Parallel Worlds (28 page)

This is a
variation of the many worlds theory: there is no need to invoke a cosmic
observer that can observe the entire universe all at once. But Hawking's wave
function is quite different from Schrodinger's wave function. In Schrodinger's
wave function, at every point in space-time, there is a wave function. In
Hawking's wave function, for every universe, there is a wave. Instead of
Schrodinger's
psi
function
describing all possible states of the electron, Hawking introduces a
psi
function that represents all possible states of the universe.
In ordinary quantum mechanics, the electron exists in ordinary space. However,
in the wave function of the universe, the wave function exists in "super
space," the space of all possible universes, introduced by Wheeler.

This master wave
function (the mother of all wave functions) obeys not the Schrodinger equation
(which only works for single electrons) but the Wheeler-DeWitt equation, which
works for all possible universes. In the early 1990s, Hawking wrote that he
was able to partially solve his wave function of the universe and show that the
most likely universe was one with a vanishing cosmological constant. This
paper provoked quite a bit of controversy because it depended on summing over
all possible universes. Hawking performed this sum by including wormholes
connecting our universe with all possible universes. (Imagine an infinite sea
of soap bubbles floating in air, all connected by thin filaments or wormholes,
and then adding them all together.)

Ultimately,
doubts were raised about Hawking's ambitious method. It was pointed out that
the sum of all possible universes was a mathematically unreliable one, at least
until we had a "theory of everything" to guide us. Until a theory of
everything is constructed, critics have argued that one cannot really trust any
of the calculations about time machines, wormholes, the instant of the big
bang, and wave functions of the universe.

Today, however,
scores of physicists believe that we have finally found the theory of
everything, although it is not yet in its final form: string theory, or
M-theory. Will it allow us to "read the Mind of God," as Einstein
believed?

To someone who could grasp the Universe from a unified
standpoint the entire creation would appear as a unique truth and necessity.

—J. D'Alembert

I feel that we are so close with string theory that—in my
moments of greatest optimism—I imagine that any day, the final form of the
theory might drop out of the sky and land in someone's lap. But more
realistically, I feel that we are now in the process of constructing a much
deeper theory than anything we have had before and that well into the
twenty-first century, when I am too old to have any useful thoughts on the
subject, younger physicists will have to decide whether we have in fact found
the final theory.

—Edward Witten

H. G.
Wells's classic novel
of 1897,
The Invisible Man,
begins with a strange tale. One
cold wintry day, a stranger comes in from the darkness dressed in a bizarre
fashion. His face is completely covered; he is wearing dark blue glasses, and a
white bandage blankets his entire face.

At first, the villagers take pity on him, thinking that he
was in a

horrible
accident. But strange things happen around the village. One day, his landlady
entered his empty room and screamed when she saw clothing moving about by
itself. Hats were whirling across the room, the bedclothes leaped into the air,
chairs moved, and "the furniture went mad," she recalled in horror.

Soon, the entire
village is buzzing with rumors of these unusual occurrences. Finally, a group
of villagers gathers and confronts the mysterious stranger. To their amazement,
he slowly begins to unwrap his bandages. The crowd is aghast. Without the
bandages, the stranger's face is completely missing. In fact, he is invisible.
Chaos erupts, as people yell and scream. The villagers try to chase the invisible
man, who easily fights them off.

After committing
a string of petty crimes, the invisible man seeks out an old acquaintance and
recounts his remarkable story. His true name is Mr. Griffen of University
College. Although he started out learning medicine, he stumbled upon a
revolutionary way in which to change the refractive and reflective properties
of flesh. His secret is the fourth dimension. He exclaims to Dr. Kemp, "I
found a general principle ... a formula, a geometrical expression involving
four dimensions."

Sadly, instead
of using this great discovery to help humanity, his thoughts are of robbery and
private gain. He proposes to recruit his friend as an accomplice. Together, he
claims, they can plunder the world. But the friend is horrified and reveals Mr.
Griffen's presence to the police. This leads to a final manhunt, in which the
invisible man is mortally wounded.

As with the best
science fiction novels, there is a germ of science in many of H. G. Wells's
tales. Anyone who can tap into the fourth spatial dimension (or what is today
called the fifth dimension, with time being the fourth dimension) can indeed
become invisible, and can even assume the powers normally ascribed to ghosts
and gods. Imagine, for the moment, that a race of mythical beings can inhabit
the two-dimensional world of a tabletop, as in Edwin Abbot's 1884 novel
Flatland.
They conduct their affairs unaware that an entire universe,
the third dimension, surrounds them.

But if a
Flatland scientist could perform an experiment that allows him to hover inches
off the table, he would become invisible, because light would pass below him as
if he didn't exist. Floating just above Flatland, he could see events unfolding
below on the tabletop. Hovering in hyperspace has decided advantages, for anyone
looking down from hyperspace would have the powers of a god.

Not only would
light pass beneath him, making him invisible, he could also pass over objects.
In other words, he could disappear at will and walk through walls. By simply
leaping into the third dimension, he would vanish from the universe of
Flatland. And if he jumped back onto the tabletop, he would suddenly
rematerialize out of nowhere. He could therefore escape from any jail. A prison
in Flatland would consist of a circle drawn around a prisoner, so it would be
easy to simply jump into the third dimension and be outside.

It would be
impossible to keep secrets away from a hyperbeing. Gold that is locked in a
vault could be easily seen from the vantage point of the third dimension, since
the vault is just an open rectangle. It would be child's play to reach into
the rectangle and lift the gold out without ever breaking into the vault.
Surgery would be possible without cutting the skin.

Similarly, H. G.
Wells wanted to convey the idea that in a four- dimensional world, we are the
Flatlanders, oblivious of the fact that higher planes of existence might hover
right above ours. We believe that our world consists of all that we can see,
unaware that there may be entire universes right above our noses. Although
another universe might be hovering just inches above us, floating in the fourth
dimension, it would appear to be invisible.

Because a
hyperbeing would possess superhuman powers usually ascribed to a ghost or a
spirit, in another science fiction story, H. G. Wells pondered the question of
whether supernatural beings might inhabit higher dimensions. He raised a key
question that is today the subject of great speculation and research: could
there be new laws of physics in these higher dimensions? In his 1895 novel
The Wonderful Visit,
a vicar's gun accidentally hits an
angel, who happens to be passing through our dimension. For some cosmic reason,
our dimension and a parallel universe temporarily collided, allowing this angel
to fall into our world. In the story, Wells writes, "There may be any
number of three-dimensional Universes packed side by side." The vicar
questions the wounded angel. He is shocked to find that our laws of nature no
longer apply in the angel's world. In his universe, for example, there are no
planes, but rather cylinders, so space itself is curved. (Fully twenty years
before Einstein's general theory of relativity, Wells was entertaining thoughts
about universes existing on curved surfaces.) As the vicar puts it,
"Their geometry is different because their space has a curve in it so
that all their planes are cylinders; and their law of Gravitation is not
according to the law of inverse squares, and there are four-and-twenty primary
colours instead of only three." More than a century after Wells wrote his
tale, physicists today realize that new laws of physics, with different sets of
subatomic particles, atoms, and chemical interactions, might indeed exist in
parallel universes. (As we see in chapter 9, several experiments are now being
conducted to detect the presence of parallel universes that might be hovering
just above ours.)

The concept of
hyperspace has intrigued artists, musicians, mystics, theologians, and
philosophers, especially near the beginning of the twentieth century. According
to art historian Linda Dalrymple Henderson, Pablo Picasso's interest in the
fourth dimension influenced the creation of cubism. (The eyes of the women he
painted look directly at us, even though their noses face to the side, allowing
us to view the women in their entirety. Similarly, a hyperbeing looking down
on us will see us in our entirety: front, back, and sides simultaneously.) In
his famous painting
Christus
Hypercubus,
Salvador DaH painted Jesus Christ crucified in front of an
unraveled four- dimensional hypercube, or a tesseract. In his painting
The Persistence of Memory,
DaH tried to
convey the idea of time as the fourth dimension with melted clocks. In Marcel
Duchamp's painting
Nude Descending a Staircase
(No. 2),
we see a nude in time-lapse motion walking down the stairs,
in another attempt to capture the fourth dimension of time on a
two-dimensional surface.

M-THEORY

Today, the
mystery and lore surrounding the fourth dimension are being resurrected for an
entirely different reason: the development of string theory and its latest
incarnation, M-theory. Historically, the concept of hyperspace has been
resisted strenuously by physicists; they scoffed that higher dimensions were
the province of mystics and charlatans. Scientists who seriously proposed the
existence of unseen worlds were subject to ridicule.

With the coming
of M-theory, all that has changed. Higher dimensions are now in the center of
a profound revolution in physics because physicists are forced to confront the
greatest problem facing physics today: the chasm between general relativity and
the quantum theory. Remarkably, these two theories comprise the sum total of
all physical knowledge about the universe at the fundamental level. At present,
only M-theory has the ability to unify these two great, seemingly contradictory
theories of the universe into a coherent whole, to create a "theory of
everything." Of all the theories proposed in the past century, the only
candidate that can potentially "read the Mind of God," as Einstein
put it, is M-theory.

Only in ten- or
eleven-dimensional hyperspace do we have "enough room" to unify all
the forces of nature in a single elegant theory. Such a fabulous theory would
be able to answer the eternal questions: What happened before the beginning?
Can time be reversed? Can dimensional gateways take us across the universe?
(Although its critics correctly point out that testing this theory is beyond
our present experimental ability, there are a number of experiments currently
being planned that may change this situation, as we shall see in chapter 9.)

All attempts for
the past fifty years to create a truly unified description of the universe
have ended in ignominious failure. Conceptually, this is easy to understand.
General relativity and the quantum theory are diametrical opposites in almost
every way. General relativity is a theory of the very large: black holes, big
bangs, quasars, and the expanding universe. It is based on the mathematics of
smooth surfaces, like bed sheets and trampoline nets. The quantum theory is
precisely the opposite—it describes the world of the very tiny: atoms, protons
and neutrons, and quarks. It is based on a theory of discrete packets of energy
called quanta. Unlike relativity, the quantum theory states that only the
probability of events can be calculated, so we can never know for sure
precisely where an electron is located. These two theories are based on
different mathematics, different assumptions, different physical principles,
and different domains. It is not surprising that all attempts to unify them
have floundered.

The giants of
physics—Erwin Schrodinger, Werner Heisenberg, Wolfgang Pauli, and Arthur
Eddington—who have followed Einstein have tried their hand at a unified field
theory, only to fail miserably. In 1928, Einstein accidentally created a media
stampede with an early version of his unified field theory. The
New York Times
even published parts of the paper, including his equations.
Over a hundred reporters swarmed outside his house. Writing from England,
Edding- ton commented to Einstein, "You may be amused to hear that one of
our great department stores in London (Selfridges) has posted on its window
your paper (the six pages pasted up side by side) so that passers-by can read
it all through. Large crowds gather around to read it."