Albert Einstein was born in Ulm, in the Kingdom of Württemberg in the German Empire on March 14, 1879.[6] 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.[9][10] As he grew, Einstein built models and mechanical devices for fun, and began to show a talent for mathematics.[6] 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").[11] Albert Einstein in 1893 (age 14). From Euclid, Einstein began to understand deductive reasoning, and by the age of twelve, he had learned Euclidean geometry. Soon after he began to investigate infinitesimal calculus. At age 16, he performed the first of his famous thought experiments in which he visualized traveling alongside a beam of light.
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.[6] 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.[14] The Einsteins sent Albert to Aarau, in northern Switzerland to finish secondary school.[6] 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.)[15] 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
Albert Einstein and Mileva 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.[22] 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".[23]
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.[24]
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.[25]
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.[5][6] 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.[26]
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.[27] 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.[29]
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.[30] 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.[31] 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.[32][33] This equation suggests that tiny amounts of mass could be converted into huge amounts of energy and presaged the development of nuclear power.[34] Einstein's 1905 work on relativity remained controversial for many years, but was accepted by leading physicists, starting with Max Planck.[35][36]
Photons
In a 1905 paper,[37] 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.[38]
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.[39] 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.[40]
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, and noted that it would be indistinguishable from a box in a 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.[41] German astronomer Erwin Finlay-Freundlich publicized Einstein's challenge to scientists around the world.[42]
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 [43]. 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.[44]
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.[45] In 1918, the Lick Observatory, also in California, announced that it too had disproved Einstein's prediction, although its findings were not published.[46]
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.[42] Nobel laureate Max Born praised general relativity as the "greatest feat of human thinking about nature";[48] fellow laureate Paul Dirac was quoted saying it was "probably the greatest scientific discovery ever made".[49] 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.[47] The deflection of light during a solar eclipse was confirmed by later, more accurate observations.[50] Some resented the newcomer's fame, notably among some German physicists, who later started the Deutsche Physik (German Physics) movement.[51][52]
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[53]
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.
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.[55] 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 [56]. 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.[57] 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.[26]
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." [58] 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.[59]
- 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.
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