String Theory For Big Blokes

Was the big bang really the beginning of time? Or did the universe exist
before then? Such a question seemed almost blasphemous only a decade ago.
Most cosmologists insisted that it simply made no sense--that to contemplate
a time before the big bang was like asking for directions to a place north
of the North Pole. But developments in theoretical physics, especially the
rise of string theory, have changed their perspective. The pre-bang universe
has become the latest frontier of cosmology.
The new willingness to consider what might have happened before the bang is
the latest swing of an intellectual pendulum that has rocked back and forth
for millennia. In one form or another, the issue of the ultimate beginning
has engaged philosophers and theologians in nearly every culture. It is
entwined with a grand set of concerns, one famously encapsulated in an 1897
painting by Paul Gauguin: D'ou venons-nous? Que sommes-nous? Ou allons-nous?
"Where do we come from? What are we? Where are we going?" The piece depicts
the cycle of birth, life and death--origin, identity and destiny for each
individual--and these personal concerns connect directly to cosmic ones. We
can trace our lineage back through the generations, back through our animal
ancestors, to early forms of life and protolife, to the elements synthesized
in the primordial universe, to the amorphous energy deposited in space
before that. Does our family tree extend forever backward? Or do its roots
terminate? Is the cosmos as impermanent as we are?

The ancient Greeks debated the origin of time fiercely. Aristotle, taking
the no-beginning side, invoked the principle that out of nothing, nothing
comes. If the universe could never have gone from nothingness to
somethingness, it must always have existed. For this and other reasons, time
must stretch eternally into the past and future. Christian theologians
tended to take the opposite point of view. Augustine contended that God
exists outside of space and time, able to bring these constructs into
existence as surely as he could forge other aspects of our world. When
asked, "What was God doing before he created the world?" Augustine answered,
"Time itself being part of God's creation, there was simply no before!"

Einstein's general theory of relativity led modern cosmologists to much the
same conclusion. The theory holds that space and time are soft, malleable
entities. On the largest scales, space is naturally dynamic, expanding or
contracting over time, carrying matter like driftwood on the tide.
Astronomers confirmed in the 1920s that our universe is currently expanding:
distant galaxies move apart from one another. One consequence, as physicists
Stephen Hawking and Roger Penrose proved in the 1960s, is that time cannot
extend back indefinitely. As you play cosmic history backward in time, the
galaxies all come together to a single infinitesimal point, known as a
singularity--almost as if they were descending into a black hole. Each
galaxy or its precursor is squeezed down to zero size. Quantities such as
density, temperature and spacetime curvature become infinite. The
singularity is the ultimate cataclysm, beyond which our cosmic ancestry
cannot extend.

Strange Coincidence

The unavoidable singularity poses serious problems for cosmologists. In
particular, it sits uneasily with the high degree of homogeneity and
isotropy that the universe exhibits on large scales. For the cosmos to look
broadly the same everywhere, some kind of communication had to pass among
distant regions of space, coordinating their properties. But the idea of
such communication contradicts the old cosmological paradigm.

To be specific, consider what has happened over the 13.7 billion years since
the release of the cosmic microwave background radiation. The distance
between galaxies has grown by a factor of about 1,000 (because of the
expansion), while the radius of the observable universe has grown by the
much larger factor of about 100,000 (because light outpaces the expansion).
We see parts of the universe today that we could not have seen 13.7 billion
years ago. Indeed, this is the first time in cosmic history that light from
the most distant galaxies has reached the Milky Way.

Nevertheless, the properties of the Milky Way are basically the same as
those of distant galaxies. It is as though you showed up at a party only to
find you were wearing exactly the same clothes as a dozen of your closest
friends. If just two of you were dressed the same, it might be explained
away as coincidence, but a dozen suggests that the partygoers had
coordinated their attire in advance. In cosmology, the number is not a dozen
but tens of thousands--the number of independent yet statistically identical
patches of sky in the microwave background.

One possibility is that all those regions of space were endowed at birth
with identical properties--in other words, that the homogeneity is mere
coincidence. Physicists, however, have thought about two more natural ways
out of the impasse: the early universe was much smaller or much older than
in standard cosmology. Either (or both, acting together) would have made
intercommunication possible.

The most popular choice follows the first alternative. It postulates that
the universe went through a period of accelerating expansion, known as
inflation, early in its history. Before this phase, galaxies or their
precursors were so closely packed that they could easily coordinate their
properties. During inflation, they fell out of contact because light was
unable to keep pace with the frenetic expansion. After inflation ended, the
expansion began to decelerate, so galaxies gradually came back into one
another's view.

Physicists ascribe the inflationary spurt to the potential energy stored in
a new quantum field, the inflaton, about 10-35 second after the big bang.
Potential energy, as opposed to rest mass or kinetic energy, leads to
gravitational repulsion. Rather than slowing down the expansion, as the
gravitation of ordinary matter would, the inflaton accelerated it. Proposed
in 1981, inflation has explained a wide variety of observations with
precision [see "The Inflationary Universe," by Alan H. Guth and Paul J.
Steinhardt; Scientific American, May 1984; and "Four Keys to Cosmology,"
Special report; Scientific American, February]. A number of possible
theoretical problems remain, though, beginning with the questions of what
exactly the inflaton was and what gave it such a huge initial potential
energy.

A second, less widely known way to solve the puzzle follows the second
alternative by getting rid of the singularity. If time did not begin at the
bang, if a long era preceded the onset of the present cosmic expansion,
matter could have had plenty of time to arrange itself smoothly. Therefore,
researchers have reexamined the reasoning that led them to infer a
singularity.

One of the assumptions--that relativity theory is always valid--is
questionable. Close to the putative singularity, quantum effects must have
been important, even dominant. Standard relativity takes no account of such
effects, so accepting the inevitability of the singularity amounts to
trusting the theory beyond reason. To know what really happened, physicists
need to subsume relativity in a quantum theory of gravity. The task has
occupied theorists from Einstein onward, but progress was almost zero until
the mid-1980s.

Evolution of a Revolution

Today two approaches stand out. One, going by the name of loop quantum
gravity, retains Einstein's theory essentially intact but changes the
procedure for implementing it in quantum mechanics [see "Atoms of Space and
Time," by Lee Smolin; Scientific American, January]. Practitioners of loop
quantum gravity have taken great strides and achieved deep insights over the
past several years. Still, their approach may not be revolutionary enough to
resolve the fundamental problems of quantizing gravity. A similar problem
faced particle theorists after Enrico Fermi introduced his effective theory
of the weak nuclear force in 1934. All efforts to construct a quantum
version of Fermi's theory failed miserably. What was needed was not a new
technique but the deep modifications brought by the electroweak theory of
Sheldon L. Glashow, Steven Wein-berg and Abdus Salam in the late 1960s.

The second approach, which I consider more promising, is string theory--a
truly revolutionary modification of Einstein's theory. This article will
focus on it, although proponents of loop quantum gravity claim to reach many
of the same conclusions.

String theory grew out of a model that I wrote down in 1968 to describe the
world of nuclear particles (such as protons and neutrons) and their
interactions. Despite much initial excitement, the model failed. It was
abandoned several years later in favor of quantum chromodynamics, which
describes nuclear particles in terms of more elementary constituents,
quarks. Quarks are confined inside a proton or a neutron, as if they were
tied together by elastic strings. In retrospect, the original string theory
had captured those stringy aspects of the nuclear world. Only later was it
revived as a candidate for combining general relativity and quantum theory.

The basic idea is that elementary particles are not pointlike but rather
infinitely thin one-dimensional objects, the strings. The large zoo of
elementary particles, each with its own characteristic properties, reflects
the many possible vibration patterns of a string. How can such a
simple-minded theory describe the complicated world of particles and their
interactions? The answer can be found in what we may call quantum string
magic. Once the rules of quantum mechanics are applied to a vibrating
string--just like a miniature violin string, except that the vibrations
propagate along it at the speed of light--new properties appear. All have
profound implications for particle physics and cosmology.

First, quantum strings have a finite size. Were it not for quantum effects,
a violin string could be cut in half, cut in half again and so on all the
way down, finally becoming a massless pointlike particle. But the Heisenberg
uncertainty principle eventually intrudes and prevents the lightest strings
from being sliced smaller than about 10-34 meter. This irreducible quantum
of length, denoted ls, is a new constant of nature introduced by string
theory side by side with the speed of light, c, and Planck's constant, h. It
plays a crucial role in almost every aspect of string theory, putting a
finite limit on quantities that otherwise could become either zero or
infinite.

Second, quantum strings may have angular momentum even if they lack mass. In
classical physics, angular momentum is a property of an object that rotates
with respect to an axis. The formula for angular momentum multiplies
together velocity, mass and distance from the axis; hence, a massless object
can have no angular momentum. But quantum fluctuations change the situation.
A tiny string can acquire up to two units of h of angular momentum without
gaining any mass. This feature is very welcome because it precisely matches
the properties of the carriers of all known fundamental forces, such as the
photon (for electromagnetism) and the graviton (for gravity). Historically,
angular momentum is what clued in physicists to the quantum-gravitational
implications of string theory.

Third, quantum strings demand the existence of extra dimensions of space, in
addition to the usual three. Whereas a classical violin string will vibrate
no matter what the properties of space and time are, a quantum string is
more finicky. The equations describing the vibration become inconsistent
unless spacetime either is highly curved (in contradiction with
observations) or contains six extra spatial dimensions.

Fourth, physical constants--such as Newton's and Coulomb's constants, which
appear in the equations of physics and determine the properties of
nature--no longer have arbitrary, fixed values. They occur in string theory
as fields, rather like the electromagnetic field, that can adjust their
values dynamically. These fields may have taken different values in
different cosmological epochs or in remote regions of space, and even today
the physical "constants" may vary by a small amount. Observing any variation
would provide an enormous boost to string theory.

One such field, called the dilaton, is the master key to string theory; it
determines the overall strength of all interactions. The dilaton fascinates
string theorists because its value can be reinterpreted as the size of an
extra dimension of space, giving a grand total of 11 spacetime dimensions.

Tying Down the Loose Ends

Finally, quantum strings have introduced physicists to some striking new
symmetries of nature known as dualities, which alter our intuition for what
happens when objects get extremely small. I have already alluded to a form
of duality: normally, a short string is lighter than a long one, but if we
attempt to squeeze down its size below the fundamental length ls, the string
gets heavier again.

Another form of the symmetry, T-duality, holds that small and large extra
dimensions are equivalent. This symmetry arises because strings can move in
more complicated ways than pointlike particles can. Consider a closed string
(a loop) located on a cylindrically shaped space, whose circular cross
section represents one finite extra dimension. Besides vibrating, the string
can either turn as a whole around the cylinder or wind around it, one or
several times, like a rubber band wrapped around a rolled-up poster.

The energetic cost of these two states of the string depends on the size of
the cylinder. The energy of winding is directly proportional to the cylinder
radius: larger cylinders require the string to stretch more as it wraps
around, so the windings contain more energy than they would on a smaller
cylinder. The energy associated with moving around the circle, on the other
hand, is inversely proportional to the radius: larger cylinders allow for
longer wavelengths (smaller frequencies), which represent less energy than
shorter wavelengths do. If a large cylinder is substituted for a small one,
the two states of motion can swap roles. Energies that had been produced by
circular motion are instead produced by winding, and vice versa. An outside
observer notices only the energy levels, not the origin of those levels. To
that observer, the large and small radii are physically equivalent.

Although T-duality is usually described in terms of cylindrical spaces, in
which one dimension (the circumference) is finite, a variant of it applies
to our ordinary three dimensions, which appear to stretch on indefinitely.
One must be careful when talking about the expansion of an infinite space.
Its overall size cannot change; it remains infinite. But it can still expand
in the sense that bodies embedded within it, such as galaxies, move apart
from one another. The crucial variable is not the size of the space as a
whole but its scale factor--the factor by which the distance between
galaxies changes, manifesting itself as the galactic redshift that
astronomers observe. According to T-duality, universes with small scale
factors are equivalent to ones with large scale factors. No such symmetry is
present in Einstein's equations; it emerges from the unification that string
theory embodies, with the dilaton playing a central role.

For years, string theorists thought that T-duality applied only to closed
strings, as opposed to open strings, which have loose ends and thus cannot
wind. In 1995 Joseph Polchinski of the University of California at Santa
Barbara realized that T-duality did apply to open strings, provided that the
switch between large and small radii was accompanied by a change in the
conditions at the end points of the string. Until then, physicists had
postulated boundary conditions in which no force acted on the ends of the
strings, leaving them free to flap around. Under T-duality, these conditions
become so-called Dirichlet boundary conditions, whereby the ends stay put.

Any given string can mix both types of boundary conditions. For instance,
electrons may be strings whose ends can move around freely in three of the
10 spatial dimensions but are stuck within the other seven. Those three
dimensions form a subspace known as a Dirichlet membrane, or D-brane. In
1996 Petr Horava of the University of California at Berkeley and Edward
Witten of the Institute for Advanced Study in Princeton, N.J., proposed that
our universe resides on such a brane. The partial mobility of electrons and
other particles explains why we are unable to perceive the full
10-dimensional glory of space.

Taming the Infinite

All the magic properties of quantum strings point in one direction: strings
abhor infinity. They cannot collapse to an infinitesimal point, so they
avoid the paradoxes that collapse entails. Their nonzero size and novel
symmetries set upper bounds to physical quantities that increase without
limit in conventional theories, and they set lower bounds to quantities that
decrease. String theorists expect that when one plays the history of the
universe backward in time, the curvature of spacetime starts to increase.
But instead of going all the way to infinity (at the traditional big bang
singularity), it eventually hits a maximum and shrinks once more. Before
string theory, physicists were hard-pressed to imagine any mechanism that
could so cleanly eliminate the singularity.

Conditions near the zero time of the big bang were so extreme that no one
yet knows how to solve the equations. Nevertheless, string theorists have
hazarded guesses about the pre-bang universe. Two popular models are
floating around.

The first, known as the pre-big bang scenario, which my colleagues and I
began to develop in 1991, combines T-duality with the better-known symmetry
of time reversal, whereby the equations of physics work equally well when
applied backward and forward in time. The combination gives rise to new
possible cosmologies in which the universe, say, five seconds before the big
bang expanded at the same pace as it did five seconds after the bang. But
the rate of change of the expansion was opposite at the two instants: if it
was decelerating after the bang, it was accelerating before. In short, the
big bang may not have been the origin of the universe but simply a violent
transition from acceleration to deceleration.

The beauty of this picture is that it automatically incorporates the great
insight of standard inflationary theory--namely, that the universe had to
undergo a period of acceleration to become so homogeneous and isotropic. In
the standard theory, acceleration occurs after the big bang because of an ad
hoc inflaton field. In the pre-big bang scenario, it occurs before the bang
as a natural outcome of the novel symmetries of string theory.

According to the scenario, the pre-bang universe was almost a perfect mirror
image of the post-bang one. If the universe is eternal into the future, its
contents thinning to a meager gruel, it is also eternal into the past.
Infinitely long ago it was nearly empty, filled only with a tenuous, widely
dispersed, chaotic gas of radiation and matter. The forces of nature,
controlled by the dilaton field, were so feeble that particles in this gas
barely interacted.

As time went on, the forces gained in strength and pulled matter together.
Randomly, some regions accumulated matter at the expense of their
surroundings. Eventually the density in these regions became so high that
black holes started to form. Matter inside those regions was then cut off
from the outside, breaking up the universe into disconnected pieces.

Inside a black hole, space and time swap roles. The center of the black hole
is not a point in space but an instant in time. As the infalling matter
approached the center, it reached higher and higher densities. But when the
density, temperature and curvature reached the maximum values allowed by
string theory, these quantities bounced and started decreasing. The moment
of that reversal is what we call a big bang. The interior of one of those
black holes became our universe.

Not surprisingly, such an unconventional scenario has provoked controversy.
Andrei Linde of Stanford University has argued that for this scenario to
match observations, the black hole that gave rise to our universe would have
to have formed with an unusually large size--much larger than the length
scale of string theory. An answer to this objection is that the equations
predict black holes of all possible sizes. Our universe just happened to
form inside a sufficiently large one.

A more serious objection, raised by Thibault Damour of the Institut des
Hautes ?tudes Scientifiques in Bures-sur-Yvette, France, and Marc Henneaux
of the Free University of Brussels, is that matter and spacetime would have
behaved chaotically near the moment of the bang, in possible contradiction
with the observed regularity of the early universe. I have recently proposed
that a chaotic state would produce a dense gas of miniature "string
holes"--strings that were so small and massive that they were on the verge
of becoming black holes. The behavior of these holes could solve the problem
identified by Damour and Henneaux. A similar proposal has been put forward
by Thomas Banks of Rutgers University and Willy Fischler of the University
of Texas at Austin. Other critiques also exist, and whether they have
uncovered a fatal flaw in the scenario remains to be determined.

Bashing Branes

The other leading model for the universe before the bang is the ekpyrotic
("conflagration") scenario. Developed three years ago by a team of
cosmologists and string theorists--Justin Khoury of Columbia University,
Paul J. Steinhardt of Princeton University, Burt A. Ovrut of the University
of Pennsylvania, Nathan Seiberg of the Institute for Advanced Study and Neil
Turok of the University of Cambridge--the ekpyrotic scenario relies on the
idea that our universe is one of many D-branes floating within a
higher-dimensional space. The branes exert attractive forces on one another
and occasionally collide. The big bang could be the impact of another brane
into ours.

In a variant of this scenario, the collisions occur cyclically. Two branes
might hit, bounce off each other, move apart, pull each other together, hit
again, and so on. In between collisions, the branes behave like Silly Putty,
expanding as they recede and contracting somewhat as they come back
together. During the turnaround, the expansion rate accelerates; indeed, the
present accelerating expansion of the universe may augur another collision.

The pre?big bang and ekpyrotic scenarios share some common features. Both
begin with a large, cold, nearly empty universe, and both share the
difficult (and unresolved) problem of making the transition between the pre-
and the post-bang phase. Mathematically, the main difference between the
scenarios is the behavior of the dilaton field. In the pre?big bang, the
dilaton begins with a low value--so that the forces of nature are weak--and
steadily gains strength. The opposite is true for the ekpyrotic scenario, in
which the collision occurs when forces are at their weakest.

The developers of the ekpyrotic theory initially hoped that the weakness of
the forces would allow the bounce to be analyzed more easily, but they were
still confronted with a difficult high-curvature situation, so the jury is
out on whether the scenario truly avoids a singularity. Also, the ekpyrotic
scenario must entail very special conditions to solve the usual cosmological
puzzles. For instance, the about-to-collide branes must have been almost
exactly parallel to one another, or else the collision could not have given
rise to a sufficiently homogeneous bang. The cyclic version may be able to
take care of this problem, because successive collisions would allow the
branes to straighten themselves.

Leaving aside the difficult task of fully justifying these two scenarios
mathematically, physicists must ask whether they have any observable
physical consequences. At first sight, both scenarios might seem like an
exercise not in physics but in metaphysics--interesting ideas that observers
could never prove right or wrong. That attitude is too pessimistic. Like the
details of the inflationary phase, those of a possible pre-bangian epoch
could have observable consequences, especially for the small variations
observed in the cosmic microwave background temperature.

First, observations show that the temperature fluctuations were shaped by
acoustic waves for several hundred thousand years. The regularity of the
fluctuations indicates that the waves were synchronized. Cosmologists have
discarded many cosmological models over the years because they failed to
account for this synchrony. The inflationary, pre-big bang and ekpyrotic
scenarios all pass this first test. In these three models, the waves were
triggered by quantum processes amplified during the period of accelerating
cosmic expansion. The phases of the waves were aligned.

















Second, each model predicts a different distribution of the temperature
fluctuations with respect to angular size. Observers have found that
fluctuations of all sizes have approximately the same amplitude.
(Discernible deviations occur only on very small scales, for which the
primordial fluctuations have been altered by subsequent processes.)
Inflationary models neatly reproduce this distribution. During inflation,
the curvature of space changed relatively slowly, so fluctuations of
different sizes were generated under much the same conditions. In both the
stringy models, the curvature evolved quickly, increasing the amplitude of
small-scale fluctuations, but other processes boosted the large-scale ones,
leaving all fluctuations with the same strength. For the ekpyrotic scenario,
those other processes involved the extra dimension of space, the one that
separated the colliding branes. For the pre-big bang scenario, they involved
a quantum field, the axion, related to the dilaton. In short, all three
models match the data.

Third, temperature variations can arise from two distinct processes in the
early universe: fluctuations in the density of matter and rippling caused by
gravitational waves. Inflation involves both processes, whereas the pre-big
bang and ekpyrotic scenarios predominantly involve density variations.
Gravitational waves of certain sizes would leave a distinctive signature in
the polarization of the microwave background [see "Echoes from the Big
Bang," by Robert R. Caldwell and Marc Kamionkowski; Scientific American,
January 2001]. Future observatories, such as European Space Agency's Planck
satellite, should be able to see that signature, if it exists--providing a
nearly definitive test.

A fourth test pertains to the statistics of the fluctuations. In inflation
the fluctuations follow a bell-shaped curve, known to physicists as a
Gaussian. The same may be true in the ekpyrotic case, whereas the pre-big
bang scenario allows for sizable deviation from Gaussianity.

Analysis of the microwave background is not the only way to verify these
theories. The pre-big bang scenario should also produce a random background
of gravitational waves in a range of frequencies that, though irrelevant for
the microwave background, should be detectable by future gravitational-wave
observatories. Moreover, because the pre-big bang and ekpyrotic scenarios
involve changes in the dilaton field, which is coupled to the
electromagnetic field, they would both lead to large-scale magnetic field
fluctuations. Vestiges of these fluctuations might show up in galactic and
intergalactic magnetic fields.

So, when did time begin? Science does not have a conclusive answer yet, but
at least two potentially testable theories plausibly hold that the
universe--and therefore time--existed well before the big bang. If either
scenario is right, the cosmos has always been in existence and, even if it
recollapses one day, will never end.




























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