 1919, a team led by the British astronomer Arthur Stanley Eddington claimed to have confirmed Einstein’s prediction of gravitational deflection of starlight by the Sun while photographing a solar eclipse in Sobral, northern Brazil, and Príncipe. Nobel laureate Max Born praised general relativity as the “greatest feat of human thinking about nature”; fellow laureate Paul Dirac was quoted saying it was “probably the greatest scientific discovery ever made”. The international media guaranteed Einstein’s global renown. There have been later claims that scrutiny of the specific photographs taken on the Eddington expedition showed the experimental uncertainty to be comparable to the same magnitude as the effect Eddington claimed to have demonstrated, and that a 1962 British expedition concluded that the method was inherently unreliable. The deflection of light during a solar eclipse was confirmed by later, more accurate observations. Some resented the newcomer’s fame, notably among some German physicists, who later started the Deutsche Physik (German Physics) movement.

Cosmology

In 1917, Einstein applied the General theory of relativity to model the structure of the universe as a whole. 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. With a positive cosmological constant, the universe could be an eternal static sphere 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.

After her husband’s many relocations, Mileva established a permanent home with the children in Zürich in 1914. Einstein went alone to Berlin, where he became a member of the Prussian Academy of Sciences and a professor at the Humboldt University of Berlin, although with a special clause in his contract that freed him from most teaching obligations. He also directed of the Kaiser Wilhelm Institute for Physics (1914-1932).

Modern quantum theory

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. 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 . 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. 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.

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 noncovariante 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 Schrodinger 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, which would allow the explanation of electromagnetism. In 1950, he described his “unified field theory” in a Scientific American article entitled “On the Generalized Theory of Gravitation.” 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.

Wormholes

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 Schwartschild 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.

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 has since been shown to be incompatible with experiments.

Equations of motion

The theory of general relativity has two fundamental laws— the Einstein equations which describe how space curves, and the geodesic equation which describes how particles move.

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.

Einstein’s mistakes

In addition to his well-accepted results, some of Einstein’s papers contain mistakes:

1905: In the original German version of the special relativity paper, and in some English translations, Einstein gives a wrong expression for the transverse mass of a fast moving particle. The transverse mass is the antiquated name for the ratio of the 3-force to the 3-acceleration when the force is perpendicular to the velocity. Einstein gives this ratio as , while the actual value is (corrected by Max Planck).

1905: In his PhD dissertation, the friction in dilute solutions has an miscalculated numerical prefactor, which makes the estimate of Avogadro’s number off by a factor of 3. The mistake is corrected by Einstein in a later publication.

1905: An expository paper explaining how airplanes fly includes an example which is incorrect. There is a wing which he claims will generate lift. This wing is flat on the bottom, and flat on the top, with a small bump at the center. It is designed to generate lift by Bernoulli’s principle, and Einstein claims that it will. Simple action reaction considerations, though, show that the wing will not generate lift, at least if it is long enough.

1911: Einstein predicted how much the sun’s gravity would deflect nearby starlight, but used an approximation which gives an answer which is half as big as the correct one.

1913: Einstein started writing papers based on his belief that the hole argument made general covariance impossible in a theory of gravity.

1922: Einstein published a qualitative theory of superconductivity based on the vague idea of electrons shared in orbits. This paper predated modern quantum mechanics, and is well understood to be completely wrong. The correct BCS theory of low temperature superconductivity was only worked out in 1957, thirty years after the establishing of modern quantum mechanics.

1937: Einstein believed that the focussing properties of geodesics in general relativity would lead to an instability which causes plane gravitational waves to collapse in on themselves. While this is true to a certain extent in some limits, because gravitational instabilities can lead to a concentration of energy density into black holes, for plane waves of the type Einstein and Rosen considered in their paper, the instabilities are under control. Einstein retracted this position a short time later, but his collaborator Nathan Rosen continued to maintain that gravitational waves are unstable until his death.

1939: Einstein denied that black holes could form several times, the last time in print. He published a paper that argues that a star collapsing would spin faster and faster, spinning at the speed of light with infinite energy well before the point where it is about to collapse into a black hole. This paper received no citations, and the conclusions are well understood to be wrong. Einstein’s argument itself is inconclusive, since he only shows that stable spinning objects have to spin faster and faster to stay stable before the point where they collapse. But it is well understood today (and understood well by some even then) that collapse cannot happen through stationary states the way Einstein imagined.

In addition to these well established mistakes, there are other arguments whose deduction is considered correct, but whose interpretation or philosophical conclusion is considered to have been incorrect:

In the Bohr–Einstein debates and the papers following this, Einstein tries to poke holes in the uncertainty principle, ingeniously, but unsuccessfully.

In the EPR paper, Einstein concludes that quantum mechanics must be replaced by local hidden variables. The measured violations of Bell’s inequality show that hidden variables, if they exist, must be nonlocal.

Einstein himself considered his 1917 paper founding cosmology as a ‘blunder’. The theory of General Relativity predicted an expanding or contracting universe, but Einstein wanted a universe which is an unchanging three dimensional sphere, like the surface of a three dimensional ball in four dimensions. He wanted this for philosophical reasons, so as to incorporate Mach’s principle in a reasonable way. He stabilized his solution by introducing a cosmological constant, and when the universe was shown to be expanding, he retracted the constant as a blunder. This is not really much of a blunder— the cosmological constant is necessary within General Relativity as it is currently understood, and it is widely believed to have a nonzero value today. Einstein took the wrong side in a few scientific debates.

He briefly flirted with transverse and longitudinal mass concepts, before rejecting them.

Einstein initially opposed Minkowski’s geometrical formulation of special relativity, changing his mind completely a few years later.

Based on his cosmological model, Einstein rejected expanding universe solutions by Friedman and Lemaitre as unphysical, changing his mind when the universe was shown to be expanding a few years later.

Finding it too formal, Einstein believed that Heisenberg’s matrix mechanics was incorrect. He changed his mind when Schrödinger and others demonstrated that the formulation in terms of the Schrodinger equation, based on Einstein’s wave-particle duality was equivalent to Heisenberg’s matrices.

Einstein rejected work on black holes by Chandrasekhar, Oppenheimer, and others, believing, along with Eddington, that collapse past the horizon (then called the ‘Schwartschild singularity’) would never happen. So big was his influence, that this opinion was not rejected until the early 1960s, almost a decade after his death.

Einstein believed that some sort of nonlinear instability could lead to a field theory whose solutions would collapse into pointlike objects which would behave like quantum particles. While there are many field theories with point-like particle solutions, none of them behave like quantum particles. It is widely believed that quantum mechanics would be impossible to reproduce from a local field theory of the type Einstein considered, because of Bell’s inequality.

In addition to these well known mistakes, it is sometimes claimed that the general line of Einstein’s reasoning in the 1905 relativity paper is flawed, or the photon paper, or one or another of the most famous papers. None of these claims are widely accepted.

Collaboration with other scientists

In addition to long time collaborators Leopold Infeld and Nathan Rosen, 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 Schrodinger 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.

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

Bohr versus Einstein

Einstein and Niels Bohr. Einstein’s disagreement with Bohr revolved around the idea of scientific determinism. Repercussions of the Einstein-Bohr debate have found their way into philosophical discourse as well. Photo taken by Paul Ehrenfest during their 1925 Leiden visit.In the 1920s, quantum mechanics developed into a more complete theory. Einstein was unhappy with the Copenhagen interpretation of quantum theory developed by Niels Bohr and Werner Heisenberg. In this interpretation, quantum phenomena are inherently probabilistic, with definite states resulting only upon interaction with classical systems. A public debate between Einstein and Bohr followed, lasting on and off for many years (including during the Solvay Conferences). Einstein formulated thought experiments against the Copenhagen interpretation, which were all rebutted by Bohr. In a 1926 letter to Max Born, Einstein wrote: “I, at any rate, am convinced that He [God] does not throw dice.” Einstein was never satisfied by what he perceived to be quantum theory’s intrinsically incomplete description of nature, and in 1935 he further explored the issue in collaboration with Boris Podolsky and Nathan Rosen, noting that the theory seems to require non-local interactions; this is known as the EPR paradox. The EPR experiment has since been performed, with results confirming quantum theory’s predictions.

Religious views

The question of scientific determinism gave rise to questions about Einstein’s position on theological determinism, and whether or not he believed in God, or in a god. In 1929, Einstein told Rabbi Herbert S. Goldstein “I believe in Spinoza’s God, who reveals Himself in the lawful harmony of the world, not in a God Who concerns Himself with the fate and the doings of mankind.” In a 1950 letter to M. Berkowitz, Einstein stated that “My position concerning God is that of an agnostic. I am convinced that a vivid consciousness of the primary importance of moral principles for the betterment and ennoblement of life does not need the idea of a law-giver, especially a law-giver who works on the basis of reward and punishment.” Einstein also stated: “I have repeatedly said that in my opinion the idea of a personal God is a childlike one. You may call me an agnostic, but I do not share the crusading spirit of the professional atheist whose fervor is mostly due to a painful act of liberation from the fetters of religious indoctrination received in youth.” He is reported to have said in a conversation with Hubertus, Prince of Löwenstein-Wertheim-Freudenberg, “In view of such harmony in the cosmos which I, with my limited human mind, am able to recognize, there are yet people who say there is no God. But what really makes me angry is that they quote me for the support of such views.” Einstein clarified his religious views in a letter he wrote in response to those who claimed that he worshipped a Judeo-Christian god: “It was, of course, a lie what you read about my religious convictions, a lie which is being systematically repeated. I do not believe in a personal god and I have never denied this but have expressed it clearly. If something is in me which can be called religious then it is the unbounded admiration for the structure of the world so far as our science can reveal it.” In his book The World as I See It, he wrote: “A knowledge of the existence of something we cannot penetrate, of the manifestations of the profoundest reason and the most radiant beauty, which are only accessible to our reason in their most elementary forms—it is this knowledge and this emotion that constitute the truly religious attitude; in this sense, and in this alone, I am a deeply religious man.”

Politics

With increasing public demands, his involvement in political, humanitarian, and academic projects in various countries, and his new acquaintances with scholars and political figures from around the world, Einstein was less able to achieve the productive isolation that he needed in order to work. Due to his fame and genius, Einstein found himself called on to give conclusive judgments on matters that had nothing to do with theoretical physics or mathematics. He was not timid, and he was aware of the world around him, with no illusion that ignoring politics would make world events fade away. His very visible position allowed him to speak and write frankly, even provocatively, at a time when many people of conscience could only flee to the underground or keep doubts about developments within their own movements to themselves for fear of internecine fighting. Einstein flouted the ascendant Nazi movement, tried to be a voice of moderation in the tumultuous formation of the State of Israel and braved anti-communist politics and resistance to the civil rights movement in the United States. He participated in the 1927 congress of the League against Imperialism in Brussels.

Zionism

Einstein was a socialist Zionist who supported the creation of a Jewish national homeland in the British mandate of Palestine. In 1931, The Macmillan Company published About Zionism: Speeches and Lectures by Professor Albert Einstein. Querido, an Amsterdam publishing house, collected eleven of Einstein’s essays into a 1933 book entitled Mein Weltbild, translated to English as The World as I See It; Einstein’s foreword dedicates the collection “to the Jews of Germany”. In the face of Germany’s rising militarism, Einstein wrote and spoke for peace.

Einstein publicly stated reservations about the proposal to partition the British-supervised British Mandate of Palestine into independent Arab and Jewish countries. In a 1938 speech, “Our Debt to Zionism”, he said: “My awareness of the essential nature of Judaism resists the idea of a Jewish state with borders, an army, and a measure of temporal power, no matter how modest. I am afraid of the inner damage Judaism will sustain—especially from the development of a narrow nationalism within our own ranks, against which we have already had to fight strongly, even without a Jewish state. … If external necessity should after all compel us to assume this burden, let us bear it with tact and patience.” In a 1947 letter to Indian Prime Minister Jawaharlal Nehru, Einstein stated that the Balfour Declaration’s proposal to establish a national home for Jews in Palestine “redresses the balance” of justice and history. The United Nations did divide the mandate, demarcating the borders of several new countries including the State of Israel, and war broke out immediately. Einstein was one of the authors of an open letter to the New York Times in 1948 criticizing Menachem Begin’s Herut (Freedom) Party for the Deir Yassin massacre (Einstein et al. 1948).

Einstein served on the Board of Governors of The Hebrew University of Jerusalem. In his Will of 1950, Einstein bequeathed literary rights to his writings to The Hebrew University, where many of his original documents are held in the Albert Einstein Archives.

When President Chaim Weizmann died in 1952, Einstein was asked to be Israel’s second president, but he declined, stating that he had “neither the natural ability nor the experience to deal with human beings.” He wrote: “I am deeply moved by the offer from our State of Israel, and at once saddened and ashamed that I cannot accept it.”

Anti-Nazism

Einstein had moved to the United States in December 1932, where he had been at the California Institute of Technology in Pasadena, California, and also was a guest lecturer at Abraham Flexner’s newly founded Institute for Advanced Study in Princeton, New Jersey.

Einstein receiving his certificate of American citizenship from Judge Phillip Forman in 1940. He retained his Swiss citizenship. During the 1930s and into World War II, Einstein wrote affidavits recommending United States visas for European Jews who were trying to flee persecution. He raised money for Zionist organizations and was, in part, responsible for the 1933 formation of the International Rescue Committee.

In Germany, Deutsche Physik activists published pamphlets and even textbooks denigrating Einstein. Nobel laureates Philipp Lenard and Johannes Stark led a campaign to eliminate Einstein’s work from the German lexicon as unacceptable “Jewish physics” (Jüdische Physik). Instructors who taught his theories were blacklisted, including Nobel laureate Werner Heisenberg, who had debated quantum probability with Bohr and Einstein. Philipp Lenard claimed that the mass–energy equivalence formula needed to be credited to Friedrich Hasenöhrl to make it an Aryan creation. A man convicted of conspiring to kill Einstein was fined a mere six dollars.

Atomic bomb

Concerned scientists, many of them refugees from European anti-Semitism in the U.S., recognized the danger of German scientists developing an atomic bomb based on the newly discovered phenomena of nuclear fission. In 1939, the Hungarian émigré Leó Szilárd, having failed to arouse U.S. government interest on his own, worked with Einstein to write a letter to U.S. President Franklin Delano Roosevelt, which Einstein signed, urging U.S. development of such a weapon. On 11 October 1939 Alexander Sachs, an adviser to Roosevelt on economic affairs, delivered the Einstein-Szilárd letter and persuaded the president of its importance. “This requires action”, Roosevelt told an aide, and authorized secret research into the harnessing of nuclear fission for military purposes.

Einstein-Szilárd letterBy 1942 this effort had become the Manhattan Project, the largest secret scientific endeavor undertaken up to that time. By late 1945, the U.S. had developed operational nuclear weapons, and used them on the Japanese cities of Hiroshima and Nagasaki. Einstein himself did not play a role in the development of the atomic bomb other than signing the letter although he did help the United States Navy with some unrelated theoretical questions it was working on during the war.

According to Linus Pauling, Einstein later expressed regret about his letter to Roosevelt. In 1947, Einstein wrote an article for The Atlantic Monthly arguing that the United States should not try to pursue an atomic monopoly, and instead should equip the United Nations with nuclear weapons for the sole purpose of maintaining deterrence.

Cold War era

Einstein, 1947. Age 68.When he was a visible figure working against the rise of Nazism, Einstein had sought help and developed working relationships in both the West and what was to become the Soviet bloc. After World War II, enmity between the former allies became a very serious issue for people with international résumés. To make things worse, during the first days of McCarthyism Einstein was writing about a single world government; it was at this time that he wrote, “I do not know how the third World War will be fought, but I can tell you what they will use in the Fourth—rocks!” In a 1949 Monthly Review article entitled “Why Socialism?” Albert Einstein described a chaotic capitalist society, a source of evil to be overcome, as the “predatory phase of human development” (Einstein 1949). With Albert Schweitzer and Bertrand Russell, Einstein lobbied to stop nuclear testing and future bombs. Days before his death, Einstein signed the Russell-Einstein Manifesto, which led to the Pugwash Conferences on Science and World Affairs.

Einstein’s house in Princeton, NJEinstein was a member of several civil rights groups, including the Princeton chapter of the NAACP. When the aged W. E. B. Du Bois was accused of being a Communist spy, Einstein volunteered as a character witness, and the case was dismissed shortly afterward. Einstein’s friendship with activist Paul Robeson, with whom he served as co-chair of the American Crusade to End Lynching, lasted twenty years.

In 1946, Einstein collaborated with Rabbi Israel Goldstein, Middlesex University heir C. Ruggles Smith, and activist attorney George Alpert on the Albert Einstein Foundation for Higher Learning, which was formed to create a Jewish-sponsored secular university, open to all students, on the grounds of the former Middlesex University in Waltham, Massachusetts. Middlesex was chosen in part because it was accessible from both Boston and New York City, Jewish cultural centers of the U.S. Their vision was a university “deeply conscious both of the Hebraic tradition of Torah looking upon culture as a birthright, and of the American ideal of an educated democracy.” The collaboration was stormy, however. Finally, when Einstein wanted to appoint British economist Harold Laski as the university’s president, George Alpert wrote that Laski was “a man utterly alien to American principles of democracy, tarred with the Communist brush.” Einstein withdrew his support and barred the use of his name. The university opened in 1948 as Brandeis University. In 1953, Brandeis offered Einstein an honorary degree, but he declined.

Given Einstein’s links to Germany and Zionism, his socialist ideals, and his links to Communist figures, the U.S. Federal Bureau of Investigation kept a file on Einstein that grew to 1,427 pages. Many of the documents in the file were sent to the FBI by concerned citizens: some objected to his immigration, while others asked the FBI to protect him.

Death

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. 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. 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.” He died in Princeton Hospital early the next morning at the age of 76, having continued to work until near the end. Einstein’s remains were cremated and his ashes were scattered around the grounds of the Institute for Advanced Study, Princeton, New Jersey. During the autopsy, the pathologist of Princeton Hospital, Thomas Stoltz Harvey removed Einstein’s brain for preservation, without the permission of his family, in hope that the neuroscience of the future would be able to discover what made Einstein so intelligent. Forty years later, at age 86, Harvey, along with a journalist, returned Einstein’s brain to Einstein’s granddaughter.

Legacy

While travelling, Einstein had written daily to his wife Elsa and adopted stepdaughters, Margot and Ilse, and 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). 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. The United States’ National Academy of Sciences commission.