Parallel Worlds (18 page)

To understand
these questions, we must first understand the nature of wormholes, negative
energy, and, of course, those mysterious objects called black holes.

BLACK HOLES

In 1783, British
astronomer John Michell was the first to wonder what would happen if a star
became so large that light itself could not escape. Any object, he knew, had an
"escape velocity," the velocity required to leave its gravitational
pull. (For Earth, for example, the escape velocity is 25,000 miles per hour,
the speed that any rocket must attain in order to break free of Earth's
gravity.)

Michell wondered
what might happen if a star became so massive that its escape velocity was
equal to the speed of light. Its gravity would be so immense that nothing could
escape it, not even light itself, and hence the object would appear black to
the outside world. Finding such an object in space would in some sense be
impossible, since it would be invisible.

The question of
Michell's "dark stars" was largely forgotten for a century and a
half. But the matter resurfaced in 1916, when Karl Schwarzschild, a German
physicist serving the German army on the Russian front, found an exact solution
of Einstein's equations for a massive star. Even today, the Schwarzschild
solution is known to be the simplest and most elegant exact solution of
Einstein's equations. Einstein was astonished that Schwarzschild could find a
solution to his complex tensor equations while dodging artillery shells. He was
equally astonished that Schwarzschild's solution had peculiar properties.

The
Schwarzschild solution, from a distance, could represent the gravity of an
ordinary star, and Einstein quickly used the solution to calculate the gravity
surrounding the Sun and check his earlier calculations, in which he had made
approximations. For this he was eternally thankful to Schwarzschild. But in
Schwarzschild's second paper, he showed that surrounding a very massive star
there was an imaginary "magic sphere" with bizarre properties. This
"magic sphere" was the point of no return. Anyone passing through the
"magic sphere" would be immediately sucked by gravity into the star,
never to be seen again. Not even light could escape if it fell into this
sphere. Schwarzschild did not realize that he was rediscovering Michell's dark
star, through Einstein's equations.

He next
calculated the radius for this magic sphere (called the Schwarzschild radius).
For an object the size of our Sun, the magic sphere was about 3 kilometers
(roughly 2 miles). (For Earth, its Schwarzschild radius was about a
centimeter.) This meant that if one could compress the Sun down to 2 miles,
then it would become a dark star and devour any object that passed this point
of no return.

Experimentally,
the existence of the magic sphere caused no problems, since it was impossible
to squeeze the sun down to 2 miles. No mechanism was known to create such a
fantastic star. But theoretically, it was a disaster. Although Einstein's
general theory of relativity could yield brilliant results, like the bending
of starlight around the Sun, the theory made no sense as you approached the
magic sphere itself, where gravity became infinite.

A Dutch
physicist, Johannes Droste, then showed that the solution was even crazier.
According to relativity, light beams, he showed, would bend severely as they
whipped around the object. In fact, at 1.5 times the Schwarzschild radius,
light beams actually orbited in circles around the star. Droste showed that
the distortions of time found in general relativity around these massive stars
were much worse than those found in special relativity. He showed that, as you
approached this magic sphere, someone from a distance would say that your
clocks were getting slower and slower, until your clocks stopped totally when
you hit the object. In fact, someone from the outside would say that you were
frozen in time as you reached the magic sphere. Because time itself would stop
at this point, some physicists believed that such a bizarre object could never
exist in nature. To make matters even more interesting, mathematician Herman
Weyl showed that if one investigated the world inside the magic sphere, there
seemed to be another universe on the other side.

This was all so
fantastic that even Einstein could not believe it. In 1922, during a conference
in Paris, Einstein was asked by mathematician Jacques Hadamard what would
happen if this "singularity" were real, that is, if gravity became
infinite at the Schwarzschild radius. Einstein replied, "It would be a
true disaster for the theory; and it would be very difficult to say
a priori
what could happen physically because the formula does not
apply anymore." Einstein would later call this the "Hadamard
disaster." But he thought that all this controversy around dark stars was
pure speculation. First, no one had ever seen such a bizarre object, and
perhaps they didn't exist, that is, they were unphysical. Moreover, you would
be crushed to death if you ever fell into one. And since one could never pass
through the magic sphere (since time has stopped), no one could never enter
this parallel universe.

In the 1920s,
physicists were thoroughly confused about this issue. But in 1932, an
important breakthrough was made by Georges Lemaitre, father of the big bang theory.
He showed that the magic sphere was not a singularity at all where gravity
became infinite; it was just a mathematical illusion caused by choosing an
unfortunate set of mathematics. (If one chose a different set of coordinates or
variables to examine the magic sphere, the singularity disappeared.)

Taking this
result, the cosmologist H. P. Robertson then reexamined Droste's original
result that time stops at the magic sphere. He found that time stopped only
from the vantage point of an observer watching a rocket ship enter the magic
sphere. From the vantage point of the rocket ship itself, it would only take a
fraction of a second for gravity to suck you right past the magic sphere. In
other words, a space traveler unfortunate enough to pass through the magic
sphere would find himself crushed to death almost instantly, but to an observer
watching from the outside, it would appear to take thousands of years.

This was an
important result. It meant that the magic sphere was reachable and could no
longer be dismissed as a mathematical monstrosity. One had to seriously
consider what might happen if one passed through the magic sphere. Physicists
then calculated what a journey through the magic sphere might look like.
(Today, the magic sphere is called the event horizon. The horizon refers to the
farthest point one can see. Here, it refers to the farthest point light can
travel. The radius of the event horizon is called the Schwarzschild radius.)

As you
approached the black hole in a rocket ship, you would see light that had been
captured billions of years ago by the black hole, dating back to when the black
hole itself was first created. In other words, the life history of the black
hole would be revealed to you. As you got closer, tidal forces would gradually
rip the atoms of your body apart, until even the nuclei of your atoms would
look like spaghetti. The journey through the event horizon would be a oneway
trip, because gravity would be so intense that you would inevitably be sucked
right into the center, where you will be crushed to death. Once inside the
event horizon, there could be no turning back. (To leave the event horizon, one
would have to travel faster than light, which is impossible.)

In 1939,
Einstein wrote a paper in which he tried to dismiss such dark stars, claiming
that they cannot be formed by natural processes. He started by assuming that a
star forms from a swirling collection of dust, gas, and debris rotating in a
sphere, gradually coming together because of gravity. He then showed that this
collection of swirling particles will never collapse to within its
Schwarzschild radius, and hence will never become a black hole. At best, this
swirling mass of particles will approach 1.5 times the Schwarzschild radius,
and hence black holes will never form. (To go below 1.5 times the Schwarzschild
radius, one would have to travel faster than the speed of light, which is
impossible.) "The essential result of this investigation is a clear
understanding of why the 'Schwarzschild singularities' do not exist in physical
reality," Einstein wrote.

Arthur
Eddington, too, had deep reservations about black holes and bore a lifelong
suspicion that they could never exist. He once said that there should "be
a law of Nature to prevent a star from behaving in this absurd way."

Ironically, that
same year, J. Robert Oppenheimer (who would later build the atomic bomb) and
his student Hartland Snyder showed that a black hole
could
indeed form, via another mechanism. Instead of assuming that
a black hole came about from a swirling collection of particles collapsing
under gravity, they used as their starting point an old, massive star that has
used up its nuclear fuel and hence implodes under the force of gravity. For
example, a dying, giant star forty times the mass of the Sun might exhaust its
nuclear fuel and be compressed by gravity to within its Schwarzschild radius of
80 miles, in which case it would inevitably collapse into a black hole. Black
holes, they suggested, were not only possible, they might be the natural end
point for billions of dying giant stars in the galaxy. (Perhaps the idea of
implosion, pioneered in 1939 by Oppenheimer, gave him the inspiration for the
implosion mechanism used in the atomic bomb just a few years later.)

EINSTEIN-ROSEN BRIDGE

Although
Einstein thought that black holes were too incredible to exist in nature, he
then ironically showed that they were even stranger than anyone thought,
allowing for the possibility of worm- holes lying at the heart of a black hole.
Mathematicians call them multiply connected spaces. Physicists call them
wormholes because, like a worm drilling into the earth, they create an
alternative shortcut between two points. They are sometimes called dimensional
portals, or gateways. Whatever you call them, they may one day provide the
ultimate means for interdimensional travel.

The first person
to popularize wormholes was Charles Dodgson, who wrote under the pen name of
Lewis Carroll. In
Through the Looking
Glass,
he introduced the wormhole as the looking glass, which
connected the countryside of Oxford to Wonderland. As a professional
mathematician and Oxford don, Dodgson was familiar with these multiply
connected spaces. By definition, a multiply connected space is one in which a
lasso cannot be shrunk down to a point. Usually, any loop can effortlessly be
collapsed to a point. But if we analyze a doughnut, then it's possible to place
the lasso on its surface so that it encircles the doughnut hole. As we slowly
collapse the loop, we find that it cannot be compressed to a point; at best, it
can be shrunk to the circumference of the hole.

Mathematicians
delighted in the fact that they had found an object that was totally useless
in describing space. But in 1935, Einstein and his student Nathan Rosen
introduced wormholes into the world of physics. They were trying to use the
black hole solution as a model for elementary particles. Einstein never liked
the idea, dating back to Newton, that a particle's gravity became infinite as
you approached it. This "singularity," thought Einstein, should be
removed because it made no sense.

Einstein and
Rosen had the novel idea of representing an electron (which was usually
thought of as a tiny point without any structure) as a black hole. In this way,
general relativity could be used to explain the mysteries of the quantum world
in a unified field theory. They started with the standard black hole solution,
which resembles a large vase with a long throat. They then cut the throat, and
merged it with another black hole solution that was flipped over. To Einstein,
this strange but smooth configuration would be free of the singularity at the
origin of the black hole and might act like an electron.

Unfortunately,
Einstein's idea of representing an electron as a black hole failed. But today,
cosmologists speculate that the Einstein- Rosen bridge can act as a gateway
between two universes. We could move about freely in one universe until
accidentally falling into a black hole, where we would be suddenly sucked
through the hole to emerge on the other side (through a white hole).

To Einstein, any
solution of his equations, if it began with a physically plausible starting
point, should correspond to a physically possible object. But he wasn't worried
about someone falling into a black hole and entering a parallel universe. The
tidal forces would become infinite at the center, and anyone unfortunate enough
to fall into a black hole would have their atoms ripped apart by the gravitational
field. (The Einstein-Rosen bridge does open up momentarily, but it closes so
fast that no object can pass through it in time to reach

The
Einstein-Rosen bridge. At the center of a black hole, there is a
"throat" that connects space-time to another universe or another
point in our universe. Although travel through a stationary black hole would be
fatal, rotating black holes have a ringlike singularity, such that it may be
possible to pass through the ring and through the Einstein-Rosen bridge,
although this is still speculative.

the
other side.) Einstein's attitude was that, while wormholes may exist, living
creatures could never pass through one and live to tell about it.