Albert Einstein

How to use this course

Albert Einstein is the most famous scientist of the twentieth century, and fame has buried much of what he actually did. He did not only invent relativity. He also argued for the reality of atoms, introduced the light quantum, explained stimulated emission, predicted Bose–Einstein condensation, founded relativistic cosmology and posed the sharpest challenge to quantum mechanics. This course presents that work in technical detail, alongside the life of a man who moved between six countries and three citizenships.

Each technical lesson opens with a paragraph for the general reader, then gives precise statements, derivations and exercises with folded solutions. Lessons 04 to 06 cover the papers of 1905. Lessons 07 and 08 cover gravitation (1907–1918). Lesson 09 gathers his quantum work from 1916 to 1935, and Lesson 10 his cosmology and the long search for a unified theory. We use the metric signature \((-,+,+,+)\) and keep factors of \(c\) and \(G\) visible.

Timeline

Ulm, Munich, Aarau, 1879–1896

Albert Einstein was born on 14 March 1879 in Ulm, in the Kingdom of Württemberg, into a secular Jewish family. His father Hermann and his uncle Jakob ran an electrical engineering business, which took the family to Munich in 1880. His sister Maja was born in 1881. The firm built dynamos and electric lighting, so the boy grew up around the technology of Maxwell’s theory.

Einstein later recalled two early wonders. At about five, a compass showed him that something hidden in empty space could steer a needle. At about twelve, a small geometry book showed him that statements about the world could be proved with complete certainty. A family friend, the medical student Max Talmud, brought him popular science books and Euclid, and he taught himself calculus in his early teens.

He attended a Catholic elementary school and from 1888 the Luitpold Gymnasium. He was a good student, but he disliked its drill and authority. In 1894 the family business failed in Munich and moved to Italy. Einstein was left behind to finish school, and at the end of December he left the Gymnasium without a diploma and joined his parents in Pavia.

Aarau

In 1895, two years younger than the usual age, he sat the entrance examination of the Swiss Federal Polytechnic (ETH) in Zurich. He did very well in mathematics and physics but failed the general part. On the advice of the director, he spent a year at the cantonal school in Aarau, whose liberal teaching he loved. There he first asked himself what a light wave would look like to someone running alongside it, the thought experiment he later traced to the origins of relativity. In January 1896 he gave up his Württemberg citizenship, partly to avoid military service, and he was stateless until 1901. He passed the Matura in September 1896.

Zurich and the lean years, 1896–1902

In autumn 1896 Einstein entered the ETH programme for teachers of mathematics and physics. His physics professor, Heinrich Weber, taught classical physics well but did not cover Maxwell’s electromagnetism, which Einstein studied on his own from the books of August Föppl and others, together with the works of Ludwig Boltzmann, Hermann von Helmholtz, Heinrich Hertz and Ernst Mach. He often skipped lectures and relied on the careful notes of his friend Marcel Grossmann.

Minkowski as teacher

Among his mathematics teachers was Hermann Minkowski. Einstein attended his courses irregularly and saw little point, at the time, in advanced mathematics for physics. Minkowski reportedly later told Max Born that he remembered the student as a lazy dog who never bothered about mathematics. Einstein later admitted that he had underrated mathematics as a student and only learned its value while working on gravitation. The two would meet again, intellectually, in 1908 (Lesson 06).

Mileva Marić

In his class was Mileva Marić, a Serbian physics student and the only woman in the section. They became a couple and studied together. Einstein graduated in July 1900; Marić failed the final examinations twice. In early 1902 she gave birth to a daughter, Lieserl, whose fate is unknown. They married in January 1903 over the objections of his family.

Without a post

After graduation every application for an assistantship failed, including letters to Wilhelm Ostwald and Heike Kamerlingh Onnes. Einstein lived on temporary teaching and private tutoring. He became a Swiss citizen in February 1901 and published his first paper, on capillary forces, the same year. In 1902, through the help of Grossmann’s father, he obtained a post at the Federal Patent Office in Bern. His father died in October 1902.

The patent office, 1902–1909

Einstein started at the patent office in Bern in June 1902 as a technical expert, third class. He examined applications for electrical devices, a job that rewarded clear thinking about how a machine is really supposed to work. The post was made permanent and he was promoted to second class in 1906. He later called the office a worldly cloister where he hatched his finest ideas.

With Maurice Solovine and Conrad Habicht he formed a reading group, the self-styled Olympia Academy, which read David Hume, Mach, Henri Poincaré’s Science and Hypothesis and Baruch Spinoza. His closest scientific confidant was Michele Besso, an engineer at the office and a friend from Zurich. The 1905 relativity paper cites no literature and thanks only Besso. A son, Hans Albert, was born in May 1904.

1905

Between March and September 1905 Einstein sent five papers to Annalen der Physik and completed a doctoral thesis. Any one of the papers on light quanta, Brownian motion and relativity would have made a career. The thesis, Eine neue Bestimmung der Moleküldimensionen, dated 30 April 1905, was accepted by Alfred Kleiner at the University of Zurich, and the degree was formally conferred in January 1906. Lessons 04 to 06 treat the 1905 work in detail.

Recognition came slowly but surely. Max Planck took up relativity at once and lectured on it in Berlin. In 1907 Einstein found the equivalence principle while writing a review. In 1908 he qualified as Privatdozent at the University of Bern with a thesis on radiation. In 1909 he received his first honorary doctorate, from Geneva, spoke at the Salzburg meeting of German scientists on the dual nature of light, and left the patent office to become extraordinary professor at the University of Zurich.

Light quanta and the photoelectric effect

For the general reader. In 1905 light was firmly understood as a wave. Einstein proposed that, for some purposes, light behaves as if it consisted of independent packets of energy. He predicted that electrons knocked out of a metal by light would have energies set by the colour of the light, not its brightness. The idea was resisted for almost twenty years, and it is the work for which he received the Nobel Prize.

The entropy argument

The March 1905 paper, Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt, did not start from Planck’s law. It started from Wien’s law, valid for high frequencies, \(\rho(\nu,T)=\alpha\nu^3e^{-h\nu/kT}\), written here in modern notation (Einstein used \(R\beta/N\) for \(h\)). From thermodynamics, the entropy of monochromatic radiation of energy \(E\) in volume \(V\) then depends on volume as

For \(n\) independent point particles, the probability that all lie in a subvolume \(V\) of \(V_0\) is \((V/V_0)^n\), so Boltzmann’s principle gives \(S-S_0=nk\ln(V/V_0)\). The two expressions agree if \(n=E/h\nu\).

The photoelectric law

If one quantum gives all its energy to one electron, and the electron must spend a work \(W\) to leave the metal, the maximum kinetic energy of the emitted electrons is

The law predicts a threshold frequency \(\nu_0=W/h\), electron energies independent of intensity, and a universal slope \(h\) of \(K_{\max}\) against \(\nu\). Robert Millikan, who set out to refute it, confirmed it in 1914–1916 and measured \(h\) from the slope. The momentum \(h\nu/c\) of the quantum came later, in 1916–17 (Lesson 09), and Arthur Compton’s X-ray scattering of 1923 convinced most physicists.

Fluctuations: waves and particles together (1909)

For a system in contact with a heat bath, energy fluctuations satisfy \(\langle\Delta E^2\rangle=kT^2\,\partial\langle E\rangle/\partial T\). Applying this to blackbody radiation of volume \(V\) in a frequency band \(d\nu\), with Planck’s law, Einstein found

He concluded at Salzburg that the next theory of light would have to fuse wave and particle pictures, an early statement of wave–particle duality.

Specific heats (1907)

Einstein applied quantization to matter as well. Treating a solid as \(3N\) independent oscillators of one frequency \(\nu\), each with mean energy \(h\nu/(e^{h\nu/kT}-1)\), gives

which explains why the specific heat of diamond falls far below the Dulong–Petit value \(3Nk\) at room temperature. Walther Nernst’s low-temperature measurements after 1910 confirmed the trend, and Peter Debye refined the model in 1912.

Brownian motion and the reality of atoms

For the general reader. In 1905 some leading scientists still doubted that atoms were real. Einstein showed that if they are, a microscopic particle floating in water must jitter at random, and he predicted exactly how far it should wander in a given time. Jean Perrin’s measurements matched the prediction and gave a value for the number of molecules in a mole. The debate over atoms was effectively closed.

The thesis

The doctoral thesis treated sugar molecules in water as small rigid spheres of radius \(a\) in a viscous fluid. Einstein derived two relations: the diffusion coefficient of the solute, and the increase in viscosity it causes. Combining them with measured data gave both \(a\) and Avogadro’s number \(N_A\). His viscosity formula contained an error, found in 1911 with the help of his student Ludwig Hopf after experiments by Jacques Bancelin; the corrected result is

where \(\varphi\) is the volume fraction occupied by the spheres.

Diffusion meets friction

The May 1905 paper argued that a suspended particle and a dissolved molecule differ only in size. Both exert osmotic pressure, so a suspension of \(n(x)\) particles per volume in equilibrium under an external force \(F\) per particle satisfies \(F\,n=k T\,\partial n/\partial x\). Equilibrium also means that the drift current \(n F/(6\pi\eta a)\), from Stokes’s law, balances the diffusion current \(D\,\partial n/\partial x\). Eliminating \(F\):

The random walk

Einstein then derived the diffusion equation \(\partial_t n=D\,\partial_x^2n\) from a probabilistic model of independent displacements in short time intervals. Its solution for particles starting at the origin is a Gaussian, so

The displacement grows as \(\sqrt t\), which is why earlier attempts to measure the particle’s velocity had failed: the apparent speed depends on the time between observations. Marian Smoluchowski reached the same results independently in 1906. Perrin’s experiments of 1908–1909 with gamboge and mastic grains gave \(N_A\) close to the modern value, and he received the Nobel Prize in 1926.

Special relativity, Minkowski and E = mc²

For the general reader. Einstein took two simple principles seriously: the laws of physics are the same for all observers in uniform motion, and light always travels at the same speed. Together they force clocks in motion to run slow and moving rods to shrink, and they mean that simultaneity depends on the observer. A short sequel showed that mass and energy are two forms of one quantity.

The 1905 paper

Zur Elektrodynamik bewegter Körper (received 30 June 1905) begins with an asymmetry: in Maxwell’s theory as then interpreted, a magnet moving past a conductor and a conductor moving past a magnet are described differently, though the observed current is the same. Einstein raised the relativity principle to a postulate, added the constancy of the speed of light, and defined simultaneity operationally by exchanging light signals. Hendrik Lorentz and Poincaré had found the transformation group earlier, for electrodynamics. Einstein derived it kinematically, from the two postulates alone, and gave its quantities physical meaning.

Consequences: a clock at rest in \(S'\) runs slow by \(\gamma\) as seen from \(S\); a rod at rest in \(S'\) is contracted by \(1/\gamma\) along \(x\); events simultaneous in \(S\) at different \(x\) are not simultaneous in \(S'\); velocities compose as \(u=(u'+v)/(1+u'v/c^2)\). The same paper transformed Maxwell’s equations and derived the relativistic Doppler effect and aberration.

E = mc²

In Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? (received 27 September 1905), a body at rest emits two light pulses of energy \(L/2\) in opposite directions. In a frame where the body moves with speed \(v\), the pulses have energies \(\frac L2\gamma(1\pm\frac vc\cos\phi)\), whose sum is \(\gamma L\). Energy conservation in both frames then shows that the body’s kinetic energy drops by

In modern form, a particle has four-momentum \(p^\mu=(E/c,\mathbf p)\) with \(E^2=(pc)^2+(mc^2)^2\).

Minkowski’s spacetime

On 21 September 1908, at the meeting of German scientists in Cologne, Minkowski gave the lecture Raum und Zeit. He announced that space by itself and time by itself were doomed to fade into shadows, and that only a union of the two would survive. Relativity, in his formulation, is the geometry of a four-dimensional space with the invariant interval

and Lorentz transformations are its rotations. Minkowski introduced worldlines, the light cone and four-vectors, and he wrote electrodynamics in four-dimensional form. He died suddenly of appendicitis in January 1909, aged 44.

Einstein’s first reaction was cool. According to later recollections he regarded the four-dimensional reformulation as superfluous learnedness. He changed his mind when he needed it. The general theory is built on Minkowski’s idea, with the flat metric \(\eta_{\mu\nu}\) replaced by a curved metric \(g_{\mu\nu}\), and Einstein acknowledged this debt in his 1916 review.

General relativity: from equivalence to field equations

For the general reader. Newton’s gravity acts instantly across space, which special relativity forbids. Einstein spent eight years replacing it. His answer is that gravity is not a force: matter curves spacetime, and freely falling bodies follow the straightest possible paths in that curved geometry. The final equations came in November 1915, in a race with the mathematician David Hilbert.

The happiest thought (1907)

While writing a 1907 review of relativity, Einstein realized that a person falling freely from a roof would not feel their own weight. He later called it the happiest thought of his life. A uniform gravitational field is locally indistinguishable from a uniformly accelerated frame.

From this alone Einstein derived in 1907 and 1911 that clocks lower in a gravitational potential run slower (gravitational redshift, \(\Delta\nu/\nu\approx\Delta\Phi/c^2\)) and that light bends near the Sun. His 1911 deflection, 0.83″, was half the correct value, because it omitted the curvature of space.

Grossmann and the Entwurf

In 1912, back at the ETH, Einstein realized that gravity must be described by a metric \(g_{\mu\nu}\) and asked Marcel Grossmann for help with the geometry. Grossmann pointed him to the absolute differential calculus of Gregorio Ricci-Curbastro and Tullio Levi-Civita and to the Riemann curvature tensor. Their 1913 Entwurf (outline) theory had the right geometry for the motion of matter. Its field equations were not generally covariant. Einstein had considered equations built from the Ricci tensor and wrongly rejected them, and he justified the restriction with the hole argument, which seemed to show that generally covariant equations could not determine the metric uniquely. He later understood that points of spacetime have no identity apart from the fields, which dissolves the argument.

Göttingen and November 1915

From late June to early July 1915 Einstein gave six two-hour lectures on the Entwurf theory at Göttingen, at Hilbert’s invitation. He wrote afterwards that he had convinced Hilbert and Felix Klein. Hilbert began working on the problem himself, combining Einstein’s gravity with Gustav Mie’s theory of matter in a variational principle. That autumn Einstein found that the Entwurf equations failed to give the perihelion of Mercury and to admit rotating frames, and he returned to general covariance. He presented four communications to the Prussian Academy, on 4, 11, 18 and 25 November 1915, while corresponding with Hilbert. On 18 November he computed the perihelion advance of Mercury correctly. On 25 November he gave the final field equations.

Einstein wrote them in the equivalent trace-reversed form \(R_{\mu\nu}=\kappa\big(T_{\mu\nu}-\tfrac12g_{\mu\nu}T\big)\). Hilbert submitted Die Grundlagen der Physik to the Göttingen Society of Sciences on 20 November, five days earlier, and it was published in March 1916. For decades this suggested that Hilbert had found the field equations first. In 1997 Leo Corry, Jürgen Renn and John Stachel published the surviving page proofs, dated 6 December 1915. The proofs do not contain the explicit field equations, part of one page is cut away, and the theory they present is not generally covariant. The published version was revised after Einstein’s paper and cites it. The question is still debated, but the evidence favours independent work in which Einstein reached the equations of his own theory first, while Hilbert gave the elegant derivation from an action principle. Hilbert himself never claimed priority. The relationship was strained in late November 1915, and Einstein wrote to Hilbert on 20 December offering reconciliation.

Energy and Noether

The new theory raised a puzzle about energy. The gravitational field has no local energy–momentum tensor, and Hilbert noticed that his energy law seemed to hold as an identity. In 1915 Hilbert and Klein brought Emmy Noether to Göttingen to study the question. Her 1918 paper Invariante Variationsprobleme proved that invariance under a group depending on arbitrary functions, such as the diffeomorphisms of general relativity, yields identities among the field equations: here the contracted Bianchi identities \(\nabla_\mu G^{\mu\nu}\equiv0\). They force \(\nabla_\mu T^{\mu\nu}=0\), so matter obeys local conservation as a consequence of the field equations. Einstein, who published his own analysis of the energy law in 1918, wrote to Hilbert in May 1918 praising Noether’s penetrating mathematical thinking.

Classical tests and gravitational waves

For the general reader. A new theory of gravity had to agree with Newton almost everywhere and differ measurably somewhere. Einstein proposed three tests: the slow turning of Mercury’s orbit, the bending of starlight by the Sun, and the reddening of light climbing out of a gravitational field. He also predicted ripples in spacetime itself, which took a century to detect directly.

The Schwarzschild solution

In December 1915, while serving on the Russian front, Karl Schwarzschild found the exact solution outside a spherical mass \(M\). With \(r_s=2GM/c^2\),

Einstein had already computed the leading effects by approximation on 18 November 1915.

Derivation sketch for the perihelion

Geodesics of the Schwarzschild metric with \(u=1/r\) satisfy

where \(\ell\) is the angular momentum per unit mass. Without the last term, the solution is the Kepler ellipse \(u_0=\frac{GM}{\ell^2}(1+e\cos\phi)\). Substituting \(u_0\) into the small correction produces a resonant term \(\propto\phi\sin\phi\), and the solution becomes \(u\approx\frac{GM}{\ell^2}\big(1+e\cos[(1-\varepsilon)\phi]\big)\) with \(\varepsilon=3G^2M^2/(c^2\ell^2)\). The perihelion returns after \(2\pi/(1-\varepsilon)\approx2\pi(1+\varepsilon)\), and \(\ell^2=GMa(1-e^2)\) gives the formula above.

Testing

Urbain Le Verrier had found in 1859 that Mercury’s perihelion advanced faster than planetary perturbations allow; the excess is about 43″ per century, which general relativity explains exactly. Einstein later said that this result left him beside himself with excitement for days. Light deflection was tested at the total eclipse of 29 May 1919 by expeditions organized by Frank Dyson and Arthur Eddington, to Sobral in Brazil and Príncipe off West Africa. The results, announced in London on 6 November 1919, favoured the full Einstein value and made him world-famous overnight. The measurements were imprecise; radio interferometry since the 1970s has confirmed the prediction to better than one part in a thousand. The redshift was measured cleanly in the laboratory by Robert Pound and Glen Rebka in 1959, after Einstein’s death.

Gravitational waves

In June 1916 Einstein linearized his equations around flat spacetime, \(g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}\) with \(|h|\ll1\). With the trace-reversed field \(\bar h_{\mu\nu}=h_{\mu\nu}-\frac12\eta_{\mu\nu}h\) in the Lorenz gauge \(\partial^\mu\bar h_{\mu\nu}=0\), the equations become a wave equation:

The waves travel at speed \(c\) and have two transverse polarizations. The 1916 paper contained an error; Einstein corrected it in 1918 and derived the quadrupole formula.

Einstein doubted the physical reality of the waves more than once. In 1936 he and Nathan Rosen submitted a paper to Physical Review claiming that they do not exist. An anonymous referee, later identified as Howard Percy Robertson, found an error. Einstein angrily withdrew the paper, but after discussions with Robertson through Leopold Infeld he corrected it, and it appeared in 1937 in another journal with the opposite conclusion. Indirect evidence came from the binary pulsar discovered by Russell Hulse and Joseph Taylor in 1974, whose orbit decays exactly as the quadrupole formula predicts (Nobel Prize 1993). LIGO detected waves from merging black holes on 14 September 2015, and Rainer Weiss, Barry Barish and Kip Thorne received the 2017 Nobel Prize.

Quantum theory: A and B, Bose–Einstein, EPR

For the general reader. Einstein helped create quantum theory and then became its most persistent critic. In 1916 he explained how atoms absorb and emit light, discovering the stimulated emission behind the laser. In 1924 he extended an idea of Satyendra Nath Bose to atoms and predicted a new state of matter. In 1935 he argued that quantum mechanics must be incomplete, in a paper whose questions led to quantum information science.

Emission and absorption (1916–1917)

Consider atoms with two levels, energies \(E_1<E_2\), degeneracies \(g_1,g_2\), with \(E_2-E_1=h\nu\), in radiation of spectral energy density \(\rho(\nu)\). Einstein postulated three processes: absorption at rate \(B_{12}\rho\) per atom, spontaneous emission at rate \(A_{21}\), and induced (stimulated) emission at rate \(B_{21}\rho\).

In the same paper, Zur Quantentheorie der Strahlung (1917), Einstein showed that thermal equilibrium of the atoms’ motion requires each emission or absorption to transfer momentum \(h\nu/c\) in a definite direction. He was also troubled that the direction and moment of spontaneous emission are left to chance, the first appearance of quantum randomness in his work. Stimulated emission is the principle of the maser (1954) and laser (1960).

Bose–Einstein statistics (1924–1925)

In 1924 Bose, at Dacca, sent Einstein a derivation of Planck’s law that counted photon states in phase space without reference to classical waves. Einstein translated it into German and had it published in Zeitschrift für Physik. He then applied the counting to a gas of atoms in three papers (1924–1925). For indistinguishable bosons the mean occupation of a single-particle state of energy \(\varepsilon\) is

For an ideal gas of density \(n\), the excited states can hold at most \(n_c=\zeta(3/2)/\lambda_T^3\) particles, where \(\lambda_T=h/\sqrt{2\pi mkT}\) and \(\zeta(3/2)\approx2.612\).

Fritz London linked condensation to superfluid helium in 1938. A pure condensate in a dilute gas was made in 1995 by Eric Cornell and Carl Wieman with rubidium-87 and by Wolfgang Ketterle with sodium (Nobel Prize 2001).

The debate with Bohr and the EPR argument

Einstein accepted the empirical success of the new quantum mechanics of Werner Heisenberg, Erwin Schrödinger and Max Born, but not that it was complete. At the Solvay Conferences of 1927 and 1930 he proposed thought experiments to evade the uncertainty relations, the most famous being a box that emits a single photon, and Niels Bohr answered each one, in 1930 using Einstein’s own gravitational redshift. In 1935, with Boris Podolsky and Nathan Rosen, Einstein changed strategy and argued for incompleteness rather than inconsistency.

Schrödinger introduced the word entanglement in his response the same year. David Bohm restated the argument for spins in 1951. In 1964 John Bell showed that any local hidden-variable theory obeys inequalities that quantum mechanics violates. Experiments by John Clauser (1972), Alain Aspect (1982) and Anton Zeilinger and others confirmed the quantum predictions, and the three shared the 2022 Nobel Prize. Locality as EPR assumed it fails; the predictions of quantum mechanics hold.

Cosmology and the unified field

For the general reader. In 1917 Einstein applied his theory to the universe as a whole, founding modern cosmology. To keep the universe static he added a new term to his equations, which he later abandoned once the expansion of the universe was found; the term returned in 1998 as dark energy. His last thirty years went into a search for a single theory uniting gravity and electromagnetism, which did not succeed.

The static universe (1917)

In Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie (February 1917), Einstein sought a finite, static universe filled uniformly with matter, partly to satisfy Mach’s idea that inertia is fixed by the distribution of matter. The 1915 equations do not allow it, so he added a term:

Willem de Sitter found the same year a solution with \(\Lambda\) and no matter at all, which disappointed Einstein’s Machian hopes. Alexander Friedmann (1922, 1924) found expanding and contracting solutions; Einstein first claimed they contained an error, then retracted in 1923. Georges Lemaître (1927) independently derived expansion and connected it to galactic redshifts, and Edwin Hubble’s 1929 data established the expansion law. Eddington showed in 1930 that Einstein’s static model is unstable. In 1931 Einstein dropped the constant, and in 1932 he and de Sitter proposed the flat, matter-dominated model. The governing equation for a homogeneous universe with scale factor \(a(t)\) is the Friedmann equation

George Gamow later reported that Einstein called the constant the biggest blunder of his life; no written record from Einstein confirms the phrase. Observations of distant supernovae in 1998 showed the expansion is accelerating, consistent with a positive \(\Lambda\).

The unified field

General relativity geometrized gravity; electromagnetism remained a separate field placed on the geometry. From 1918 onward several unifications were proposed. Hermann Weyl’s 1918 theory of a gauge-invariant geometry was rejected by Einstein because it made the rate of a clock depend on its history; its idea of gauge invariance survived in quantum theory. Theodor Kaluza sent Einstein a five-dimensional theory in 1919, which Einstein held for two years before recommending it for publication in 1921. Oskar Klein in 1926 explained why the fifth dimension is unseen: it is compact and tiny.

Einstein’s own attempts included a metric-affine theory (1923–1925), distant parallelism with a tetrad field (1928–1931), five-dimensional projective theories with Walther Mayer and later Peter Bergmann, and from 1945 a theory with a non-symmetric field \(g_{\mu\nu}\), worked out with Ernst Straus and Bruria Kaufman and printed as an appendix to The Meaning of Relativity. None produced testable predictions or accounted for the quantum. Einstein knew he was isolated, but he hoped that a classical field theory without singularities might yield particles and quantum behaviour as consequences. The question of unification itself became central to physics after his death.

Berlin, 1914–1933

Planck and Nernst recruited Einstein to Berlin in 1913 with an exceptional offer: membership of the Prussian Academy, a professorship without teaching duties, and later the directorship of a new Kaiser Wilhelm Institute for Physics, which opened in 1917. He moved in April 1914. Within months Marić returned to Zurich with their sons Hans Albert and Eduard, and war broke out. Einstein signed a pacifist counter-manifesto against the nationalist manifesto of 93 German intellectuals. He worked through the war with intense productivity and in 1917 fell seriously ill. His cousin Elsa Löwenthal nursed him, and they married in June 1919, months after his divorce. The Nobel Prize money went to Marić, as agreed in the divorce.

The eclipse announcement of November 1919 made Einstein a public figure on a scale no scientist had known. He travelled widely: to the United States with Chaim Weizmann in 1921 to raise money for the Hebrew University, to Japan in 1922, to South America in 1925. He supported Zionism as a cultural project, pacifism, and international reconciliation through the League of Nations’ committee on intellectual cooperation. The same fame drew hostility. From 1920 an antisemitic campaign attacked relativity as Jewish physics, later backed by Nobel laureates Philipp Lenard and Johannes Stark. After the assassination of the foreign minister Walther Rathenau in 1922, Einstein was warned that he too was in danger.

The Nobel Prize in Physics for 1921 was awarded to him in November 1922, for his services to theoretical physics and especially the law of the photoelectric effect. Relativity was considered too controversial to name. He also received the Copley Medal of the Royal Society (1925) and the Gold Medal of the Royal Astronomical Society (1926). In Berlin he worked with Wander de Haas on the Einstein–de Haas effect (1915), with Leo Szilard on a refrigerator without moving parts (patented 1930), and with Bose’s idea on quantum gases. His close colleagues included Planck, Nernst, Max von Laue, Fritz Haber and Erwin Schrödinger, and his friend Paul Ehrenfest in Leiden.

Einstein was in the United States when Adolf Hitler took power in January 1933. He announced he would not return. In March 1933, in Antwerp, he surrendered his passport and renounced German citizenship, and he resigned from the Prussian Academy before it could expel him. His property was confiscated. After some months in Belgium and England he sailed for America.

Princeton, death, legacy, 1933–1955

Einstein joined the new Institute for Advanced Study in Princeton in October 1933 and stayed for the rest of his life. Elsa died in December 1936. His sister Maja lived with him from 1939, and his secretary Helen Dukas ran his household. He worked on unified field theory with assistants including Bergmann, Valentine Bargmann and Straus, and on the motion of bodies in general relativity with Infeld and Banesh Hoffmann. The 1938 Einstein–Infeld–Hoffmann paper showed that the equations of motion follow from the field equations alone. With Infeld he wrote the popular The Evolution of Physics (1938). Emmy Noether, also in exile, died in 1935, and Einstein wrote a letter to the New York Times in tribute to her.

In August 1939, persuaded by Szilard and Eugene Wigner, Einstein signed a letter to President Franklin Roosevelt warning that Germany might build atomic bombs. He took no part in the Manhattan Project and later regretted the letter. He became a United States citizen in 1940. After the war he campaigned for world government and nuclear disarmament, opposed McCarthyism, and spoke for civil rights. In 1952 the Israeli government offered him the presidency, which he declined. Days before his death he signed the Russell–Einstein Manifesto against nuclear weapons.

Einstein died at Princeton Hospital on 18 April 1955, aged 76, after the rupture of an abdominal aortic aneurysm. He had refused surgery. His body was cremated the same day and his ashes scattered at an undisclosed place.

Legacy

• Relativity: special relativity is built into all of particle physics; general relativity governs black holes, neutron stars, gravitational waves, cosmology and the GPS satellite clocks.
• Quantum physics: the photon, stimulated emission and lasers, Bose–Einstein condensates, and the entanglement questions behind quantum information.
• Statistical physics: Brownian motion, fluctuation–dissipation, and the theory of random processes used from biology to finance.
• Method: the use of principles and thought experiments to constrain theories, and the search for unification, now central to theoretical physics.
• Honours: the element einsteinium (99) is named for him; 2005 was declared the World Year of Physics for the centenary of 1905; his papers are edited in The Collected Papers of Albert Einstein (Princeton University Press, from 1987).

Sources and further reading

Biography

1. Albert Einstein, Wikipedia (with extensive references).
2. J. J. O’Connor and E. F. Robertson, Albert Einstein, MacTutor History of Mathematics.
3. The Nobel Prize in Physics 1921, NobelPrize.org.
4. A. Pais, Subtle is the Lord: The Science and the Life of Albert Einstein, Oxford University Press, 1982.
5. W. Isaacson, Einstein: His Life and Universe, Simon & Schuster, 2007.
6. J. D. Norton, Einstein 1905, course notes, University of Pittsburgh.
7. The Digital Einstein Papers, Princeton University Press and Caltech.

Physics

1. A. Einstein, Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt, Ann. Phys. 17 (1905) 132–148.
2. A. Einstein, Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen, Ann. Phys. 17 (1905) 549–560.
3. A. Einstein, Zur Elektrodynamik bewegter Körper, Ann. Phys. 17 (1905) 891–921.
4. A. Einstein, Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?, Ann. Phys. 18 (1905) 639–641.
5. A. Einstein, Eine neue Bestimmung der Moleküldimensionen, Ann. Phys. 19 (1906) 289–305.
6. H. Minkowski, Raum und Zeit, Physikalische Zeitschrift 10 (1909) 104–111.
7. A. Einstein, Die Feldgleichungen der Gravitation, Sitzungsber. Preuss. Akad. Wiss. (1915) 844–847.
8. A. Einstein, Die Grundlage der allgemeinen Relativitätstheorie, Ann. Phys. 49 (1916) 769–822.
9. A. Einstein, Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie, Sitzungsber. Preuss. Akad. Wiss. (1917) 142–152.
10. A. Einstein, Zur Quantentheorie der Strahlung, Physikalische Zeitschrift 18 (1917) 121–128.
11. A. Einstein, Über Gravitationswellen, Sitzungsber. Preuss. Akad. Wiss. (1918) 154–167.
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