Parallel Worlds (34 page)

But there is a
potential flaw in this picture. Gravity represents the curvature of space.
Thus, naively we might expect that gravity can fill up all five-dimensional
space, rather than just the three- brane; in doing so, gravity would be diluted
as it leaves the three- brane. This weakens the force of gravity. This is a
good thing in supporting the theory, because gravity, we know, is so much
weaker than the other forces. But it weakens gravity too much: Newton's inverse
square law would be violated, yet the inverse square law works perfectly well
for planets, stars, and galaxies. Nowhere in space do we find an inverse cube
law for gravity. (Imagine a lightbulb illuminating a room. The light spreads
out in a sphere. The strength of the light is diluted across this sphere. Thus,
if you double the radius of the sphere, then the light is spread out over the
sphere with four times the area. In general, if a lightbulb exists in
n
dimensional space, then its light is diluted across a sphere
whose area increases as the radius is raised to the
n —
1 power.)

To answer this
question, a group of physicists, including N. Arkani-Hamed, S. Dimopoulos, and
G. Dvali, have suggested that perhaps the fifth dimension is not infinite but
is a millimeter away from ours, floating just above our universe, as in H. G.
Wells's science fiction story. (If the fifth dimension were farther than a millimeter
away, then it might create measurable violations of Newton's inverse square
law.) If the fifth dimension is only a millimeter away, this prediction could
be tested by looking for tiny deviations to Newton's law of gravity over very
small distances. Newton's law of gravity works fine over astronomical
distances, but it has never been tested down to the size of a millimeter.
Experimentalists are now rushing to test for tiny deviations from Newton's
inverse square law. This result is currently the subject of several ongoing
experiments, as we see in chapter 9.

Randall and her
colleague Raman Sundrum decided to take a new approach, to reexamine the
possibility that the fifth dimension was not a millimeter away but perhaps even
infinite. To do this, they had to explain how the fifth dimension could be
infinite without destroying Newton's law of gravity. This is where Randall
found a potential answer to the puzzle. She found that the three-brane has a
gravitational pull of its own that prevents gravitons from drifting freely into
the fifth dimension. The gravitons have to cling to the three-brane (like flies
trapped on flypaper) because of the gravity exerted by the three-brane. Thus,
when we try to measure Newton's law, we find that it is approximately correct
in our universe. Gravity is diluted and weakened as it leaves the three-brane
and drifts into the fifth dimension, but it doesn't get very far: the inverse
square law is still roughly maintained because gravitons are still attracted to
the three-brane. (Randall also introduced the possibility of a second membrane
existing parallel to ours. If we calculate the subtle interaction of gravity
across the two membranes, it can be adjusted so that we can numerically explain
the weakness of gravity.)

"There was
a lot of excitement when it was first suggested that extra dimensions provide
alternative ways to address the origin of the [hierarchy problem],"
Randall says. "Additional spatial dimensions may seem like a wild and
crazy idea at first, but there are powerful reasons to believe that there
really are extra dimensions of space."

If these
physicists are correct, then gravity is just as strong as the other forces,
except that gravity is attenuated because some of it leaks into
higher-dimensional space. One profound consequence of this theory is that the
energy at which these quantum effects become measurable may not be the Planck
energy (i0
¹⁹
billion electron volts), as previously thought. Perhaps
only trillions of electron volts are necessary, in which case the Large Hadron
Collider (scheduled for completion by 2007) may be able to pick up quantum
gravitational effects within this decade. This has stimulated considerable
interest among experimental physicists to hunt for exotic particles beyond the
Standard Model of subatomic particles. Perhaps quantum gravitational effects
are just within our reach.

Membranes also
give a plausible, though speculative, answer to the riddle of dark matter. In
H. G. Wells's novel
The Invisible Man,
the protagonist
hovered in the fourth dimension and hence was invisible. Similarly, imagine
that there is a parallel world hovering just above our own universe. Any galaxy
in that parallel universe would be invisible to us. But because gravity is
caused by the bending of hy- perspace, gravity could hop across universes. Any
large galaxy in that universe would be attracted across hyperspace to a galaxy
in our universe. Thus, when we measure the properties of our galaxies, we would
find that their gravitational pull was much stronger than expected from
Newton's laws because there is another galaxy hiding right behind it, floating
on a nearby brane. This hidden galaxy perched behind our galaxy would be
totally invisible, floating in another dimension, but it would give the appearance
of a halo surrounding our galaxy containing 90 percent of the mass. Thus, dark
matter may be caused by the presence of a parallel universe.

COLLIDING UNIVERSES

It may be a bit
premature to apply M-theory to serious cosmology. Nonetheless, physicists have
tried to apply "brane physics" to make a new twist on the usual
inflationary approach to the universe. Three possible cosmologies have
attracted some attention.

The first
cosmology tries to answer the question: why do we live in four space-time dimensions?
In principle, M-theory can be formulated in all dimensions up to eleven, so it
seems like a mystery that four dimensions are singled out. Robert Brandenberger
and Cumrun Vafa have speculated that this may be due to the particular geometry
of strings.

In their
scenario, the universe started perfectly symmetrically, with all higher
dimensions tightly curled up at the Planck scale. What kept the universe from
expanding were loops of strings that tightly coiled around the various
dimensions. Think of a compressed coil that cannot expand because it is tightly
wrapped by strings. If the strings somehow break, the coil suddenly springs
free and expands.

In these tiny
dimensions, the universe is prevented from expanding because we have windings
of both strings and antistrings (roughly speaking, antistrings wind in the
opposite direction from strings). If a string and antistring collide, then they
can annihilate and disappear, like the unraveling of a knot. In very large
dimensions, there is so much "room" that strings and antistrings
rarely collide and never unravel. However, Brandenberger and Vafa showed that
in three or fewer spatial dimensions, it is more likely that strings will
collide with antistrings. Once these collisions take place, the strings unravel,
and the dimensions spring rapidly outward, giving us the big bang. The
appealing feature of this picture is that the topology of strings explains
roughly why we see the familiar four- dimensional space-time around us.
Higher-dimensional universes are possible but less likely to be seen because
they are still wrapped up tightly by strings and antistrings.

But there are
other possibilities in M-theory as well. If universes can pinch or bud off each
other, spawning new universes, then perhaps the reverse can happen: universes
can collide, creating sparks in the process, spawning new universes. In such a
scenario, perhaps the big bang occurred because of a collision of two parallel
brane- universes rather than the budding of a universe.

This second theory
was proposed by physicists Paul Steinhardt of Princeton, Burt Ovrut of the
University of Pennsylvania, and Neil Turok of Cambridge University, who created
the "ekpyrotic" universe (meaning "conflagration" in Greek)
to incorporate the novel features of the M-brane picture, in which some of the
extra dimensions could be large and even infinite in size. They begin with two
flat, homogenous, and parallel three-branes that represent the lowest energy
state. Originally, they start as empty, cold universes, but gravity gradually
pulls them together. They eventually collide, and the vast kinetic energy of
the collision is converted into the matter and radiation making up our
universe. Some call this the "big splat" theory rather than the big
bang theory, because the scenario involves the collision of two branes.

The force of the
collision pushes the two universes apart. As these two membranes separate from
each other, they cool rapidly, giving us the universe we see today. The cooling
and expansion continue for trillions of years, until the universes approach
absolute zero in temperature, and the density is only one electron per
quadrillion cubic light-years of space. In effect, the universe becomes empty
and inert. But gravity continues to attract the two membranes, until, trillions
of years later, they collide once again, and the cycle repeats all over again.

This new
scenario is able to obtain the good results of inflation (flatness,
uniformity). It solves the question of why the universe is so flat—because the
two branes were flat to begin with. The model can also explain the horizon
problem—that is, why the universe seems so remarkably uniform in all
directions. It is because the membrane has a long time to slowly reach
equilibrium. Thus, while inflation explains the horizon problem by having the
universe inflate abruptly, this scenario solves the horizon problem in the
opposite way, by having the universe reach equilibrium in slow motion.

(This also means
that there are possibly other membranes floating out there in hyperspace that
may collide with ours in the future, creating another big splat. Given the fact
that our universe is accelerating, another collision may in fact be likely.
Steinhardt adds, "Maybe the acceleration of the expansion of the universe
is a precursor of such a collision. It is not a pleasant thought.")

Any scenario
that dramatically challenges the prevailing picture of inflation is bound to
elicit heated replies. In fact, within a week of the paper being placed on the
Web, Andrei Linde and his wife, Renata Kallosh (herself a string theorist), and
Lev Kofman of the University of Toronto issued a critique of this scenario.
Linde criticized this model because anything so catastrophic as the collision
of two universes might create a singularity, where temperatures and densities
approach infinity. "That would be like throwing a chair into a black hole,
which would vaporize the particles of the chair, and saying it somehow
preserves the shape of the chair," Linde protested.

Steinhardt fired
back, saying, "What looks like a singularity in four dimensions may not be
one in five dimensions . . . When the branes crunch together, the fifth
dimension disappears temporarily, but the branes themselves don't disappear. So
the density and temperature don't go to infinity, and time continues right
through. Although general relativity goes berserk, string theory does not. And
what once looked like a disaster in our model now seems manageable."

Steinhardt has
on his side the power of M-theory, which is known to eliminate singularities.
In fact, that is the reason theoretical physicists need a quantum theory of
gravity to begin with, to eliminate all infinities. Linde, however, points out
a conceptual vulnerability of this picture, that the branes existed in a flat,
uniform state at the beginning. "If you start with perfection, you might
be able to explain what you see . . . but you still haven't answered the
question: Why must the universe start out perfect?" Linde says. Steinhardt
answers back, "Flat plus flat equals flat." In other words, you have
to assume that the membranes started out in the lowest energy state of being
flat.

Alan Guth has
kept an open mind. "I don't think Paul and Neil come close to proving
their case. But their ideas are certainly worth looking at," he says. He
turns the tables and challenges string theorists to explain inflation:
"In the long run, I think it's inevitable that string theory and M-theory
will need to incorporate inflation, since inflation seems to be an obvious solution
to the problems it was designed to address—that is, why is the universe so
uniform and flat." So he asks the question: can M-theory derive the
standard picture of inflation?

Last, there is
another competing theory of cosmology that employs string theory, the
"pre-big bang" theory of Gabriele Veneziano, the physicist who helped
start string theory back in 1968. In his theory, the universe actually started
out as a black hole. If we want to know what the inside of a black hole looks
like, all we have to do is look outside.

In this theory,
the universe is actually infinitely old and started out in the distant past as
being nearly empty and cold. Gravity began to create clumps of matter
throughout the universe, which gradually condensed into regions so dense that
they turned into black holes. Event horizons began to form around each black
hole, permanently separating the exterior of the event horizon from the
interior. Within each event horizon, matter continued to be compressed by
gravity, until the black hole eventually reached the Planck length.

At this point,
string theory takes over. The Planck length is the minimum distance allowed by
string theory. The black hole then begins to rebound in a huge explosion,
causing the big bang. Since this process may repeat itself throughout the
universe, this means that there may be other distant black holes/universes.