Parallel Worlds (36 page)

The essence of
the hologram is that the two-dimensional surface of the hologram encodes all
the information necessary to reproduce a three-dimensional image. (Holograms
are made in the laboratory by shining laser light onto a sensitive photographic
plate and allowing the light to interfere with laser light from the original
source. The interference of the two light sources creates an interference pattern
that "freezes" the image onto the two-dimensional plate.)

Some
cosmologists have conjectured that this may also apply to the universe
itself—that perhaps we
live
in a hologram.
The origin of this strange speculation arises from black hole physics.
Bekenstein and Hawking conjecture that the total amount of information
contained in a black hole is proportional to the surface area of its event
horizon (which is a sphere). This is a strange result, because usually the
information stored in an object is proportional to its volume. For example, the
amount of information stored in a book is proportional to its size, not to the
surface area of its cover. We know this instinctively, when we say that we
cannot judge a book by its cover. But this intuition fails for black holes: we
can completely judge a black hole by its cover.

We may dismiss
this curious hypothesis because black holes are strange oddities in themselves,
where normal intuition breaks down. However, this result also applies to
M-theory, which may give us the best description of the entire universe. In
1997, Juan Maldacena, at the Institute for Advanced Study at Princeton, created
quite a sensation when he showed that string theory leads to a new type of
holographic universe.

He started with
a five-dimensional "anti-de Sitter universe" which often appears in
string theory and supergravity theory. A de Sitter universe is one with a
positive cosmological constant that creates an accelerating universe. (We
recall that our universe is currently best represented as a de Sitter
universe, with a cosmological constant pushing the galaxies away at faster and
faster velocities. An anti-de Sitter universe has a negative cosmological
constant and hence can implode.) Maldacena showed that there is a duality between
this five-dimensional universe and its "boundary," which is a
four-dimensional universe. Strangely enough, any beings living in this
five-dimensional space would be mathematically equivalent to beings living in
this four-dimensional space. There is no way to tell them apart.

By crude
analogy, think of fish swimming inside a goldfish bowl. These fish think that
their fish bowl corresponds to reality. Now imagine a two-dimensional
holographic image of these fish that is projected onto the surface of the fish
bowl. This image contains an exact replica of the original fish, except they
are flattened. Any movement the fish make in the fish bowl is mirrored by the
flat image on the surface of the fish bowl. Both the fish swimming in the bowl
and the flattened fish living on the surface of the bowl think that they are
the real fish, that the other is an illusion. Both fish are alive and act as if
they are the true fish. Which description is correct? Actually, both are,
since they are mathematically equivalent and indistinguishable.

What excited
string theorists is the fact that five-dimensional anti-de Sitter space is
relatively easy to calculate with, while four- dimensional field theories are
notoriously difficult to handle. (Even today, after decades of hard work, our
most powerful computers cannot solve the four-dimensional quark model and
derive the masses of the proton and neutron. The equations for the quarks
themselves are fairly well understood, but solving them in four dimensions to
obtain the properties of protons and neutrons has proved to be more difficult
than previously thought.) One goal is to calculate the masses and properties of
the proton and neutron, using this strange duality.

This holographic
duality may also have practical applications, such as solving the information
problem in black hole physics. In four dimensions, it is extremely difficult to
prove that information isn't lost when we throw objects through a black hole.
But such a space is dual to a five-dimensional world, in which information is
perhaps never lost. The hope is that problems that are intractable in four
dimensions (such as the information problem, calculating the masses of the
quark model, and so forth) may eventually be solved in five dimensions, where
the mathematics is simpler. And it is always possible that this analogy is
actually a reflection of the real world—that we really exist as holograms.

IS THE UNIVERSE A COMPUTER PROGRAM?

John Wheeler, as
we saw earlier, believed that all physical reality could be reduced to pure
information. Bekenstein takes the idea of black hole information one step
further into uncharted waters by asking the question: is the entire universe a
computer program? Are we just bits on a cosmic CD?

The question of
whether we are living in a computer program was brought brilliantly to the
silver screen in the movie
The Matrix,
where aliens
have reduced all physical reality to a computer program. Billions of humans
think that they are leading everyday lives, oblivious of the fact that all
this is a computer-generated fantasy, while their real bodies are asleep in
pods, where the aliens use them as a power source.

In the movie, it
is possible to run smaller computer programs that can create artificial
minirealities. If one wants to become a kung fu master or a helicopter pilot,
one just inserts a CD into a computer, the program is fed into our brain, and
presto! one instantly learns these complicated skills. As the CD is run, a
whole new subreality is created. But it raises an intriguing question: can all
of reality be placed on a CD? The computer power necessary to simulate reality
for billions of sleeping humans is truly staggering. But in theory: can the
entire universe be digitalized in a finite computer program?

The roots of
this question go back to Newton's laws of motion, with very practical
applications for commerce and our lives. Mark Twain was famous for stating,
"Everyone complains about the weather, but no one ever does anything about
it." Modern civilization cannot change the course of even a single
thunderstorm, but physicists have asked a more modest question: can we predict
the weather? Can a computer program be devised that will predict the course of
complex weather patterns on Earth? This has very practical applications for
everyone concerned about the weather, from farmers wanting to know when to
harvest their crops to meteorologists wanting to know the course of global
warming in this century.

In principle,
computers can use Newton's laws of motion to compute with almost arbitrary
accuracy the course of molecules that make up the weather. But in practice,
computer programs are extremely crude and are not reliable at predicting the
weather beyond a few days or so, at best. To predict the weather, one would
need to determine the motion of every air molecule—something that is magnitudes
beyond our most powerful computer; there is also the problem of chaos theory
and the "butterfly effect," where even the tiniest vibration from a
butterfly's wing can cause a ripple effect that, at key junctures, may
decisively change the weather hundreds of miles away.

Mathematicians
summarize this situation by stating that the smallest model that can accurately
describe the weather is the weather itself. Rather than microanalyzing each
molecule, the best we can do is to look for estimates of tomorrow's weather and
also larger trends and patterns (such as the greenhouse effect).

So it is
exceedingly difficult for a Newtonian world to be reduced to a computer
program, since there are too many variables and too many
"butterflies." But in the quantum world, strange things happen.

Bekenstein, as
we saw, showed that the total information content of a black hole is
proportional to the surface area of its event horizon. There is an intuitive
way of seeing this. Many physicists believe that the smallest possible distance
is the Planck length of 10
^-33
cm. At this incredibly small distance,
space-time is no longer smooth but becomes "foamy," resembling a
froth of bubbles. We can divide up the spherical surface of the horizon into
tiny squares, each one the size of the Planck length. If each of these squares
contains one bit of information, and we add up all the squares, we find
roughly the total information content of the black hole. This seems to indicate
that each of these "Planck squares" is the smallest unit of
information. If this is true, then Bekenstein claims that perhaps information
is the true language of physics, not field theory. As he puts it, "Field
theory, with its infinity, cannot be the final story."

Ever since the
work of Michael Faraday in the nineteenth century, physics has been formulated
in the language of fields, which are smooth and continuous, and which measure
the strength of magnetism, electricity, gravity, and so on at any point in
space-time. But field theory is based on continuous structures, not digitalized
ones. A field can occupy any value, while a digitalized number can only
represent discrete numbers based on 0s and is. This is the difference, for
example, between a smooth rubber sheet found in Einstein's theory and a fine
wire mesh. The rubber sheet can be divided up into an infinite number of
points, while a wire mesh has a smallest distance, the mesh length.

Bekenstein
suggests that "a final theory must be concerned not with fields, not even
with spacetime, but rather with information exchange among physical
processes."

If the universe
can be digitalized and reduced to 0s and is, then what is the total information
content of the universe? Bekenstein estimates that a black hole about a
centimeter across could contain 10
⁶⁶
bits of information. But if an
object a centimeter in size can hold that many bits of information, then he
estimates that the visible universe probably contains much more information, no
less than 10
¹⁰⁰
bits of information (which can in principle be
squeezed into a sphere a tenth of a light-year across. This colossal number, 1
followed by 100 zeros, is called a google.)

If this picture
is correct, we have a strange situation. It might mean that while a Newtonian
world cannot be simulated by computers (or can only be simulated by a system
as large as itself), in a quantum world, perhaps the universe itself
can
be put onto a CD! In theory, if we can put i0
ⁱ⁰⁰
bits of information on a CD, we can watch any event in our universe unfold in
our living room. In principle, one could arrange or reprogram the bits on this
CD, so that physical reality proceeds in a different fashion. In some sense,
one would have a God-like ability to rewrite the script.

(Bekenstein also
admits that the total information content of the universe could be much larger
than that. In fact, the smallest volume that can contain the information of the
universe may be the size of the universe itself. If this is true, then we are
back to where we started: the smallest system that can model the universe is
the universe itself.)

String theory,
however, offers a slightly different interpretation of the "smallest
distance" and whether we can digitalize the universe on a CD. M-theory
possesses what is called T-duality. Recall that the Greek philosopher Zeno
thought that a line could be divided into an infinite number of points, without
limit. Today, quantum physicists like Bekenstein believe that the smallest
distance may be the Planck distance of i0
^-
33 centimeters, where the
fabric of space-time becomes foamy and bubbly. But M-theory gives us a new
twist to this. Let's say that we take a string theory and wrap up one dimension
into a circle of radius
R.
Then we take
another string and wrap up one dimension into a circle of radius i/R. By
comparing these two quite different theories, we find that they are exactly the
same.

Now let
R
become extremely small, much smaller than the Planck length.
This means that the physics within the Planck length is identical to the
physics outside the Planck length. At the Planck length, space-time may become
lumpy and foamy, but the physics inside the Planck length and the physics at
very large distances can be smooth and in fact are identical.

This duality was
first found in 1984 by my old colleague Keiji Kikkawa and his student Masami
Yamasaki, of Osaka University. Although string theory apparently concludes that
there is a "smallest distance," the Planck length, physics does not
abruptly end at the Planck length. The new twist is that physics smaller than
the Planck length is equivalent to physics larger than the Planck length.

If this rather
topsy-turvy interpretation is correct, then it means that even within the
"smallest distance" of string theory, an entire universe can exist.
In other words, we can still use field theory, with its continuous (not
digitalized) structures to describe the universe even to distances well inside
the Planck energy. So perhaps the universe is not a computer program at all.
In any event, since this is a well-defined problem, time will tell.

(This T-duality
is the justification for the "pre-big bang" scenario of Veneziano I
mentioned earlier. In that model, a black hole collapses down to the Planck
length and then "bounces" back into the big bang. This bounce is not
an abrupt event but the smooth T-duality between a black hole smaller than the
Planck length and an expanding universe larger than the Planck length.)