Like Columbus
Modern theoretical physicists like to think of themselves as intellectual explor
ers, and the greatest of them have indeed discovered new and exotic physical
worlds, both microscopic and macroscopic. Travel in these intellectually distant
realms has proved hazardous because it takes the explorer far from the world of
ordinary experience. Werner Heisenberg, one of the generation of theorists who
found the way to the quantum realm, the strangest of all the physical worlds,
likened the intellectual expeditions of modern physics to the voyage of Colum
bus. Heisenberg found Columbus’s feat remarkable not because Columbus tried
to reach the East by sailing west, nor because he handled his ships masterfully,
but because he decided to “leave the known regions of the world and sail west
ward, far beyond the point from which his provisions could have got him back
home again.” The man who ranks above all others as an intellectual Columbus
is Albert Einstein. He took such expeditions far beyond “the safe anchorage of
established doctrine” into treacherous, uncharted seas. Not only was he a pioneer
in the quantum realm; he discovered and explored much of the territory of mod
ern physics.
These great explorations were started, and to a large extent completed, when
Einstein was in his twenties and working in a quiet corner of the scientific world,
the Swiss Patent Office in Bern. Life in the patent office, as Einstein found it,
was a “kind of salvation.” The work was interesting, and not demanding; without
the pressures of an academic job, he was free to exploit his marvelous ability “to
scent out that which was able to lead to fundamentals and to turn aside from
everything else, from the multitude of things which clutter up the mind and
divert it from the essential.”
Einstein had tried to place himself higher professionally, but his prospects
after graduating from the Zu¨rich Polytechnic Institute (since 1911 known as the
Swiss Technical University or ETH) were not brilliant. He had disliked and op
posed most of his formal education. The teachers in his Munich gymnasium said he would never amount to anything, and deplored his disrespectful attitude. The
gymnasium experience aroused in Einstein a profound distrust of authority, par
ticularly the kind wielded by Prussian educators. Ronald Clark, one of Einstein’s
biographers, describes the Luitpold Gymnasium Einstein attended in Munich as
probably “no better and no worse than most establishments of its kind: It is true
that it put as great a premium on a thick skin as any British public school but
there is no reason to suppose that it was particularly ogreish. Behind what might
be regarded as not more than normal discipline it held, in reserve, the ultimate
weapon of appeal to the unquestionable Prussian god of authority. Yet boys, and
even sensitive boys, have survived as much.”
Einstein’s father, Hermann, was a cheerful optimist—“exceedingly friendly,
mild and wise,” as Einstein recalled him—but prone to business failures. One of
these drove the family from Munich to Milan, with Einstein left behind to com
plete his gymnasium courses. He had few friends among his classmates, and now
with his family gone, he could no longer bear life in Munich, or anywhere else
in Germany. He abruptly joined his family members in Italy and informed them
that he planned to surrender his German citizenship. That meant no gymnasium
diploma, but Einstein planned to do the necessary studying himself to prepare
for the Zu¨rich Poly entrance examination. Life in Italy, and later in Switzerland,
was free and promising again, and it “transformed the quiet boy into a commu
nicative young man,” writes Abraham Pais, a recent Einstein biographer. For a
few happy months, Einstein celebrated his release from a dismal future by roam
ing northern Italy.
Atemporary setback, failing marks in the Poly admission examination, proved
to be a blessing. To prepare for a second try, Einstein attended a Swiss cantonal
school in Aarau, where the educational process was, for a change, a joy. In Aarau,
Einstein lived with the Winteler family. Jost Winteler was the head of the school,
and “a somewhat casual teacher,” writes Clark, “as ready to discuss work or
politics with his pupils as his fellow teachers. [He] was friendly and liberal
minded, an ornithologist never happier than when he was taking his students
and his own children for walks in the nearby mountains.” Even in old age, Ein
stein recalled vividly his year in Aarau: “This school left an indelible impression
on me because of its liberal spirit and the unaffected thoughtfulness of the teach
ers, who in no way relied on external authority.”
In early 1896, Einstein paid a fee of three marks and was issued a document
declaring that he was no longer a German citizen; he would be a stateless person
for the next five years. Later in the year he passed the Zu¨rich Poly examination
with good marks and began the four-year preparation of a fachlehrer, a special
ized high-school teacher. Hermann had suffered another business disaster, so
Einstein’s means were now limited—a monthly allowance of one hundred Swiss
francs, from which he saved twenty francs to pay for his Swiss naturalization
papers. But there was nothing meager about his vision of the future. In a letter
to Frau Winteler, he wrote, “Strenuous labor and the contemplation of God’s
nature are the angels which, reconciling, fortifying and yet ceaselessly severe,
will guide me through the tumult of life.”
On the whole, Einstein did not respond with much enthusiasm to his course
work at the Zu¨rich Poly. He recognized that some of the mathematics courses
were excellent—one of his mathematics professors, Hermann Minkowski, later
made vital contributions to the mathematical foundations of the theory of rela
tivity—but the courses in experimental and theoretical physics were uninspiring At first he was fascinated by laboratory work, but his experimental projects rarely
met with the approval of his professor, Heinrich Weber. In exasperation, Weber
f
inally told his pupil, “You are a smart boy, Einstein, a very smart boy. But you
have one great fault: you do not let yourself be told anything.”
Einstein responded by simply staying away from classes and reading in his
rooms the great nineteenth-century theorists, Kirchhoff, Helmholtz, Hertz, Max
well, Hendrik Lorentz, and Boltzmann. Fortunately, the liberal Zu¨rich program
allowed such independence. “In all there were only two examinations,” Einstein
writes in his autobiographical notes, “aside from these, one could just about do
as one pleased....This gave one freedom in the choice of pursuits until a few
months before the examination, a freedom which I enjoyed and have gladly taken
into the bargain the bad conscience connected with it as by far the lesser evil.”
The punishment appears to have been more than a bad conscience, however.
Preparation for the final examination was a nightmare, and the outcome suc
cessful largely due to the help of a friend, Marcel Grossmann, who had a talent
for taking impeccable lecture notes. Einstein tells us, again in his autobiograph
ical notes, that the pressure of that examination “had such a deterring effect [on
me] that, after I had passed...I found consideration of any scientific problems
distasteful for an entire year.” And he adds this thought concerning the heavy
hand the educational system lays on a student’s developing intellectual interests:
“It is, in fact, nothing short of a miracle that the modern methods of instruction
have not yet entirely strangled the holy curiosity of inquiry; for this delicate little
plant, aside from stimulation, stands mainly in need of freedom.”
Einstein graduated from the Poly in the fall of 1900, and a few months later
passed two important milestones in his life: he published his first paper—in
volume 4 of the Annalen der Physik, which contained, just forty pages later, Max
Planck’s inaugural paper on quantum theory—and he received his long-awaited
Swiss citizenship. Although he was to leave Switzerland nine years later, and
did not return to settle, Einstein never lost his affection for the humane, demo
cratic Swiss and their splendid country, “the most beautiful corner on Earth I
know.”
He was now job hunting. An expected assistantship at the Zu ¨rich Poly under
Weber never materialized. (“Weber...played a dishonest game with me,” Ein
stein wrote to a friend.) Two temporary teaching positions followed, and then
with the help of Marcel Grossmann’s father, Einstein was appointed technical
expert third class at the Bern Patent Office in 1902.
Now that he had steady employment, Einstein thought of marriage, and a year
later he and Mileva Maric, a classmate at the Zu¨rich Poly, were married. Mileva
came from a Slavic-Serbian background. She was pretty, tiny in stature, and
slightly crippled from tuberculosis in childhood. She had hoped to follow a ca
reer in science, and went to Zu¨rich because Switzerland was the only German
speaking country at the time admitting women to university studies. The couple
became lovers soon after both entered the program at the Zu ¨rich Poly. By 1901,
the affair had deepened: Mileva was pregnant. In 1902, a daughter, Liserl, was
born at Mileva’s parents’ home in Novi Sad. When she returned to Zu¨rich, Mileva
did not bring the baby, and in 1903, shortly after Einstein and Mileva were mar
ried, the girl was apparently given up for adoption.
The marriage was never a success. After the trials of her pregnancy, a difficult
birth, and the loss of the child, Mileva’s career plans collapsed. She was jealous
of Einstein’s freewheeling friends, and prone to periods of depression. On his side, Einstein was not a sensitive husband; too much of his intellectual and
emotional strength was spent on his work to make a difficult marriage succeed.
In old age, Einstein recalled that he had entered the marriage with a “sense of
duty.” He had, he said, “with an inner resistance, embarked on something that
simply exceeded my strength.”
Precursors
In 1905, when he was twenty-six, happily employed in the Bern Patent Office,
and yet to make the acquaintance of (another) theoretical physicist, Einstein pub
lished three papers in the Annalen der Physik. This was volume 17 of that jour
nal, and it was, as Max Born remarks, “one of the most remarkable volumes in
the whole scientific literature. It contains three papers by Einstein, each dealing
with a different subject and each today acknowledged to be a masterpiece.”
The first of the 1905 papers was a contribution to quantum theory, which
developed a theory of the photoelectric effect by picturing light beams as showers
of particles, or “quanta.” I will have more to say about that revolutionary paper
in chapter 15. The second paper, on the reality of molecules observed as colloidal
particles, was mentioned in chapter 13 above. Our concern now is with the third
paper, which presented Einstein’s version of the theory of relativity.
By the time Einstein entered the field, relativity theory had a long and distin
guished history. Einstein counted among his precursors some of the giants: Ga
lileo, Newton, Maxwell, and Lorentz. Galileo stated the relativity principle ap
plied to mechanics in his usual vividly observed style:
Shut yourself up with some friend below decks on some large ship, and have
with you some flies, butterflies, and other flying animals. Have a large bowl of
water with some fish in it; hang up a bottle that empties drop by drop into a
wide vessel beneath it. With the ship standing still, observe carefully how the
little animals fly with equal speeds to all sides of the cabin. The fish swim
indifferently in all directions; the drop falls into the vessel beneath; and in
throwing something to your friend, you need to throw it no more strongly in
one direction than another, the distances being equal; jumping with your feet
together, you pass equal spaces in every direction. When you have observed all
these things carefully (though there is no doubt that when the ship is standing
still everything must happen this way), have the ship proceed with any speed
you like, so long as the motion is uniform and not fluctuating this way and that
[not accelerating]. You will discover not the least change in all the effects
named, nor could you tell from any of them whether the ship was moving or
standing still.
Galileo’s ship, or any other system moving at constant speed, is called in mod
ern terminology an “inertial frame of reference,” or just an “inertial frame,” be
cause in it Galileo’s law of inertia is preserved. Galileo’s relativity principle,
generalized, tells us that the laws of mechanics are exactly the same in any in
ertial frame (“nor could you tell from any of the [observed effects] whether the
ship was moving or standing still”).
Newton’s statement of the relativity principle, which he derived from his three
laws of motion, was similar, except that it raised the later contentious issue of
“space at rest”: “The motions of bodies included in a given space are the same among themselves, whether that space is at rest, or moves uniformly forwards in
a right [straight] line without any circular motion.” At rest with respect to what?
Newton believed in the concept of absolute space relative to which all motion,
or lack of motion, could be referred. In the same vein, he adopted an absolute
time frame in which all motion could be measured; one time frame served all
observers.
Maxwell and his contemporaries accepted Newton’s concept of absolutespace,
and they filled it with the all-pervading medium they called ether. The principal
role of the ether for nineteenth-century theorists was to provide a mechanism for
the propagation of light and other electromagnetic fields through otherwise
empty space. The ether proved to be a versatile theoretical tool—too versatile.
British and Continental theoreticians could never reach a consensus concerning
which of the many ether models was the standard one.
The man who saw ether physics and its connections with field theory most
clearly, and at the same time helped Einstein find his way, was Hendrik Lorentz,
professor of theoretical physics at the University of Leiden from 1877 to 1912.
Lorentz was revered by generations of young physicists for his remarkable ability
to play the dual roles of creative theorist and sympathetic critic. Like Maxwell
and Gibbs, it was not his style to gather a school of research students, yet phys
icists from all over the world attended his lectures on electrodynamics. After the
turn of the century, he was recognized by one and all as the leader of the inter
national physics community. Beginning in 1911, he acted as president of the
Solvay Conferences in Brussels, named after Ernest Solvay, an industrial chemist
with formidable wealth and an amateur’s interest in physics, who paid the bill
for the participants’ elegant accommodations at the conferences. No one but Lor
entz could bring harmony to these international gatherings, which Einstein liked
to call “Witches’ Sabbaths.” “Everyone remarked on [Lorentz’s] unsurpassed
knowledge, his great tact, his ability to summarize lucidly the most tangled ar
guments, and above all his matchless linguistic skill,” writes one of Lorentz’s
biographers, Russell McCormmach. After attending the first Solvay Conference,
Einstein wrote to a friend, “Lorentz is a marvel of intelligence and exquisite tact.
A living work of art! In my opinion he was the most intelligent of the theoreti
cians present.”
As a theorist, Lorentz’s principal goal was to unify at the molecular level the
physics of matter with Maxwell’s physics of electromagnetic fields. One of the
foundations of Lorentz’s theory was the concept that the seat of electric and
magnetic fields was an absolutely stationary ether, which permeated all matter
with no measurable resistance. Another cornerstone provided the assumption
that (to some degree) matter consisted of very small charged particles, which
Lorentz eventually identified with the particles called “electrons” discovered in
1897 by J. J. Thomson in cathode rays. The electrons generated the electric and
magnetic fields, and the fields, in turn, guided the electrons through the immobile
ether. Lorentz used Maxwell’s equations, written for the ether’s stationary frame
of reference, to describe the fields, and he accepted the message of the equations
that in that frame the speed of light was the same regardless of the speed and
the direction of the light source.
To summarize, and bring the story around to Einstein’s point of view, imagine
two observers, the first at rest in the ether, and the second at rest in a room
moving at constant speed with respect to the ether. The room carries a fixed light
source, and the two observers compare notes concerning the light signals gen erated by the source. According to Lorentz’s theory, the first observer finds that
the speed of a light beam is independent of its direction. But the second observer
sees things differently: suppose one of the walls of his or her room moves away
from a light beam after it is generated, while the opposite wall moves toward it.
If the light source is fixed in the center of the room, a light beam directed toward
a wall retreating from the beam will seem to be slower than a beam directed to
a wall approaching the beam. Thus for the second observer the speed of light is
not the same in all directions.
To take this argument beyond a thought experiment, we can picture Earth as
a “room” moving through the ether and conclude that for us, the occupants of
the room, the speed of light should be different when it is propagated in different
directions. We anticipate that if we can observe this directional effect it will
define Earth’s motion with respect to the ether. Several experiments, designed
and executed in the late nineteenth century, had this motivation. The most re
f
ined of these was performed by Albert Michelson and Edward Morley in 1887.
Their conclusion, probably the most famous negative result in the history of
physics, was that the speed of light (in empty space) has no dependencewhatever
on the motion, direction, or location of the light source.
This was a damaging, but not quite fatal, blow to Lorentz’s electron theory. He
found that he could explain the Michelson-Morley result by assuming that mov
ing material objects contract slightly in their direction of motion, just enough to
frustrate the Michelson-Morley experiment and other attempts to define Earth’s
motion through the ether by measuring changes in the speed of light. The cause
of this contraction, as Lorentz saw it, was a very slight alteration of molecular
forces in the direction of the motion.
Now it is time to bring Technical Expert Third Class Einstein on stage and
follow his creation of what came to be called the special theory of relativity. He
is acquainted with Galileo’s relativity principle. He is aware of Newton’s concept
of absolute space and time. He has read Lorentz carefully, and he is impressed
that experimentalists can find no way to detect Earth’s motion relative to the
ether by measuring changes in the speed of light.
Doctrine of Space and Time
For Einstein, there were two important kinds of theories. “Most of them are con
structive,” he wrote. “They attempt to build up a picture of the more complex
phenomena out of the materials of a relatively simple formal scheme from which
they start out.” As an example, he cited the molecular theory of gases. It begins
with the hypothesis of molecular motion, and builds from that to account for a
wide variety of mechanical, thermal, and diffusional properties of gases. “When
we say that we have succeeded in understanding a group of natural processes,”
Einstein continued, “we invariably mean that a constructive theory has been
found which covers the processes in question.”
Theorists since Galileo and Newton have also created what Einstein called
“principle theories.” These are theories that “employ the analytic, not the syn
thetic, method. The elements which form their basis and starting point are not
hypothetically constructed but empirically discovered ones, general character
istics of natural processes, principles that give rise to mathematically formulated
criteria which the separate processes or the theoretical representations of them
have to satisfy.” The supreme example of a principle theory, Einstein pointed out, is thermodynamics, based on the energy and entropy principles called the
f
irst and second laws of thermodynamics.
Einstein saw relativity as a principle theory. He began his 1905 paper on rel
ativity by postulating two empirical principles on which his theory, with all its
startling conclusions, would rest. The first principle generalized Galileo’s rela
tivity principle by asserting that (as Einstein put it several years later)
The laws of nature are independent of the state of motion of the frame of ref
erence, as long as the latter is acceleration free [that is, inertial].
The phrase “laws of nature” is all-inclusive; it encompasses the laws of elec
tromagnetic and optical, as well as mechanical, origin. This is a grandly demo
cratic principle: all inertial frames of reference are equal; none is different or
preferred.
The second of Einstein’s principles gives formal recognition to the constancy
of the speed of light:
Light in empty space always propagates with a definite [speed], independent of
the state of motion of the emitting body.
Whereas Lorentz had struggled to explain the invariance of the speed of light
with a constructive theory that hypothesized motion-dependentmolecularforces,
Einstein bypassed all the complications by simply promoting the constancy to a
postulate. For Lorentz and his contemporaries, it was a problem, for Einstein a
principle.
Einstein’s two principles led him to conclude that the speed of light in free
space is the only measure of space and time that is reliably constant from one
observer to another. All else is relative. Different observers cannot express their
physical laws in a shared, absolute frame of reference, as Newton taught. Ob
servers in different inertial frames find that their physical worlds are different
according to a new “doctrine of space and time,” as Einstein put it.
converts about 1.5
10*10 kilogram of mass to energy. Nuclear reactions are
more efficient; they convert a few tenths of a percent of the mass entering the
reaction to energy. When matter meets antimatter, the conversion is complete. In
his 1905 paper, Einstein suggested that radioactive materials such as radium
might lose measurable amounts of mass as they decay, but for many years he
could see no practical consequences of the mass-energy equivalence. (In 1934,
the Pittsburgh Gazette headlined a story reporting an Einstein lecture with “Atom
Energy Hope Is Spiked by Einstein. Efforts at Loosing Vast Force [Are] Called
Fruitless.”) The full lesson of E mc2 was learned in the 1940s and 1950s with
the advent of nuclear physics, nuclear weapons, nuclear reactors, and nuclear
anxiety.
A further accomplishment of Einstein’s relativity theory was that it brought a
permanent end to the ether concept by simply depriving the ether of any good
reason to exist. If there were an ether, it would provide an absolute and preferred
frame of reference, contrary to Einstein’s first principle, and motion through the
ether would be manifested by variations in the speed of light, contradicting the
second principle. An ether obituary was written by Einstein and Leopold Infeld
in their estimable book for the lay reader, The Evolution of Physics: “It [the ether]
revealed neither its mechanical construction nor absolute motion. Nothing re
mained of all its properties except that for which it was invented, i.e., its ability
to transmit electromagnetic waves.”
Berlin
Our narrative returns to Einstein’s life now, and follows his odyssey into the
scientific world and beyond. Einstein’s accomplishments during his seven years in the Bern Patent Office were unique in their creative brilliance. Inevitably,
recognition came, and suddenly, in just five years, he reached the pinnacle of
the scientific and academic world.
In 1909, when he was thirty, and still unacquainted with a “real physicist,”
Einstein left the patent office and took a position as associate professor at the
University of Zu¨rich. He was Clausius’s successor: “There had been no professor
of theoretical physics or mathematical physics,” Abraham Pais, Einstein’s biog
rapher, notes, “since Clausius had left the university, in 1867.” Pais also paints
this picture of Einstein as a sometimes unenthusiastic teacher: “He appeared in
class in somewhat shabby attire, wearing pants that were too short and carrying
with him a slip of paper the size of a visiting card on which he had sketched his
lecture notes.” “He enjoyed explaining his ideas,” Ernst Straus, one of Einstein’s
assistants, remarks, “and was exceptionally good at it because of his own way of
thinking in intuitive and informal terms. What he presumably found irksome
was the need to prepare and present material that was not at the moment at the
center of his interest. Thus the preparation of lectures would interfere with his
own thoughts.”
In Zu¨rich, Einstein was already beginning to show signs of the restlessness
that was hard to understand in a man who always said he wanted to do nothing
but think about theoretical physics. In five years, he would live in three countries
and hold academic positions in four universities. In another five years, he would
be immersed in various political matters, including pacifism, Zionism, and in
ternational government. “In his sixties,” Pais explains, “[Einstein] once com
mented that he had sold himself body and soul to science, being in flight from
the ‘I’ and ‘we’ to the ‘it.’ Yet he did not seek distance between himself and other
people. The detachment lay within and enabled him to walk through life im
mersed in thought. What was so uncommon about this man is that at the same
time he was neither out of touch with the world nor aloof.”
His next move, in 1911, was from Zu¨rich to Prague, where he was appointed
full professor at the Karl-Ferdinand (or German) University. In Prague, he felt
isolated intellectually and culturally. There were few scientific colleagues with
whom he could discuss his work, and he had little in common with either the
Czech or the German community. Sixteen months later he was on the moveagain,
back to Zu¨rich, this time to the Swiss Technical University (ETH, previously the
Zu ¨rich Poly).
A little more than a year later, in the spring of 1913, Max Planck and Walther
Nernst arrived in Zu ¨rich with their wives for the some sightseeing—and to entice
Einstein to go to Berlin. Their offer included membership in the Prussian Acad
emy of Sciences with a handsome salary, a chair at the University of Berlin (with
no obligation to teach), and the directorship of a physics institute to be estab
lished. This was a great opportunity, but Einstein was ambivalent. He had turned
his back on Germany seventeen years earlier, and he was no less distrustful of
the Prussian character now than he was then. But for Einstein there was always
one consideration above all others. “He had had enough of teaching. All he
wanted to do was think,” as Pais puts it. His decision probably came quickly,
but to Planck and Nernst, symbols of the Prussian scientific establishment, he
said he needed to consider the offer. He told them that when they saw him again
they would know his decision: he would carry a rose, red if his answer was yes,
and white if no.
The letter Planck and Nernst wrote to the Prussian Ministry of Education in support of Einstein’s appointment tells a lot about where Einstein’s reputation
stood in 1913, alleged failures included:
[Einstein’s] interpretation of the time concept has had sweeping repercussions
on the whole of physics, especially mechanics and even epistemology....Al
though this idea of Einstein’s has proved itself so fundamental for the devel
opment of physical principles, its application still lies for the moment on the
frontier of the measurable....Farmore important for practical physics is his
penetration of other questions on which, for the moment, interest is focused.
Thus he was the first man to show the importance of the quantum theory for
the energy of atomic and molecular movements, and from this he produced the
formula for specific heats of solids....Healso linked the quantum hypothesis
with the photoelectric and photochemical effects....All inall, one can say
that among the great problems, so abundant in modern physics, there is hardly
one to which Einstein has not brought some outstanding contribution. That he
may sometimes have missed the target in his speculations, as, for example, in
his theory of light quanta [now called “photons” and indispensable as a member
of the family of elementary particles], cannot be held against him. For in the
most exact of natural sciences every innovation entails risk. At the moment he
is working on a new theory of gravitation, with what success only the future
will tell.
The rose was red, and Einstein moved to Berlin, delighted that he would be
free of lecturing, but with misgivings concerning his end of the bargain. “The
gentlemen in Berlin are gambling on me as if I were a prize hen,” he told a friend
before leaving Zu¨rich. “As for myself I don’t even know whether I’m going to lay
another egg.”
An imposing measure of the dominion of science is that it brought together
on amicable terms two men as totally dissimilar as Einstein and Planck. Einstein
avoided all formality and ceremony, detested the Prussian traditions of disci
pline, militarism, and nationalism, and for most of his life was a pacifist. Yet,
this casual, untidy, anti-Prussian pacifist had a deep respect for Max Planck, the
formal, impeccably dressed servant of the Prussian state. What Einstein saw and
appreciated in Planck was the strength of his integrity and the depth of his com
mitment to science. Einstein always had admiration—and sometimes friend
ship—for anyone who could match the intensity of his own devotion to physics.
The move to Berlin was the final blow to an already slipping marriage. Soon
after her arrival in Berlin, Mileva returned to Zu¨rich with her two sons and
remained there. Her subsequent life was not happy. She could not accept the
separation, or the divorce that came in 1919. Her means were modest, even after
Einstein transmitted to her his Nobel Prize money, received in 1921. The younger
son, Eduard, was mentally unstable for much of his life and died a schizophrenic
in a Zu¨rich psychiatric hospital.
Einstein was now a bachelor, and under the “loving care” of a “cousine,” who
he claimed “drew me to Berlin.” This was Elsa Einstein Lo¨wenthal, both a first
and second cousin to Einstein (their mothers were sisters, and their grandfathers
brothers), and a friend since childhood. She had married young, was now di
vorced, and was living with her two daughters, Margot and Ilse, in Berlin when
Einstein arrived. In 1917, Einstein suffered a serious breakdown of his health,
and Elsa was on hand to supervise his care and feeding. The patient recovered and two years later married the nurse. Although Einstein rarely expressed his
appreciation, he must have realized that Elsa was indispensable. Like some of
the other wives mentioned in these profiles, she became an efficient manager of
her husband’s nonscientific affairs, and allowed him to get on with his main
business, thinking about theoretical physics.
Pais gives us this sketch of Elsa: “gentle, warm, motherly, and prototypically
bourgeoisie, [she] loved to take care of her Albertle. She gloried in his fame.”
Charlie Chaplin, who entertained the Einsteins in California, described Elsa this
way: “She was a square-framed woman with abundant vitality; she frankly en
joyed being the wife of a great man and made no attempt to hide the fact; her
enthusiasm was endearing.”
Hardly any chapter from the Einstein story is conventional or predictable, but
the most bizarre episode by far was the public reaction to Einstein’s elaboration
of his 1905 “special” theory of relativity to a “general” theory of relativity in
1915. It was not the theory itself, which few people understood, but the an
nouncement that one of the theory’s predictions had been confirmed, thatbrought
the avalanche of attention.
Einstein had used his general theory to show that a gravitational field has a
bending effect on light rays, and he had calculated the expected effect of the
Sun’s gravity on light originating from stars and passing near the Sun before
reaching telescopes on Earth. The effect was small, but measurable if the obser
vations could be made during a solar eclipse. After failures, delays, and much
political interference—the First World War was in progress at the time—two Brit
ish expeditions, one under Arthur Eddington to the island of Principe off the
coast of West Africa, and another led by Andrew Crommelin to Sobral innorthern
Brazil, observed the eclipse of 1919, and succeeded in confirming Einstein’s
predictions.
Overnight, Einstein became the most famous scientist in the world. He was
besieged by distinguished and not-so-distinguished colleagues, learned societies,
reporters, and plain people. “Since the flood of newspaper articles,” he wrote to
a friend, “I have been so swamped with questions, invitations, challenges, that I
dream I am burning in Hell and the postman is the Devil eternally roaring at me,
throwing new bundles of letters at my head because I have not answered the old
ones.” It is all but impossible to understand what prompted this reaction to what
was after all an esoteric and theoretical effort. The mathematician and philoso
pher Alfred Whitehead expressed public sentiment on the more rational side: “a
great adventure in thought [has] at length come to safe shore.
Spacetime
The new doctrine of space and time brought by Einstein’s 1905 special theory
demanded relativity of time as well as relativity of length and space. If an ob
server in an inertial frame describes some event with the coordinates x, y, z, and
the time t, another observer in a different inertial frame uses different coordi
nates, call them x', y', z', and a different time t', to express the physics of the
event. The time variable is not separate from the spatial variables, as it is in
Newtonian physics. It enters the Einstein picture seemingly on the same footing
as the spatial variables. This point of view was taken by one of Einstein’s former
mathematics professors, Hermann Minkowski, and developed into a mathemat
ical structure that would eventually be indispensable to Einstein as he ventured beyond special relativity to general relativity. Minkowski put forward his pro
gram at the beginning of an address delivered in 1908: “The views of space and
time which I wish to lay before you have sprung from the soil of experimental
physics, and therein lies their strength. They are radical. Henceforth space by
itself, and time by itself, are doomed to fade away into mere shadows, and only
a kind of union of the two will preserve an independent reality.”
Physics is about events in space and time. We locate each event in space in a
reference frame equipped with a coordinate system. For example, two events are
located in two spatial dimensions with the coordinate pairs x1, y1 and x2, y2 (fig.
14.5), and the spatial interval l between them is calculated by constructing a
right triangle (fig. 14.6) and applying the Pythagorean theorem:
Physics as Geometry
Einstein’s 1905 theory “in diapers” had made a powerful statement about the
physical world, but Einstein knew immediately that there was room for improve
ment. For one thing, the theory seemed to be restricted to inertial systems. For
another, it was compatible with Maxwell’s electromagnetic theory, but not with
another great theory inherited by Einstein, Newton’s gravitation theory. To realize
its potential, the theory had to recognize noninertial systems, those accelerating
relative to each other, and at the same time extend its scope to gravitation.
The first step Einstein took in this direction killed both of these birds with
one stone. As he explained later, “I was sitting in a chair in the patent office at
Bern when all of a sudden a thought occurred to me: ‘If a person falls freely he
will not feel his own weight.’ I was startled. This simple thought made a deep
impression on me. It impelled me toward a theory of gravitation.” This was Ein
stein’s first mental image of what he would later call “the equivalence principle.”
The central idea is that gravitation is relative. The person in free fall, locked
inside a falling elevator, let’s say, finds no evidence of gravity: everything in the
elevator seems to be at rest and without weight. An outside observer, on the other
hand, sees the elevator accelerating in the grip of a gravitational field.
The elevator inhabitants have the opposite experience if the elevator is re
moved from the gravitational field and accelerated at a constant rate upward with
an attached rope (fig. 14.7). Now the outside observer sees no gravitational field,
while the inside observer and all his or her belongings are held to the floor of
the elevator exactly as if they were in a gravitational field. The “equivalence”
here is between an accelerating system in field-free space and an inertial system
in a gravitational field. Reasoning this way, Einstein began to see how both grav
itation and acceleration could be introduced into relativity theory.
The elevator-on-a-rope image (developed later by Einstein and Infeld) shows
how the equivalence principle justifies an initial version of Einstein’s prediction
of light rays bent by gravity, which ten years later would bring the world clam
oring to his door. Picture the elevator on a rope with a light ray traveling across
the elevator from left to right. The outside observer sees elevator and light ray as
shown in figure 14.8. Because the light ray takes a finite time to travel from wall
to wall, and the elevator is accelerated upward during that time, the outside
observer sees the light ray traveling the slightly curved path shown. The inside
observer also sees the light ray bent, but is not aware of the acceleration and
attributes the effect to the equivalent gravitational field that holds that observer
to the floor of the elevator. The inside observer believes that the light ray should
respond to a gravitational field because it has energy, and therefore, by the E
mc2 prescription, also has mass. Like any other object with mass, the light ray
responds to a gravitational field.
With the equivalence principle as his guide, Einstein began in 1907 to gen
eralize his relativity theory so that it encompassed gravity and acceleration. As
he proceeded, he became increasingly convinced that he was dealing with a
problem in a strange kind of geometry. Even in special relativity there are hints
that acceleration and the equivalent gravitation spell violations of some of Eu
clid’s theorems, such as the rule that the ratio of a circle’s circumference to its
diameter is equal to the number π. Einstein could, for example, argue fromspecial
relativity that the measured circumference-to-diameter ratio of a rapidly rotating
disk had to be slightly larger than π.
By 1912, when he returned from Prague to Zu¨rich, Einstein was hoping to find
salvation in the mathematics of non-Euclidean geometry. He got some crucial
help from his invaluable friend Marcel Grossmann, now professorofmathematics
at the Zu ¨rich ETH, who advised him to read the work of Bernhard Riemann on
differential geometry. In the 1850s, Riemann had made a general study of non
Euclidean spaces by defining the “curvature” of lines drawn in those spaces.
To calculate curvatures, Riemann used the mathematical tool that Minkowski
would borrow sixty years later, the squared line element ds2. As mathematicians
will, Riemann imagined a completely general version of the line element equa
tion involving any number of dimensions and including all possible quadratic
terms. Consider, for example, two-dimensional Euclidean geometry with the line
element
mathematical form in all frames of reference, inertial or noninertial. (Note that
G and G have different meanings.)
The tensor G is Einstein’s adaptation of Riemann’s curvature calculation; it
depends entirely on the relevant spacetime metric tensor g and its derivatives.
The tensor T supplies all the necessary information on the gravitation source by
specifying the energy and matter distribution. Thus the field equation (16) says
geometry on the left side and gravity on the right. Propose a gravitation source
(T) and the equation gives the Einstein tensor G, and ultimately the geometry in
terms of the spacetime metric tensor g.
Gravity determines geometry in Einstein’s field equations, and not surpris
ingly, geometry determines motion. Einstein continued with his physical argu
ment by deriving a generalized equation of motion whose principalmathematical
ingredient is the indispensable spacetime metric tensor g. Thus the sequence of
the entire calculation is
Gravitation source
Curvature
Metric tensor g
Equation of motion.
The gravitation source is expressed by T, the curvature by G, the metric tensor
is extracted from G, and the equation of motion is defined by g. This, in a nut
shell, is one way to tell the story of Einstein’s general theory of relativity. Notice
that no forces are mentioned: geometry is the intermediary between gravitation
and motion. The title of the story is “Physics As Geometry.”
Geometry as revealed by Einstein’s field equation (16) always means spatial
curvature or non-Euclidean geometry if gravitation is present. But, except in ex
treme cases (for example, black holes), the extent of the curvature is extremely
small. Richard Feynmann uses Einstein’s theory to estimate that the Euclidean
formula 4πr2 for calculating the surface area of a sphere from the radius r is in
error by 1.3 parts per million in the intense gravitational field at the surface of
the Sun.
Einstein offered two applications of his general theory as tests of its validity.
One was the calculation of the bending of light rays near the Sun, later to be
confirmed in the famous Eddington and Crommelin expeditions. The other was
a calculation of the orbit of Mercury, showing that the orbit is not fixed, as de
manded by Newtonian theory, but slowly changes its orientation at the rate of
42.9 seconds of arc per century. This effect had been observed and measured as
43.5 seconds. When he saw this success of his theory, Einstein was euphoric.
“For some days I was beyond myself with excitement,” he wrote to a friend. As
Pais puts it, “From that time he knew: Nature had spoken; he had to be right.”
Destiny, or God Is Subtle
It is an inescapable and mostly unfathomable aspect of scientific creativity that
it simply does not last. Einstein once wrote to a friend, “Anything really new is
invented only in one’s youth. Later one becomes more experienced, more fa
mous—and more stupid.” Most of the scientists whose stories are told in this
book did their important work when they were young, in their twenties or thir
ties. Some, notably Planck and Schro¨dinger, were approaching middle age when
they did their best work. But with the exception of Gibbs, Feynman, and Chan
drasekhar, none did outstanding work toward the end of his or her life.
Although unique in most other respects, Einstein’s creative genius was only a little less ephemeral. According to Pais, Einstein’s creativity began to decline
after 1924, when he was forty-five. Pais sketches Einstein’s career after 1913, the
year he arrived in Berlin: “With the formulation of the field equations of gravi
tation in November 1915, classical physics (that is, nonquantum physics)reached
its perfection and Einstein’s scientific career its high point....Despite much ill
ness, his years from 1916 to 1920 were productive and fruitful, both in relativity
and quantum theory. A gentle decline begins after 1920. There is a resurgence
toward the end of 1924....After that, the creative period ceases abruptly, though
scientific efforts continued unremittingly for another thirty years.”
After about 1920, Einstein became more a part of the world of politics, and
no doubt that drew on his time and energy. He traveled a lot and made many
public appearances. He despised the publicity, but at the same time it cannot be
denied that he enjoyed performing before an audience. His older son, Hans Al
bert, tells us that he was “a great ham.” The social life in Berlin was an attraction;
the Einsteins counted among their acquaintances well-known intellectuals,
statesmen, and educators. And Einstein had at least several extramarital romantic
attachments during the 1920s and 1930s.
So Einstein the extrovert weakened the creative spirit that belonged to Einstein
the introvert. But that only partly explains the decline. Two other factors may
have been more important. In 1925 and 1926, the methods of quantummechanics
made their appearance and dominated developments in theoretical physics for
many years. Einstein quickly accepted the utility of quantum mechanics, but to
the end quarreled with its interpretation. Most physicists became reconciled to
the peculiar brand of indeterminism that quantum mechanics seems to demand,
but Einstein would not have it. As a second generation of quantum physicists
introduced and exploited the revolutionary new methods, Einstein became the
conserver. He hoped to see beyond what he felt was the incompleteness of quan
tum theory, without breaking with some of the great traditions of physics that
were more important to him than temporary successes. He never found what he
was looking for, although he searched for many years. “The more one chases
after quanta, the better they hide themselves,” he wrote in a letter. In his stub
bornness, he became isolated from most of his younger colleagues.
Einstein’s tenacity—certainly one of his strongest personality traits—brought
another grand failure. In the late 1920s, he began work on a “unified field theory,”
an attempt to unite the theories of gravitation, electromagnetism, and perhaps,
quanta. He was fascinated—one might say obsessed—by this effort for the rest of
his life. The drama of Einstein struggling furiously with this theoretical problem
should answer any claim that great scientists do their work as thinking machines
without passionate commitment. In 1939, he wrote to Queen Elizabeth of Bel
gium, with whom he corresponded for many years, “I have hit upon a hopeful
trail, which I follow painfully but steadfastly in company with a few youthful
fellow workers. Whether it will lead to truth or fallacy—this I may be unable to
establish with any certainty in the brief time left to me. But I am grateful to
destiny for having made my life into an exciting experience.”
And a few years later, in a letter to a friend: “I am an old man known as a
crank who doesn’t wear socks. But I am working at a more fantastic rate than
ever, and I still hope to solve my problem of the unified physical field....Itis
no more than a hope, as every variant entails tremendous mathematical difficul
ties....Iaminanagony of mathematical torment from which I am unable to
escape.”
He must have been tired, and at times discouraged. After one approach led to
still another dead end, he told an assistant he would publish, “to save another
fool from wasting six months on the same idea.” Perhaps the most famous of
Einstein’s many quotable sayings is “God is subtle, but not malicious,” by which
he meant “Nature conceals her mystery by her essential grandeur, but not by her
cunning.” After many futile years devoted to the search for the unifying field
theory, he said to Hermann Weyl, “Who knows, perhaps he is a little malicious.”
Yet the miracle of Einstein’s creative spirit was that if he felt despair, it was
never lasting. One of Einstein’s most recent biographers, Albrecht Fo¨lsing, tells
us that “he was capable of pursuing a theoretical concept, with great enthusiasm
for months and even years at a stretch; but when grievous flaws emerged—which
invariably happened in the end—he would drop it instantly at the moment of
truth, without sentimentality or disappointment over the time and effort wasted.
The following morning, or a few days later at the most, he would have taken up
a new idea and would pursue that with the same enthusiasm.” “After all,” Ein
stein wrote to a friend, “to despair makes even less sense than to strive for an
unattainable goal.”
Letters
Einstein received an enormous volume of mail, from all kinds of people on all
kinds of subjects. When he was not overwhelmed by them, he enjoyed these
letters and answered them. Excerpts from his responses give us fragments of the
personal autobiography he never wrote.
To members of the “Sixth Form Society” of an English grammar school, who
had elected him as their rector, he wrote: “As an old schoolmaster I received
with great joy and pride the nomination to the Office of Rectorship of your so
ciety. Despite my being an old gypsy there is a tendency to respectability in old
age—so with me. I have to tell you, though, that I am a little (but not too much)
bewildered that this nomination was made independent of my consent.”
Einstein was asked many times about his religion. He was a “deeply religious
nonbeliever,” he wrote to a friend, and he explained to a sixth grader, “Every one
who is seriously involved in the pursuit of science becomes convinced that a
spirit is manifest in the laws of the Universe—a spirit vastly superior to that of
man, and one in the face of which we with our modest powers must feel humble.
In this way the pursuit of science leads to a religious feeling of a special sort,
which is indeed quite different from the religiosity of someone more naı ¨ve.” “I
do not believe in a personal God and I have never denied this but have expressed
it clearly,” he wrote to an admirer. “If something is in me which can be called
religious, then it is the unbounded admiration for the structure of the world so
far as science can reveal it.” His religion did not include morality: “Morality is
of the highest importance—but for us, not God.” In response to an evangelical
letter from a Baptist minister he wrote, “I do not believe in the immortality of
the individual, and I consider ethics to be an exclusively human concern with
no superhuman authority behind it.”
Einstein detested militarism and nationalism. “That a man can take pleasure
in marching to the strains of a band is enough to make me despise him,” he
wrote. He believed that Gandhi’s strategy of civil disobedience offered hope: “I
believe that serious progress can be achieved only when men become organized
on an international scale and refuse, as a body, to enter military or war service.”
His commitment to pacifism was at first unmitigated. In an interview, he said “I
am not only a pacifist but a militant pacifist. I am willing to fight for peace....
Is it not better for a man to die for a cause in which he believes, such as peace,
than to suffer for a cause in which he does not believe, such as war?”
But the horrors of Nazi anti-Semitism converted him from an “absolute” to a
“dedicated” pacifist: “This means that I am opposed to the use of force under
any circumstances except when confronted by an enemy who pursues the de
struction of life as an end in itself.”
Many of his correspondents wanted to know what it was like to live a life in
physics. He explained that, for him, there was a detachment: “My scientific work
is motivated by an irresistible longing to understand the secrets of nature and by
no other feelings. My love for justice and the striving to contribute towards the
improvement of human conditions are quite independent from my scientific
interests.”
And in the detachment he found another part of the motivation: “Measured
objectively, what a man can wrest from Truth by passionate striving is utterly
infinitesimal. But the striving frees us from the bonds of the self and makes us
comrades of those who are the best and the greatest.”
Bird of Passage
It was Einstein’s fate to roam and never settle in a place he could comfortably
call home. Switzerland was his favorite place, but he did not stay there long after
leaving the patent office. Berlin kept him for almost twenty years, and for a time
left him in peace. But in the 1920s the Nazis became influential and brought with
them the three scourges of nationalism, militarism, and anti-Semitism. We have
already seen the devastating effects of Nazi policies in Nernst’s time, and the
Nazi destruction of the German scientific establishment will continue to be a
morbid theme in later chapters. Anti-Semitism had been evident throughout the
1920s, but for Einstein at least not a threat. That was no longer the case in the
early 1930s when the Nazis came to power.
After short stays in Belgium, England, and California, Einstein relocated to
Princeton, where he joined the newly founded Institute for Advanced Study.
Compared to that of Berlin, the intellectual climate in Princeton was less than
exciting. “Princeton is a wonderful little spot,” he wrote to Queen Elizabeth, “a
quaint ceremonious village of puny demigods on stilts.” But it served his main
purpose: “By ignoring certain special conventions, I have been able to create for
myself an atmosphere conducive to study and free from distraction.”
In Princeton, Einstein ended his flight and returned to his routine. As always,
he was in touch with world affairs. In the 1940s, the Manhattan Project, aimed
at developing a nuclear bomb, was organized, and Einstein’s influence helped in
the initial stages. The “pet project,” unified field theory, was his major concern
in Princeton, however. More than ever, he became the “artist in science,” search
ing endlessly for the unified theory with the mathematical simplicity and beauty
that would satisfy his intuition and aesthetic sense.
Abraham Pais, whose biography of Einstein is the best of the many written,
leaves us with this glimpse of Einstein about three months before he died in
1955. He had been ill and unable to work in his office at the institute. Pais visited
him at home and went upstairs and knocked at the door of [his] study. There was a gentle
“Come.” As I entered, he was seated in his armchair, a blanket over his knees,
a pad on the blanket. He was working. He put his pad aside at once and greeted
me. We spent a pleasant half hour or so; I do not recall what was discussed.
Then I told him I should not stay any longer. We shook hands, and I said
goodbye. I walked to the door of the study, not more than four or five steps
away. I turned around as I opened the door. I saw him in his chair, his pad on
his lap, a pencil in his hand, oblivious to his surroundings. He was back at
work.
This is a gift for my best friend (Jaymin)
