14 March 1879–18 April 1955)
was a theoretical physicist who is widely regarded as one of the most influential
scientists of all time. His many contributions to physics include the special
and general theories of relativity, the founding of relativistic cosmology,
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 photon theory and wave-particle duality, the quantum
theory of atomic motion in solids, the zero-point energy concept, the semiclassical
version of the Schrödinger equation, and the quantum theory of a monatomic
gas which predicted Bose–Einstein condensation.
Einstein is best known for his theories of special relativity and general
relativity. He received the 1921 Nobel Prize in Physics “for his services
to Theoretical Physics, and especially for his discovery of the law of the
Einstein published more than 300 scientific and over 150 non-scientific
works. He is often regarded as the father of modern physics. Albert Einstein
was born in Ulm, in the Kingdom of Württemberg in the German Empire
on 14 March 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.
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. The Einsteins were non-observant Jews. Their son
attended a Catholic elementary school from the age of five until ten.
Although Einstein had early speech difficulties, he was a top student in
As he grew, Einstein built models and mechanical devices for fun and began
to show a talent for mathematics. In 1889 Max Talmud (later changed to Max
Talmey) 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"). Talmud was a poor
Jewish medical student from Poland. The Jewish community arranged for Talmud
to take meals with the Einsteins each week on Thursdays for six years. During
this time Talmud wholeheartedly guided Einstein through many secular educational
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 Matura 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
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 majority
of academic historians of science agree that she did not.
In early 1902, Einstein and Mileva Marić had a daughter they called Lieserl
in their correspondence, who was born in Novi Sad where the parents of Mileva
lived. Her full name is not known, and her fate is uncertain after 1903. Einstein
and Marić married in January 1903, and in May 1904 the couple’s first son,
Hans Albert Einstein, was born in Bern, Switzerland. Their second son, Eduard,
was born in Zurich in July 1910. In 1914, Einstein moved to Berlin, while
his wife remained in Zurich with their sons. Marić and Einstein divorced
on 14 February 1919, having lived apart for five years. Einstein married
Elsa Löwenthal (née Einstein) on 2 June 1919, after having had
a relationship with her since 1912. She was his first cousin maternally and
his second cousin paternally. In 1933, they emigrated permanently to the
United States. In 1935, Elsa Einstein was diagnosed with heart and kidney
problems and died in December, 1936.
The Einsteinhaus on the Kramgasse in Bern, where Einstein lived with his
wife during his Annus Mirabilis
Conrad Habicht, Maurice Solovine and Einstein, who founded the Olympia AcademyAfter
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.
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
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
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 a molecule with 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 temperatures
of about 1000 degrees, but at lower 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
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 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
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.
Main article: Annus Mirabilis Papers
Albert Einstein, 1905, The Miracle Year. On 30 April 1905, Einstein completed
his thesis with Alfred Kleiner, Professor of Experimental Physics, serving
as pro-forma advisor. Einstein was awarded a PhD by the University of Zurich.
His dissertation was entitled A New Determination of Molecular Dimensions.
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 and according to the statistical
interpretation, it 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.
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 kBT, 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 detected with a microscope and indeed,
as Brownian motion, had actually been observed by the botanist Robert Brown.
Einstein was able to identify this motion with that 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 non-zero and 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
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.
Thought experiments and a-priori physical principles
Einstein’s thinking underwent a transformation in 1905. He had come to understand
that quantum properties of light mean that Maxwell’s equations were only an
approximation. He knew that new laws would have to replace these, but he
did not know how to go about finding those laws. He felt that guessing formal
relations would not go anywhere.
So he decided to focus on a-priori principles instead, which are statements
about physical laws which can be understood to hold in a very broad sense
even in domains where they have not yet been shown to apply. A well accepted
example of an a-priori principle is rotational invariance. If a new force
is discovered in physics, it is assumed to be rotationally invariant almost
automatically, without thought. Einstein sought new principles of this sort,
to guide the production of physical ideas. Once enough principles are found,
then the new physics will be the simplest theory consistent with the principles
and with previously known laws.
The first general a-priori principle he found was the principle of relativity,
that uniform motion is indistinguishable from rest. This was understood by
Hermann Minkowski to be a generalization of rotational invariance from space
to space-time. Other principles postulated by Einstein and later vindicated,
are the principle of equivalence and the principle of adiabatic invariance
of the quantum number. Another of Einstein’s general principles, Mach’s principle
is fiercely debated, and whether it holds in our world or not is still not
The use of a-priori principles is a distinctive unique signature of Einstein’s
early work, which has become a standard tool in modern theoretical physics.
History of special relativity
His 1905 paper on the electrodynamics of moving bodies introduced his 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
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
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 with the statistical
interpretation, he confidently postulates that the light itself is made up
of localized particles, as this is the only reasonable interpretation of
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
This work was the foundation of condensed matter physics.
Old quantum theory
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
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 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 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 Nordström 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 ("draft") theory was the result of these investigations. As
its name suggests, it was a sketch of a theory, with the equations of motion
supplemented by additional gauge fixing conditions. Simultaneously less elegant
and more difficult than general relativity, Einstein abandoned the theory
after realizing that the hole argument was mistaken.
In 1912, Einstein returned to Switzerland to accept a professorship at his
alma mater, the ETH. Once back in Zurich, he immediately visited his old ETH
classmate Marcel Grossmann, now a professor of mathematics, 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.
Eddington’s photograph of a solar eclipse, which confirmed Einstein’s theory
that light “bends.” On 7th November 1919, the leading British newspaper The
Times printed a banner headline that read: “Revolution in Science – New Theory
of the Universe – Newtonian Ideas Overthrown.” 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 with dual expeditions in Sobral, northern
Brazil, and Príncipe, a west African island. 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
There have been 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
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. Einstein was president of
the German Physical Society (1916–1918). and also directed 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
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.
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
The use of non-covariant objects like pseudotensors was heavily criticized
in 1917 by Erwin Schrödinger and others.
Classical unified field theories
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
Einstein collaborated with others to produce a model of a wormhole. His
motivation was to model elementary particles with charge as a solution of
gravitational field equations, in line with the program outlined in the paper
"Do Gravitational Fields play an Important Role in the Constitution of the
Elementary Particles?". These solutions cut and pasted Schwarzschild black
holes to make a bridge between two patches. If one end of a wormhole was
positively charged, the other end would be negatively charged. These properties
led Einstein to believe that pairs of particles and antiparticles could be
described in this way.
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.
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.
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
In addition to his well-accepted results, some of Einstein’s papers contain
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 a 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 focusing 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 until his death his collaborator
Nathan Rosen maintained that gravitational waves are unstable.
1939: Einstein denied several times that black holes could form, 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 was 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 the use of the "fudge factor" lambda in 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
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 Schrödinger 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 ’Schwarzschild 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
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, Nathan Rosen, Peter
Bergmann and others, Einstein also had some one-shot collaborations with various
Einstein-de Haas experiment
Einstein-de Haas effect
Einstein and De Haas demonstrated that magnetization is due to the motion
of electrons, nowadays known to be the spin. In order to show this, they reversed
the magnetization in an iron bar suspended on a torsion pendulum. They confirmed
that this leads the bar to rotate, because the electron’s angular momentum
changes as the magnetization changes. This experiment needed to be sensitive,
because the angular momentum associated with electrons is small, but it definitively
established that electron motion of some kind is responsible for magnetization.
Schrödinger gas model
Einstein suggested to Erwin Schrödinger that he might be able to reproduce
the statistics of a Bose–Einstein gas by considering a box. Then to each possible
quantum motion of a particle in a box associate an independent harmonic oscillator.
Quantizing these oscillators, each level will have an integer occupation
number, which will be the number of particles in it.
This formulation is a form of second quantization, but it predates modern
quantum mechanics. Erwin Schrödinger applied this to derive the thermodynamic
properties of a semiclassical ideal gas. Schrödinger urged Einstein to
add his name as co-author, although Einstein declined the invitation.
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.
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. Repercussions of the Einstein–Bohr debate have
found their way into philosophical discourse.
Albert Einstein's 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 1954 letter, he wrote, "I do not believe in a personal God and I have
never denied this but have expressed it clearly.” In a letter to philosopher
Erik Gutkind, Einstein remarked, "The word God is for me nothing more than
the expression and product of human weakness, the Bible a collection of honorable,
but still purely primitive, legends which are nevertheless pretty childish."
Einstein had previously explored this belief that man could not understand
the nature of God when he gave an interview to Time Magazine explaining:
I'm not an atheist and I don't think I can call myself a pantheist. We are
in the position of a little child entering a huge library filled with books
in many different languages. The child knows someone must have written those
books. It does not know how. The child dimly suspects a mysterious order in
the arrangement of the books but doesn't know what it is. That, it seems to
me, is the attitude of even the most intelligent human being toward God.—Albert
Albert Einstein's political views
Einstein with Indian poet and Nobel laureate Rabindranath Tagore during
their widely publicized 14 July 1930 conversationThroughout the November
Revolution in Germany Einstein signed an appeal for the foundation of a nationwide
liberal and democratic party, which was published in the Berliner Tageblatt
on 16 November 1918, and became a member of the German Democratic Party.
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. He was a socialist Zionist who supported the creation of a Jewish
national homeland in the British mandate of Palestine.
After World War II, as enmity between the former allies became a serious
issue, Einstein 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 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.
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.
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.
Einstein bequeathed the royalties from use of his image to The Hebrew University
of Jerusalem. Corbis, successor to The Roger Richman Agency, licenses the
use of his name and associated imagery, as agent for the Hebrew University.
Albert Einstein in popular culture
In the period before World War II, Albert Einstein was so well-known in
America that he would be stopped on the street by people wanting him to explain
"that theory." He finally figured out a way to handle the incessant inquiries.
He told his inquirers "Pardon me, sorry! Always I am mistaken for Professor
Albert Einstein has been the subject of or inspiration for many novels,
films, and plays. Einstein is a favorite model for depictions of mad scientists
and absent-minded professors; his expressive face and distinctive hairstyle
have been widely copied and exaggerated. Time magazine’s Frederic Golden wrote
that Einstein was "a cartoonist’s dream come true."
Einstein’s association with great intelligence and originality has made
the name Einstein synonymous with genius.
Max Planck presents Albert Einstein with the Max Planck medal of the German
Physical Society, 28 June 1929, in Berlin, GermanyIn 1922, Einstein was awarded
the 1921 Nobel Prize in Physics, "for his services to Theoretical Physics,
and especially for his discovery of the law of the photoelectric effect".
This refers to his 1905 paper on the photoelectric effect, "On a Heuristic
Viewpoint Concerning the Production and Transformation of Light", which was
well supported by the experimental evidence by that time. The presentation
speech began by mentioning "his theory of relativity [which had] been the
subject of lively debate in philosophical circles [and] also has astrophysical
implications which are being rigorously examined at the present time." (Einstein
It was long reported that Einstein gave the Nobel prize money directly to
his first wife, Mileva Marić, in compliance with their 1919 divorce settlement.
However, personal correspondence made public in 2006 shows that he invested
much of it in the United States, and saw much of it wiped out in the Great
Einstein traveled to New York City in the United States for the first time
on 2 April 1921. When asked where he got his scientific ideas, Einstein explained
that he believed scientific work best proceeds from an examination of physical
reality and a search for underlying axioms, with consistent explanations that
apply in all instances and avoid contradicting each other. He also recommended
theories with visualizable results (Einstein 1954).
In 1999, Albert Einstein was named Person of the Century by Time magazine