Parallel Worlds (6 page)

Although 1901-02
was perhaps the worst period in Einstein's life, what saved his career from
oblivion was the recommendation of a classmate, Marcel Grossman, who was able
to pull some strings and secure a job for him as a lowly clerk at the Swiss
Patent Office in Bern.

PARADOXES OF RELATIVITY

On the surface,
the Patent Office was an unlikely place from which to launch the greatest
revolution in physics since Newton. But it had its advantages. After quickly
disposing of the patent applications piling up on his desk, Einstein would sit
back and return to a dream he had when he was a child. In his youth, Einstein
had read a book, Aaron Bernstein's
People's
Book on
Natural Science,
"a work
which I read with breathless attention," he recalled. Bernstein asked the
reader to imagine riding alongside electricity as it raced down a telegraph
wire. When he was sixteen, Einstein asked himself a similar question: what
would a light beam look like if you could catch up to it? Einstein would
recall, "Such a principle resulted from a paradox upon which I had already
hit at the age of sixteen: If I pursue a beam of light with the velocity
c
(velocity of light in a vacuum), I should observe such a
beam of light as a spatially oscillatory electromagnetic field at rest.
However, there seems to be no such thing, whether on the basis of experience or
according to Maxwell's equations." As a child, Einstein thought that if
you could race alongside a light beam, it should appear frozen, like a
motionless wave. However, no one had ever seen frozen light, so something was
terribly wrong.

At the turn of
the century, there were two great pillars of physics upon which everything
rested: Newton's theory of mechanics and gravity, and Maxwell's theory of
light. In the 1860s, Scottish physicist James Clerk Maxwell had shown that
light consists of vibrating electric and magnetic fields constantly changing
into each other. What Einstein discovered, much to his shock, was that these
two pillars were in contradiction to each other, and that one of them had to
fall.

Within Maxwell's
equations, he found the solution to the puzzle that had haunted him for ten
years. Einstein found something that Maxwell himself had missed: Maxwell's
equations showed that light traveled at a constant velocity, no matter how fast
you tried to catch up to it. The speed of light
c
was the same in all inertial frames (that is, frames traveling at constant
velocity). Whether you were standing still, riding on a train, or sitting on a
speeding comet, you would see a light beam racing ahead of you at the same
speed. No matter how fast you moved, you could never outrace light.

This immediately
led to a thicket of paradoxes. Imagine, for the moment, an astronaut trying to
catch up to a speeding light beam. The astronaut blasts off in his rocket ship
until he is racing neck- and-neck with the light beam. A bystander on Earth
witnessing this hypothetical chase would claim that the astronaut and the light
beam were moving side by side to each other. However, the astronaut would say
something completely different, that the light beam sped away from him, just as
if his rocket ship were at rest.

The question
confronting Einstein was: how can two people have such different
interpretations of the same event? In Newton's theory, one could always catch
up to a light beam; in Einstein's world, this was impossible. There was, he
suddenly realized, a fundamental flaw in the very foundation of physics. In the
spring of 1905, Einstein recalled, "a storm broke out in my mind." In
one stroke, he finally found the solution:
time beats at different rates, depending
on how
fast you move.
In fact, the faster you move, the slower time progresses.

Time is not an
absolute, as Newton once thought. According to Newton, time beat uniformly
throughout the universe, so that the passage of one second on Earth was
identical to one second on Jupiter or Mars. Clocks beat in absolute
synchronization throughout the universe. To Einstein, however, different clocks
beat at different rates throughout the universe.

If time could
change depending on your velocity, Einstein realized, then other quantities,
such as length, matter, and energy, should also change. He found that the faster
you moved, the more distances contracted (which is sometimes called the
Lorentz- FitzGerald contraction). Similarly, the faster you moved, the heavier
you became. (In fact, as you approached the speed of light, time would slow
down to a stop, distances would contract to nothing, and your mass would become
infinite, which are all absurd. This is the reason why you cannot break the
light barrier, which is the ultimate speed limit in the universe.)

This strange
distortion of space-time led one poet to write:

There was a young fellow named Fisk Whose fencing was
exceedingly brisk. So fast was his action, The FitzGerald contraction Reduced
his rapier to a disk.

In the same way
that Newton's breakthrough unified Earth- bound physics with heavenly physics,
Einstein unified space with time. But he also showed that matter and energy are
unified and hence can change into each other. If an object becomes heavier the
faster it moves, then it means that the energy of motion is being transformed
into matter. The reverse is also true—matter can be converted into energy.
Einstein computed how much energy would be converted into matter, and he came
up with the formula
E = mc
²
,
that is, even a
tiny amount of matter
m
is multiplied
by a huge number (the square of the speed of light) when it turns into energy
E.
Thus, the secret energy source of the stars themselves was
revealed to be the conversion of matter into energy via this equation, which
lights up the universe. The secret of the stars could be derived from the
simple statement that the speed of light is the same in all iner- tial frames.

Like Newton
before him, Einstein changed our view of the stage of life. In Newton's world,
all the actors knew precisely what time it was and how distances were measured.
The beating of time and the dimensions of the stage never changed. But
relativity gave us a bizarre way of understanding space and time. In Einstein's
universe, all the actors have wristwatches that read different times. This
means that it is impossible to synchronize all the watches on the stage.
Setting rehearsal time for noon means different things to different actors. In
fact, strange things happen when actors race across the stage. The faster they
move, the slower their watches beat and the heavier and flatter their bodies
become.

It would take
years before Einstein's insight would be recognized by the larger scientific
community. But Einstein did not stand still; he wanted to apply his new theory
of relativity to gravity itself. He realized how difficult this would be; he
would be tampering with the most successful theory of his time. Max Planck,
founder of the quantum theory, warned him, "As an older friend, I must
advise you against it for in the first place you will not succeed, and even if
you succeed, no one will believe you."

Einstein
realized that his new theory of relativity violated the Newtonian theory of
gravity. According to Newton, gravity traveled instantaneously throughout the
universe. But this raised a question that even children sometimes ask:
"What happens if the Sun disappears?" To Newton, the entire universe
would witness the disappearance of the Sun instantly, at the same time. But
according to special relativity, this is impossible, since the disappearance of
a star was limited by the speed of light. According to relativity, the sudden
disappearance of the Sun should set off a spherical shock wave of gravity that
spreads outward at the speed of light. Outside the shock wave, observers would
say that the Sun is still shining, since gravity has not had time to reach
them. But inside the wave, an observer would say that the Sun has disappeared.
To resolve this problem, Einstein introduced an entirely different picture of
space and time.

FORCE AS THE BENDING OF SPACE

Newton embraced
space and time as a vast, empty arena in which events could occur, according to
his laws of motion. The stage was full of wonder and mystery, but it was
essentially inert and motionless, a passive witness to the dance of nature.
Einstein, however, turned this idea upside down. To Einstein, the stage itself
would become an important part of life. In Einstein's universe, space and time
were not a static arena as Newton had assumed, but were dynamic, bending and curving
in strange ways. Assume the stage of life is replaced by a trampoline net, such
that the actors gently sink under their own weight. On such an arena, we see
that the stage becomes just as important as the actors themselves.

Think of a
bowling ball placed on a bed, gently sinking into the mattress. Now shoot a
marble along the warped surface of the mattress. It will travel in a curved
path, orbiting around the bowling ball. A Newtonian, witnessing the marble
circling the bowling ball from a distance, might conclude that there was a
mysterious force that the bowling ball exerted on the marble. A Newtonian might
say that the bowling ball exerted an instantaneous pull which forced the marble
toward the center.

To a relativist,
who can watch the motion of the marble on the bed from close up, it is obvious
that there is no force at all. There is just the bending of the bed, which
forces the marble to move in a curved line. To the relativist, there is no
pull, there is only a push, exerted by the curved bed on the marble. Replace
the marble with Earth, the bowling ball with the Sun, and the bed with empty
space- time, and we see that Earth moves around the Sun not because of the pull
of gravity but because the Sun warps the space around Earth, creating a push
that forces Earth to move in a circle.

Einstein was
thus led to believe that gravity was more like a fabric than an invisible
force that acted instantaneously throughout the universe. If one rapidly shakes
this fabric, waves are formed which travel along the surface at a definite
speed. This resolves the paradox of the disappearing sun. If gravity is a
by-product of the bending of the fabric of space-time itself, then the
disappearance of the Sun can be compared to suddenly lifting the bowling ball
from the bed. As the bed bounces back to its original shape, waves are sent
down the bed sheet traveling at a definite speed. Thus, by reducing gravity to
the bending of space and time, Einstein was able to reconcile gravity and
relativity.

Imagine an ant
trying to walk across a crumpled sheet of paper. He will walk like a drunken
sailor, swaying to the left and right, as he tries to walk across the wrinkled
terrain. The ant would protest that he is not drunk, but that a mysterious
force is tugging on him, yanking him to the left and to the right. To the ant,
empty space is full of mysterious forces that prevent him from walking in a
straight path. Looking at the ant from a close distance, however, we see that
there is no force at all pulling him. He is being pushed by the folds in the
crumpled sheet of paper. The forces acting on the ant are an illusion caused by
the bending of space itself. The "pull" of the force is actually the
"push" created when he walks over a fold in the paper. In other
words, gravity does not pull; space pushes.

By 1915,
Einstein was finally able to complete what he called the general theory of
relativity, which has since become the architecture upon which all of cosmology
is based. In this startling new picture, gravity was not an independent force
filling the universe but the apparent effect of the bending of the fabric of
space-time. His theory was so powerful that he could summarize it in an
equation about an inch long. In this brilliant new theory, the amount of
bending of space and time was determined by the amount of matter and energy it
contained. Think of throwing a rock into a pond, which creates a series of
ripples emanating from the impact. The larger the rock, the more the warping of
the surface of the pond. Similarly, the larger the star, the more the bending
of space-time surrounding the star.

THE BIRTH OF COSMOLOGY

Einstein
tried to use this picture to describe the universe as a whole. Unknown to him,
he would have to face Bentley's paradox, formulated centuries earlier. In the
1920s, most astronomers believed that the universe was uniform and static. So
Einstein started by assuming that the universe was filled uniformly with dust
and stars. In one model, the universe could be compared to a large balloon or
bubble. We live on the skin of the bubble. The stars and galaxies that we see
surrounding us can be compared to dots painted on the surface of the balloon.

To his surprise,
whenever he tried to solve his equations, he found that the universe became
dynamic. Einstein faced the same problem identified by Bentley over two hundred
years earlier. Since gravity is always attractive, never repulsive, a finite
collection of stars should collapse into a fiery cataclysm. This, however,
contradicted the prevailing wisdom of the early twentieth century, which
stated that the universe was static and uniform.