Albert Einstein ( ; ; 14 March 1879–18 April
1955) was a
theoretical
physicist. 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
photoelectric
effect.”
Einstein published
more than 300
scientific and over 150 non-scientific works. He is often
regarded as the father of
modern
physics.
Early life and education
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 .
In 1880,
the family moved to Munich, where his
father and his uncle founded Elektrotechnische Fabrik
J. Einstein & Cie, a company that
manufactured electrical equipment based on
direct current.
The Einsteins 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 elementary
school. 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 interests.
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 ) 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 teaching post.
In the same year, Einstein’s future wife,
Mileva Marić, also entered the Polytechnic
to study mathematics and physics, the only woman in the academic
cohort. Over the next few years, Einstein and Marić’s friendship
developed into romance. In a letter to her, Einstein called Marić
“a creature who is my equal and who is as strong and independent as
I am.”Letter Einstein to Marić on 3 October 1900 (
Collected
Papers Vol. 1, document 79). 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.
Marriages and children
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.This conclusion
is from Einstein’s correspondence with Marić. Lieserl is first
mentioned in a letter from Einstein to Marić (who was staying with
her family in or near Novi Sad at the time of Lieserl’s birth)
dated 4 February 1902 (Collected papers Vol. 1, document
134). 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.
Patent office
After
graduating, Einstein spent almost two frustrating years searching
for a teaching post, but a former classmate’s father helped him
secure a job in Bern, at the
Federal
Office for Intellectual Property, the patent office, as an
assistant examiner. He
evaluated
patent applications for
electromagnetic devices. In 1903, Einstein’s position at the Swiss
Patent Office became permanent, although he was passed over for
promotion until he "fully mastered machine technology".
Much of his work at the patent office related to questions about
transmission of electric signals and electrical-mechanical
synchronization of time, two technical problems that show up
conspicuously in the
thought
experiments that eventually led Einstein to his radical
conclusions about the nature of light and the fundamental
connection between space and time.
With friends he met in Bern, Einstein formed a weekly discussion
club on science and philosophy, which he jokingly named "The
Olympia Academy." Their readings
included
Henri Poincaré,
Ernst Mach, and
David Hume, who influenced Einstein’s scientific
and philosophical outlook. The next year, Einstein published a
paper in the prestigious
Annalen
der Physik on the
capillary
forces of a straw.
Scientific career
Throughout his life, Einstein published hundreds of books and
articles. Most were about physics, but a few expressed leftist
political opinions about
pacifism,
socialism, and
zionism. In
addition to the work he did by himself he also collaborated with
other scientists on additional projects including the Bose-Einstein
statistics, the Einstein refrigerator and others.
Physics in 1900
Einstein’s early papers all come from attempts to demonstrate that
atoms exist and have a finite nonzero size. At the time of his
first paper in 1902, it was not yet completely accepted by
physicists that atoms were real, even though chemists had good
evidence ever since
Antoine
Lavoisier’s work a century earlier. The reason physicists were
skeptical was because no 19th century theory could fully explain
the properties of matter from the properties of atoms.
Ludwig Boltzmann was a leading 19th
century atomist physicist, who had struggled for years to gain
acceptance for atoms. Boltzmann had given an interpretation of the
laws of thermodynamics, suggesting that the law of entropy increase
is statistical. In Boltzmann’s way of thinking, the entropy is the
logarithm of the number of ways a system could be configured
inside. The reason the entropy goes up is only because it is more
likely for a system to go from a special state with only a few
possible internal configurations to a more generic state with many.
While Boltzmann’s statistical interpretation of entropy is
universally accepted today, and Einstein believed it, at the turn
of the 20th century it was a minority position.
The statistical idea was most successful in explaining the
properties of gases.
James Clerk
Maxwell, another leading atomist, had found the distribution of
velocities of atoms in a gas, and derived the surprising result
that the
viscosity of a gas should be
independent of density. Intuitively, the friction in a gas would
seem to go to zero as the density goes to zero, but this is not so,
because the
mean free path of atoms
becomes large at low densities. A subsequent experiment by Maxwell
and his wife confirmed this surprising prediction. Other
experiments on gases and vacuum, using a rotating slitted drum,
showed that atoms in a gas had velocities distributed according to
Maxwell’s distribution law.
In addition to these successes, there were also inconsistencies.
Maxwell noted that at cold temperatures, atomic theory predicted
specific heats that are too large. In classical
statistical mechanics, every
spring-like motion has thermal
energy
k_{B}T on average at temperature
T, so that the
specific heat
of every spring is
Boltzmann’s constant
k_{B}. 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 3
N
springs, so the specific heat of every solid is
3
Nk_{B}, 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
k_{B}T at high temperatures, and should
contribute an extra
k_{B} 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 physics.
The most glaring inconsistency was in the theory of light waves.
Continuous waves in a box can be thought of as infinitely many
spring-like motions, one for each possible
standing wave. Each standing wave has a
specific heat of
k_{B}, so the total specific heat
of a continuous wave like light should be infinite in classical
mechanics. This is obviously wrong, because it would mean that all
energy in the universe would be instantly sucked up into light
waves, and everything would slow down and stop.
These inconsistencies led some people to say that atoms were not
physical, but mathematical. Notable among the skeptics was
Ernst Mach, whose logical positivist philosophy
led him to demand that if atoms are real, it should be possible to
see them directly. Mach believed that atoms were a useful fiction,
that in reality they could be assumed to be infinitesimally small,
that
Avogadro’s number was
infinite, or so large that it might as well be infinite, and
k_{B} was infinitesimally small. Certain
experiments could then be explained by atomic theory, but other
experiments could not, and this is the way it will always be.
Einstein opposed this position. Throughout his career, he was a
realist. He believed that a single consistent theory should explain
all observation, and that this theory would be a description what
was really going on, underneath it all. So he set out to show that
the atomic point of view was correct. This led him first to
thermodynamics, then to statistical physics, and to the theory of
specific heats of solids.
In 1905, while he was working in the patent office, the leading
German language physics journal
Annalen der Physik published four of
Einstein’s papers. The four papers eventually were recognized as
revolutionary, and 1905 became known as Einstein’s "
Miracle Year", and the papers, as the
Annus Mirabilis
Papers.
Thermodynamic fluctuations and statistical physics
Einstein’s earliest papers were concerned with
thermodynamics. He wrote a paper establishing
a
thermodynamic identity in
1902, and a few other papers which attempted to interpret phenomena
from a statistical atomic point of view.
His research in 1903 and 1904 was mainly concerned with the effect
of finite atomic size on diffusion phenomena. As in Maxwell’s work,
the finite nonzero size of atoms leads to effects which can be
observed. This research, and the thermodynamic identity, were well
within the mainstream of physics in his time. They would eventually
form the content of his PhD thesis.
His first major result in this field was the theory of
thermodynamic fluctuations. When in equilibrium, a system has a
maximum entropy 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. This makes a connection between microscopic and macroscopic
objects.
Searching for ways to test this relation, his great breakthrough
came in 1905. The theory of fluctuations, he realized, would have a
visible effect for an object which could move around freely. Such
an object would have a velocity which is random, and would move
around randomly, just like an individual atom. The average kinetic
energy of the object would be k_BT, and the time decay of the
fluctuations would be entirely determined by the law of
friction.
The law of friction for a small ball in a viscous fluid like water
was discovered by
George
Stokes. He showed that for small velocities, the friction force
would be proportional to the velocity, and to the radius of the
particle (see
Stokes’ law). This
relation could be used to calculate how far a small ball in water
would travel due to its random thermal motion, and Einstein noted
that such a ball, of size about a
micron,
would travel about a few microns per second. This motion could be
easily observed with a microscope.Such a motion had already been
observed with a microscope by a Botanist named Brown, and had been
called
Brownian motion. Einstein was
able to identify this motion with the motion predicted by his
theory. Since the fluctuations which give rise to Brownian motion
are just the same as the fluctuations of the velocities of atoms,
measuring the precise amount of Brownian motion using Einstein’s
theory would show that Boltzmann’s constant is nonzero. It would
measure Avogadro’s number.
These experiments were carried out a few years later, and gave a
rough estimate of Avogadro’s number consistent with the more
accurate estimates due to
Max Planck’s
theory of blackbody light, and
Robert
Millikan’s measurement of the charge of the electron. Unlike
the other methods, Einstein’s required very few theoretical
assumptions or new physics, since it was directly measuring atomic
motion on visible grains.
Einstein’s theory of Brownian motion was the first paper in the
field of
statistical physics. It
established that thermodynamic fluctuations were related to
dissipation. This was shown by Einstein to be true for
time-independent fluctuations, but in the Brownian motion paper he
showed that dynamical relaxation rates calculated from classical
mechanics could be used as statistical relaxation rates to derive
dynamical diffusion laws. These relations are known as
Einstein relations.
The theory of Brownian motion was the least revolutionary of
Einstein’s
Annus mirabilis papers,
but it had an important role in securing the acceptance of the
atomic theory by physicists.
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 definitively established.
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.
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 =
mc^{2}. This
equation suggests that tiny amounts of mass could be
converted into huge amounts of
energy and presaged the development of
nuclear power.Einstein’s 1905 work on
relativity remained controversial for many years, but was accepted
by leading physicists, starting with
Max
Planck.
Photons
In a 1905 paper, Einstein postulated that light itself consists of
localized particles (
quanta). Einstein’s light quanta were
nearly universally rejected by all physicists, including
Max Planck and
Niels
Bohr. This idea only became universally accepted in 1919, with
Robert Millikan’s detailed
experiments on the photoelectric effect, and with the measurement
of
Compton scattering.
Einstein’s paper on the light particles was almost entirely
motivated by thermodynamic considerations. He was not at all
motivated by the detailed experiments on the photoelectric effect,
which did not confirm his theory until fifteen years later.Einstein
considers the entropy of light at temperature
T, and
decomposes it into a low-frequency part and a high-frequency part.
The high-frequency part, where the light is described by
Wien’s law, has an entropy which looks
exactly the same as the entropy of a gas of classical
particles.
Since the entropy is the logarithm of the number of possible
states, Einstein concludes that the number of states of short
wavelength light waves in a box with volume
V is equal to
the number of states of a group of localizable particles in the
same box. Since (unlike others) he was comfortable 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 the entropy.
This leads him to conclude that each wave of frequency
f
is associated with a collection of
photons
with energy
hf each, where
h is
Planck’s constant. He does not say
much more, because he is not sure how the particles are related to
the wave. But he does suggest that this idea would explain certain
experimental results, notably the
photoelectric effect.
Quantized atomic vibrations
Einstein continued his work on quantum mechanics in 1906, by
explaining the specific heat anomaly in solids. This was the first
application of quantum theory to a mechanical system.Since Planck’s
distribution for light oscillators had no problem with infinite
specific heats, the same idea could be applied to solids to fix the
specific heat problem there. Einstein showed in a
simple model that the hypothesis that solid
motion is quantized explains why the specific heat of a solid goes
to zero at zero temperature.
Einstein’s model treats each atom as connected to a single spring.
Instead of connecting all the atoms to each other, which leads to
standing waves with all sorts of different frequencies, Einstein
imagined that each atom was attached to a fixed point in space by a
spring. This is not physically correct, but it still predicts that
the specific heat is 3
Nk_{B}, 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
k_{B}T is much smaller than
hf,
the motion is frozen, and the specific heat goes to zero.
So Einstein concluded that quantum mechanics would solve the main
problem of classical physics, the specific heat anomaly. The
particles of sound implied by this formulation are now called
phonons. Because all of Einstein’s springs
have the same stiffness, they all freeze out at the same
temperature, and this leads to a prediction that the specific heat
should go to zero exponentially fast when the temperature is low.
The solution to this problem is to solve for the independent
normal modes individually, and to
quantize those. Then each normal mode has a different frequency,
and long wavelength vibration modes freeze out at colder
temperatures than short wavelength ones. This was done by
Debye, and after this modification, Einstein’s
quantization method reproduced quantitatively the behavior of the
specific heats of solids at low temperatures.
This work was the foundation of
condensed matter physics.
Adiabatic principle and action-angle variables
Throughout the 1910s, quantum mechanics expanded in scope to cover
many different systems. After
Ernest
Rutherford discovered the nucleus and proposed that electrons
orbit like planets,
Niels Bohr was able
to show that the same quantum mechanical postulates introduced by
Planck and developed by Einstein would explain the discrete motion
of electrons in atoms, and the
periodic table of the
elements.
Einstein contributed to these developments by linking them with the
1898 arguments
Wilhelm Wien had made.
Wien had shown that the hypothesis of
adiabatic invariance of a thermal
equilibrium state allows all the
blackbody curves at different
temperature to be derived from one another by a
simple shifting process.
Einstein noted in 1911 that the same adiabatic principle shows that
the quantity which is quantized in any mechanical motion must be an
adiabatic invariant.
Arnold
Sommerfeld identified this adiabatic invariant as the
action variable of classical
mechanics. The law that the action variable is quantized was the
basic principle of the quantum theory as it was known between 1900
and 1925.
Wave-particle duality
Although the patent office promoted Einstein to Technical Examiner
Second Class in 1906, he had not given up on
academia.
In 1908,
he became a privatdozent at
the University
of Bern.In "über die Entwicklung unserer
Anschauungen über das Wesen und die Konstitution der Strahlung"
("
The
Development of Our Views on the Composition and Essence of
Radiation"), on the
quantization of light, and in an
earlier 1909 paper, Einstein showed that
Max
Planck’s
energy quanta must have well-defined
momenta and act in some respects as independent,
point-like particles. This paper
introduced the
photon concept
(although the name
photon was introduced later by
Gilbert N. Lewis in 1926) and inspired the notion of
wave-particle duality in
quantum mechanics.
Theory of Critical Opalescence
Einstein returned to the problem of thermodynamic fluctuations,
giving a treatment of the density variations in a fluid at its
critical point. Ordinarily the density fluctuations are controlled
by the second derivative of the free energy with respect to the
density. At the critical point, this derivative is zero, leading to
large fluctuations. The effect of density fluctuations is that
light of all wavelengths is scattered, making the fluid look milky
white. Einstein relates this to
Raleigh scattering, which is what happens
when the fluctuation size is much smaller than the wavelength, and
which explains why the sky is blue.
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
hf, 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. (also in
Collected Papers Vol. 3, document
23) 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.
General relativity
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.
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 global renown.
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
Physics) movement.
Cosmology
In 1917, Einstein applied the General theory of relativity to model
the structure of the universe as a whole. He wanted the universe to
be eternal and unchanging, but this type of universe is not
consistent with relativity. To fix this, Einstein modified the
general theory by introducing a new notion, the
cosmological constant. With a positive
cosmological constant, the universe could be an
eternal static sphere
Einstein believed a spherical static universe is philosophically
preferred, because it would obey
Mach’s principle. He had shown that
general relativity incorporates Mach’s principle to a certain
extent in
frame dragging by
gravitomagnetic fields, but he knew that
Mach’s idea would not work if space goes on forever. In a closed
universe, he believed that Mach’s principle would hold.
Mach’s principle has generated much controversy over the
years.
Modern quantum theory
In 1917, at the height of his work on relativity, Einstein
published an article in
Physikalische Zeitschrift that
proposed the possibility of
stimulated emission, the physical
process that makes possible the
maser and the
laser.This article showed that the statistics
of absorption and emission of light would only be consistent with
Planck’s distribution law if the emission of light into a mode with
n photons would be enhanced statistically compared to the emission
of light into an empty mode. This paper was enormously influential
in the later development of quantum mechanics, because it was the
first paper to show that the statistics of atomic transitions had
simple laws.Einstein discovered
Louis
de Broglie’s work, and supported his ideas, which were received
skeptically at first. In another major paper from this era,
Einstein gave a wave equation for
de Broglie
waves, which Einstein suggested was the
Hamilton–Jacobi equation of
mechanics. This paper would inspire Schrödinger’s work of
1926.
Bose-Einstein statistics
In 1924, Einstein received a description of a
statistical model from Indian
physicist
Satyendra Nath Bose,
based on a counting method that assumed that light could be
understood as a gas of indistinguishable particles. Einstein noted
that Bose’s statistics applied to some atoms as well as to the
proposed light particles, and submitted his translation of Bose’s
paper to the
Zeitschrift
für Physik. Einstein also published his own articles
describing the model and its implications, among them the
Bose-Einstein condensate phenomenon
that some particulates should appear at very low temperatures.
It was
not until 1995 that the first such condensate was produced
experimentally by Eric Allin
Cornell and Carl Wieman using
ultra-cooling equipment built at the
NIST–JILA laboratory at the University
of Colorado at Boulder. Bose-Einstein statistics are now
used to describe the behaviors of any assembly of
bosons. Einstein’s sketches for this project may be
seen in the Einstein Archive in the library of the
Leiden University.
Energy momentum pseudotensor
General relativity includes a dynamical spacetime, so it is
difficult to see how to identify the conserved energy and momentum.
Noether’s theorem allows
these quantities to be determined from a
Lagrangian with
translation invariance, but
general covariance makes translation
invariance into something of a
gauge
symmetry. The energy and momentum derived within general
relativity by Noether’s presecriptions do not make a real tensor
for this reason.
Einstein argued that this is true for fundamental reasons, because
the gravitational field could be made to vanish by a choice of
coordinates. He maintained that the noncovariante energy momentum
pseudotensor was in fact the best description of the energy
momentum distribution in a gravitational field. This approach has
been echoed by
Lev Landau and
Evgeny Lifshitz, and others, and has become
standard.
The use of non-covariant objects like pseudotensors was heavily
criticized in 1917 by
Erwin
Schrödinger and others.
Unified field theory
Following his research on general relativity, Einstein entered into
a series of attempts to generalize his geometric theory of
gravitation, which would allow the explanation of electromagnetism.
In 1950, he described his "
unified
field theory" in a
Scientific American article
entitled "On the Generalized Theory of Gravitation." Although he
continued to be lauded for his work, Einstein became increasingly
isolated in his research, and his efforts were ultimately
unsuccessful.In his pursuit of a unification of the fundamental
forces, Einstein ignored some mainstream developments in physics,
most notably the
strong and
weak nuclear forces, which were
not well understood until many years after his death. Mainstream
physics, in turn, largely ignored Einstein’s approaches to
unification. Einstein’s dream of unifying other laws of physics
with gravity motivates modern quests for a
theory of everything and in particular
string theory, where geometrical
fields emerge in a unified quantum-mechanical setting.
Wormholes
Einstein collaborated with others to produce a model of a
wormhole. His motivation was to model elementary
particles with charge as a solution of gravitational field
equations, in line with the program outlined in the paper "Do
Gravitational Fields play an Important Role in the Constitution of
the Elementary Particles?". These solutions cut and pasted
Schwarzschild black holes to make a
bridge between two patches.
If one end of a wormhole was positively charged, the other end
would be negatively charged. These properties led Einstein to
believe that pairs of particles and antiparticles could be
described in this way.
Einstein-Cartan theory
In order to incorporate spinning point particles into general
relativity, the affine connection needed to be generalized to
include an antisymmetric part, called the
torsion. This modification was made by Einstein and
Cartan in the 1920s.
Einstein-Podolsky-Rosen paradox
In 1935, Einstein returned to the question of quantum mechanics. He
considered how a measurement on one of two entangled particles
would affect the other. He noted, along with his collaborators,
that by performing different measurements on the distant particle,
either of position or momentum, different properties of the
entangled partner could be discovered without disturbing it in any
way.
He then used a hypothesis of
local
realism to conclude that the other particle had these
properties already determined. The principle he proposed is that if
it is possible to determine what the answer to a position or
momentum measurement would be, without in any way disturbing the
particle, then the particle actually has values of position or
momentum.
This principle distilled the essence of Einstein’s objection to
quantum mechanics. As a physical principle, it has since been shown
to be incompatible with experiments.
Equations of motion
The theory of general relativity has two fundamental laws –
the
Einstein equations which
describe how space curves, and the
geodesic equation which describes how
particles move.
Since the equations of general relativity are non-linear, a lump of
energy made out of pure gravitational fields, like a black hole,
would move on a trajectory which is determined by the Einstein
equations themselves, not by a new law. So Einstein proposed that
the path of a singular solution, like a black hole, would be
determined to be a geodesic from general relativity itself.
This was established by Einstein, Infeld and Hoffmann for pointlike
objects without angular momentum, and by
Roy
Kerr for spinning objects.
Einstein’s mistakes
In addition to his well-accepted results, some of Einstein’s papers
contain mistakes:
- 1905: In the original German version of the special relativity
paper, and in some English translations, Einstein gives a wrong
expression for the transverse mass of a fast moving particle. The
transverse mass is the antiquated name for the ratio of the 3-force
to the 3-acceleration when the force is perpendicular to the
velocity. Einstein gives this ratio as \scriptstyle m/(1 -
v^2/c^2), while the actual value is \scriptstyle m/\sqrt{1 -
v^2/c^2} (corrected by Max Planck).
- 1905: In his PhD dissertation, the friction in dilute solutions
has an miscalculated numerical prefactor, which makes the estimate
of Avogadro’s number off by a factor of 3. The mistake is corrected
by Einstein in a later publication.
- 1905: An expository paper explaining how airplanes fly includes
an example which is incorrect. There is a wing which he claims will
generate lift. This wing is flat on the bottom, and flat on the
top, with a small bump at the center. It is designed to generate
lift by Bernoulli’s
principle, and Einstein claims that it will. Simple action
reaction considerations, though, show that the wing will not
generate lift, at least if it is long enough.
- 1911: Einstein predicted how much the sun’s gravity would
deflect nearby starlight, but used an approximation which gives an
answer which is half as big as the correct one.
- 1913: Einstein started writing papers based on his belief that
the hole argument made general
covariance impossible in a theory of gravity.
- 1922: Einstein published a qualitative theory of
superconductivity based on the vague idea of electrons shared in
orbits. This paper predated modern quantum mechanics, and is well
understood to be completely wrong. The correct BCS theory of low temperature superconductivity
was only worked out in 1957, thirty years after the establishing of
modern quantum mechanics.
- 1937: Einstein believed that the 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 rejecting them.
- Einstein initially opposed Minkowski’s geometrical formulation
of special relativity, changing his mind completely a few years
later.
- Based on his cosmological model, Einstein rejected expanding
universe solutions by Friedman and Lemaitre as unphysical, changing his mind when the
universe was shown to be expanding a few years later.
- Finding it too formal, Einstein believed that Heisenberg’s
matrix mechanics was incorrect. He
changed his mind when Schrödinger and others demonstrated that the
formulation in terms of the 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 inequality.
In addition to these well known mistakes, it is sometimes claimed
that the general line of Einstein’s reasoning in the 1905
relativity paper is flawed, or the photon paper, or one or another
of the most famous papers. None of these claims are widely
accepted.
Collaboration with other scientists
In addition to long time collaborators
Leopold Infeld,
Nathan Rosen,
Peter
Bergmann and others, Einstein also had some one-shot
collaborations with various scientists.
Einstein-de Haas experiment
Einstein and De Haas demonstrated that magnetization is due to the
motion of electrons, nowadays known to be the spin. In order to
show this, they reversed the magnetization in an iron bar suspended
on a
torsion pendulum. They
confirmed that this leads the bar to rotate, because the electron’s
angular momentum changes as the magnetization changes. This
experiment needed to be sensitive, because the angular momentum
associated with electrons is small, but it definitively established
that electron motion of some kind is responsible for
magnetization.
Schrödinger gas model
Einstein suggested to
Erwin
Schrödinger that he might be able to reproduce the statistics
of a
Bose-Einstein gas by
considering a box. Then to each possible quantum motion of a
particle in a box associate an independent harmonic oscillator.
Quantizing these oscillators, each level will have an integer
occupation number, which will be the number of particles in
it.
This formulation is a form of
second
quantization, but it predates modern quantum mechanics.
Erwin Schrödinger applied
this to derive the
thermodynamic
properties of a
semiclassical ideal gas. Schrödinger urged Einstein to add his
name as co-author, although Einstein declined the invitation.
Einstein refrigerator
In 1926, Einstein and his former student
Leó Szilárd co-invented (and in 1930,
patented) the
Einstein
refrigerator. This
Absorption refrigerator was then
revolutionary for having no moving parts and using only heat as an
input. On 11 November 1930, 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
In the 1920s,
quantum mechanics
developed into a more complete theory. Einstein was unhappy with
the
Copenhagen
interpretation of quantum theory developed by
Niels Bohr and
Werner Heisenberg. In this interpretation,
quantum phenomena are inherently probabilistic, with definite
states resulting only upon interaction with
classical systems. A public
debate between Einstein and
Bohr followed, lasting on and off for many years (including during
the
Solvay Conferences). Einstein
formulated
thought experiments
against the Copenhagen interpretation, which were all rebutted by
Bohr. In a 1926 letter to
Max Born,
Einstein wrote: "I, at any rate, am convinced that He [God] does
not throw dice."
Einstein was never satisfied by what he perceived to be quantum
theory’s intrinsically incomplete description of nature, and in
1935 he further explored the issue in collaboration with
Boris Podolsky and
Nathan Rosen, noting that the theory seems to
require
non-local interactions; this is
known as the
EPR paradox. The EPR
experiment has since been performed, with results confirming
quantum theory’s predictions.
Religious views
The question of scientific determinism gave rise to questions about
Einstein’s position on
theological determinism, and whether
or not he believed in God, or in a god. In 1929, Einstein told
Rabbi
Herbert S. Goldstein "I believe in
Spinoza’s God, who reveals Himself
in the lawful harmony of the world, not in a God Who concerns
Himself with the fate and the doings of mankind."
Politics
Throughout 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” . 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.
Death
On 17 April 1955, Albert Einstein experienced internal bleeding
caused by the rupture of an
abdominal aortic aneurysm, which
had previously been reinforced surgically by
Dr. Rudolph Nissen in 1948. He took
the draft of a speech he was preparing for a television appearance
commemorating the State of Israel’s seventh anniversary with him to
the hospital, but he did not live long enough to complete it.
Einstein refused surgery, saying: "I want to go when I want. It is
tasteless to prolong life artificially. I have done my share, it is
time to go. I will do it elegantly." He died in Princeton Hospital
early the next morning at the age of 76, having continued to work
until near the end. Einstein’s remains were cremated and his ashes
were scattered around the grounds of the Institute for Advanced
Study, Princeton, New Jersey.During the autopsy, the pathologist of
Princeton Hospital,
Thomas Stoltz
Harvey removed
Einstein’s brain for
preservation, without the permission of his family, in hope that
the neuroscience of the future would be able to discover what made
Einstein so intelligent.
Legacy
While
travelling, Einstein had written daily to his wife Elsa and adopted
stepdaughters, Margot and Ilse, and the letters were included in
the papers bequeathed to The Hebrew University. Margot Einstein permitted the personal
letters to be made available to the public, but requested that it
not be done until twenty years after her death (she died in 1986).
Barbara Wolff, of The Hebrew University’s Albert Einstein Archives,
told the
BBC that there are about 3,500 pages of
private correspondence written between 1912 and 1955.
The
United States’ National Academy of Sciences commissioned the Albert
Einstein Memorial, a monumental bronze and marble sculpture by
Robert Berks, dedicated in 1979 at its
Washington,
D.C. campus adjacent to the National Mall.
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.
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
Einstein."
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 has made the name
Einstein synonymous with genius.
Awards
In 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."
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 Depression.
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 .
In 1999, Albert Einstein was named
Person of the Century by
Time magazine, a
Gallup poll recorded him as the fourth most
admired
person of the 20th century in the U.S. and according to
The 100: A Ranking of the Most Influential
Persons in History, Einstein is "the greatest scientist of
the twentieth century and one of the supreme intellects of all
time."
Honors
Albert Einstein has been recognized many times over for his
achievements. The
International
Union of Pure and Applied Physics named 2005 the “
World Year of Physics” in
commemoration of the 100th anniversary of the publication of the
Annus Mirabilis Papers.
The
Albert Einstein Memorial in central Washington, D.C. is a monumental bronze
statue depicting Einstein seated with
manuscript papers in hand. The statue is located in a grove of trees
at the southwest corner of the grounds of the National Academy of Sciences on Constitution Avenue, near the Vietnam Veterans Memorial.
The
chemical element 99,
einsteinium, was named for him in August 1955,
four months after Einstein’s death.
In 1999
Time magazine named
him the
Person of the Century,
beating contenders like
Mahatma
Gandhi and
Franklin
Roosevelt, and in the words of a biographer, “to the
scientifically literate and the public at large, Einstein is
synonymous with genius.”
2001 Einstein is an inner
main belt
asteroid discovered on 5 March 1973.
The Albert Einstein Award (sometimes called the
Albert Einstein
Medal because it is accompanied with a gold medal) is an award
in
theoretical physics, that was
established to recognize high achievement in the natural sciences.
It was endowed by the Lewis and Rosa Strauss Memorial Fund in honor
of Albert Einstein’s 70th birthday. It was first awarded in 1951
and included a prize money of $ 15,000, which was later
reduced to $ 5,000.
The winner is selected by a committee (the
first of which consisted of Einstein, Oppenheimer, von Neumann and Weyl) of the Institute
for Advanced Study, which administers the award. Lewis L. Strauss used to be one of the trustees of
the institute.
The
Albert Einstein Peace Prize is an award that is given yearly by the
Chicago,
Illinois-based Albert Einstein Peace Prize
Foundation. Winners of the prize receive $50,000.
In 1990,
his name was added to the Walhalla temple.
See also
Publications
- The following publications by Albert Einstein are
referenced in this article. A more complete list of his
publications may be found at List of
scientific publications by Albert Einstein.
- . This annus mirabilis paper on the photoelectric effect was
received by Annalen der Physik 18^{th} March.
- . This PhD thesis was completed 30^{th} April and
submitted 20^{th} July.
- . This annus mirabilis paper on Brownian motion was received
11^{th} May.
- . This annus mirabilis paper on special relativity was received
30^{th} June.
- . This annus mirabilis paper on mass-energy equivalence was
received 27^{th} September.
- . First of a series of papers on this topic.
- . On Baer’s law and meanders in the courses of rivers.
- . The chasing a light beam thought experiment is
described on pages 48–51.
- Collected Papers: Further information about
the volumes published so far can be found on the webpages of the
Einstein Papers Project and on the Princeton
University Press Einstein Page
Notes
Further reading
- Moring, Gary (2004): The complete idiot’s guide to understanding
Einstein ( 1st ed. 2000). Indianapolis IN: Alpha books
(Macmillan USA). ISBN 0028631803
- Abraham Pais (1982): Subtle is
the Lord: The science and the life of Albert Einstein. Oxford
University Press. The definitive biography to date.
- -------- (1994): Einstein Lived Here. Oxford
University Press.
- Parker, Barry (2000): Einstein’s Brainchild.
Prometheus Books. A review of Einstein’s career and
accomplishments, written for the lay public.
- Isaacson, Walter (2007): Einstein: His Life and Universe. Simon
& Schuster. ISBN-13: 978-0-7432-6473-0
- Schweber, Sylvan S. (2008): Einstein and Oppenheimer: The Meaning of
Genius. Harvard University Press. ISBN 978-0674028289.
External links
nan:Albert Einstein