Hiding in the Mirror (27 page)

Nevertheless, aside from this “minor”
inadequacy, you may recall that I promised you a theory with a
really large extra dimension, not the puny compactified extra
dimension that Randall and Sundrum proposed. Happily, for those who
find the unbridled optimism of the last paragraph less than
convincing, these researchers discovered, within a month of their
original suggestion, that a compactified extra dimension was, in
fact, completely unnecessary in their warped five-dimensional
space-time model. If the space outside our local three-brane was
warped, they discovered that the size of the extra dimension(s)
could in fact be infinite . . . namely, just as big as the three
dimensions of our experience!

To reach this conclusion, they
considered—instead of a fivedimensional space with a compactified
extra dimension—an infinitely large five-dimensional space with two
three-branes located a very small distance apart. The finite volume
between the branes mimicked the compactified space of their original
model. They then assumed that we live on one of the two
three-branes, and considered what happens as one slowly increases
the separation of the two branes.

You will recall that in their original
scenario, the warping of space-time near our three-brane caused the
strength of gravity to fall off exponentially as one approached our
brane from anywhere else in the space. In this case, they switched
things around, having the strength of gravity fall off
exponentially
away
from our brane. One
finds, accordingly, that the force of gravity is effectively tied to
our brane and, since gravity is our only probe of the extra
dimension, even in the limit that the other brane is removed to
infinite distances in the fifth dimension the effects of this large
extra dimension are completely hidden. Also, it turns out that the
masses of the tower of states that occur in higher dimensional
theories all tend toward zero, just like the (zero-mass) graviton
that is responsible for conveying the gravitational force in our
three-dimensional space. But, fortunately all these extra states
essentially decouple from matter in our space, and therefore cannot
be produced in any present or planned accelerators, and remain
completely unobservable. Moreover, any corrections they might
provide to the nature of the gravitational force between test
particles is suppressed by the ratio of the distance between the
test particles divided by the curvature scale in the extra
dimension. If this latter quantity is on the order of the Planck
scale, then the effect will be unobservably small in any
conceivable experiment that might be performed in the future. What
this second Randall-Sundrum model demonstrates is that the
conventional wisdom about extra dimensions, stretching back all the
way to Kaluza-Klein, was wrong. It is completely possible to hide
behind the mirror not only a microscopic extra dimension, as
originally envisaged, or even merely a tiny extra dimension, as
Arkani-Hamed and colleagues envisaged, but also an
infinite
extra dimension, which would exist in
concert with our own three-dimensional space.

Beyond this, what the models of Arkani-Hamed
and coworkers and Randall-Sundrum have shown is that if our
three-dimensional universe comprises a three-brane within a
higher-dimensional space, then it might be possible to resolve at
least one fundamental mystery in particle physics while providing a
possible new set of signatures that could open up both the extra
dimensions, and the complexities of string theory or M-theory to
the bright light of experiment.

That is the good news. Once again, however,
just below the surface in these models lies a host of problems that
suggest, that as far as the possible existence of extra dimensions
are concerned, it is very difficult to have one’s cake and eat it,
too.

First, note that in the second Randall-Sundrum
model, which switches branes around from their earlier compactified
model, the whole extradimensional solution of the hierarchy problem
disappears. In the first model the exponential falloff of gravity
near our brane is sufficient to make gravity anomalously weak
compared to the other forces in nature, while in their second
model, unless one fine-tunes things, the four-dimensional Planck
scale is identical to the fundamental curvature scale in the higher
dimension, which is presumably related to the string scale in this
higherdimensional space. All of the scales are vastly different
than the electroweak scale. One must then find another mechanism to
enforce the wide disparity between the strength of gravity and the
other observed forces in our world. This is inconvenient and,
frankly, reduces the motivation for introducing an extra dimension
in the first place. Were it not for the fact that three-branes and
extra dimensions arise within the context of string/M-theory, one
might wonder what one would gain from this albeit fascinating
mathematical construction. But there are other, more fundamental
concerns. The key to all of these interesting recent results is the
newly recognized possible existence within string theory of
three-branes, onto which all nongravitational charges and fields
could be constrained, and a higher-dimensional bulk space into
which gravity can propagate. However, string theory appears to
naturally incorporate branes of all dimensions up to perhaps ten
dimensions itself, with all of these comprising all possible
orientations within the context of the complicated and as-of-yet
not understood ground state of string/M-theory. The notion that our
world should lie completely within an isolated three-brane is quite
frankly not suggested by anything that is known about string theory
at the present time.

From my point of view there is another more
immediate issue that strongly diminishes the beauty of the proposed
extra-dimensional solutions of the hierarchy problem. The one
profoundly important experimental fact we know about the
fundamental forces of nature on the scales that we can probe them
is that as these scales become smaller and smaller, the strengths
of the forces appear to approach a common value. It was this fact
that provided one of the most direct pieces of evidence suggesting
the existence of a possible grand unified theory in the first place,
and that still provides one of the best reasons to believe in
supersymmetry as a symmetry of nature. Recall that this symmetry is
really the underpinning of all of modern string theory.

But remember, too, that the scale at which this
evidence suggests the forces may unify is unambiguously fourteen to
fifteen orders of magnitude smaller than the scale at which the weak
and electromagnetic interactions themselves unify, and within a few
orders of magnitude of the Planck scale itself. Moreover, the other
new great discovery of the past twenty-five years in particle
physics is the remarkable fact that neutrinos, the ghostly
particles that experience only the weak force, are not absolutely
massless, but rather have a very small mass, more than a hundred
thousand times smaller than that of the next lightest particle, the
electron. Such masses are not explicable within the context of the
standard model, which incorporates all known physics up to the
electroweak scale. However, if one adds new physics at the grand
unified scale, one can naturally arrive at neutrino masses in this
range.

Thus, if one makes the electroweak scale the
fundamental scale in nature on which extra dimensions, gravity, and
string phenomena arise, one might remove the hierarchy between our
four-dimensional Planck scale and the electroweak scale, but in
doing so one swims strongly against the tide of experimental
evidence. This is not a good precedent for what is supposed to be
an empirical science.

It could be that the apparent unification of the
strengths of the known nongravitational forces, and the existence
of neutrino masses, are just coincidences with no fundamental
explanation in terms of grand unification near the Planck scale. But
here I paraphrase Einstein: Nature may be subtle, but she is not
malicious. If the only evidence that nature seems to be providing
us about fundamental scales turns out to be a red herring, this
would break a tradition that has stood us in good stead for over
four hundred years. Finally, we once again return to the Achilles
heel of all theories of quantum gravity: Einstein’s cosmological
constant, the energy of empty space. It turns out that in order for
our three-dimensional space to exist as a flat three-brane within a
warped higher-dimensional space, the vacuum energy associated with
the higher-dimensional space would have to be very large, and
negative. It would then have to be precisely cancelled on our brane
by a contribution that is large and positive in order for the
observed energy of three-dimensional space to be both very small
and nonzero. In short, the biggest fine-tuning problem known in
nature becomes even more significant in these models, which, after
all, were motivated by a desire to solve a much less severe
numerical issue. Still, I come here not to bury these new ideas
about extra dimensions but to praise them. For all their potential
weaknesses, they have revealed as at least experimentally allowable
a whole host of possible extra dimensions that had hitherto been
considered ruled out. And whenever new theoretical possibilities
exist, there is always the chance that nature will actually take
advantage of them.

All the problems and challenges aside, the
realization that the world of our experience could, in principle,
be embedded in a larger space that could become directly
experimentally accessible in the near future has caused a
tremendous explosion of energy devoted to exploring all the
potential consequences of (possibly large) extra dimensions and the
branes that may exist within them.

The sociology of physics is a strange and
wonderful thing. The reaction to the Arkani-Hamed and coworkers and
Randall-Sundrum papers was nothing short of phenomenal. Within six
years, no fewer than 2,500 separate scientific papers appeared
exploring their ramifications. Like a well-timed drama that somehow
captures the public’s imagination, the notions of large extra
dimensions and/or a low-energy string scale seemed to have
everything going for them in the theoretical physics community.
They were novel, sexy, and potentially testable.

New phenomena associated with strings and extra
dimensions that had previously been assumed to be forever
inaccessible are, if these ideas are correct (and I remain
dubious), possibly on the verge of being measured in the
laboratory. Direct probes of gravity on scales smaller than one mm
are being developed that might probe for a change from the inverse
square law. Alternatively, if the Planck scale coincides with the
electroweak scale, then because we can probe the latter scale with
modern particle accelerators, perhaps we could directly use these
devices to probe extradimensional quantum gravitational phenomena.
But as interesting to physicists as these direct tests might be,
the poetic and philosophical implications of potentially large
extra dimensions lie elsewhere. Other branes could represent
possibly infinitely large alternate universes that could exist,
literally, less than a fingernail’s width away from our own. Each of
these universes could have laws of physics that might be
dramatically different from our own as well as a dramatically
different life history. And so, even if possible extra dimensions
continue to elude the able probes of direct laboratory experiments,
it could be that observations associated with the origin and
evolution of our entire universe may unlock the door to their
discovery.

Evidence for the existence or absence of extra
dimensions is likely to come ultimately not from an attempt to
understand the dynamics of objects within our universe, but rather
from an attempt to understand the dynamics of our universe itself
and to address the ultimate questions that have beset science since
it first emerged from the fog of history: How did the universe
begin? How will it end?

And it is here, as I earlier suggested, that
string theory, too, must ultimately face the music. If it is really
ever to provide an explanation of anything we see, much less
everything we see, it must address the fundamental nature of that
which we cannot see but which we know is there. It must explain the
energy of nothing.

Wherever you go, there you
are.

—The Adventures of Buckaroo
Banzai across the Eighth Dimension

W
hat could be more
romantic than the notion that extra dimensions might not be truly
hidden, but that objects from our universe might cross over into
this new realm? And since physics is a two-way street, with that
possibility comes a more exciting or perhaps terrifying one: What
if material or information from these extra dimensions can “leak”
into our own world? What if, ultimately, the source of our own
existence lies across that invisible boundary?

As we have seen, these questions have been the
fodder for speculation and belief for almost four centuries, since
sixteenth-century theologians first speculated that spirits and
angels emerge from the extra-dimensional universe. But now they
have reemerged in a new scientific context that might actually be
testable.

For a literary mind, the science fiction
possibilities of these concepts are endless, and Buckaroo Banzai’s
adventures are merely one particularly wacky manifestation. So,
too, for physicists and their graduate students, long starved of
new calculations that might be performed and even tested, the
possibility of large extra dimensions and the existence of other
branes than our own have provided countless new opportunities for
exploration and creative expression. These have become popularly
known as “Braneworld” scenarios, which sounds like a science fiction
movie title as much as anything ever did. Even Stephen Hawking has
gotten into the act with a recent popular lecture entitled “Brane
New World.”

In some sense it is appropriate that this
research area does sound like science fiction, because most of it
probably is. What is too often underappreciated about science is
that almost all of the ideas it proposes turn out to be wrong. If
they weren’t, the line between science and science fiction would be
much less firm. But the “present” can perhaps be defined as that time
when we teeter on the edge of understanding, and where the line
between speculative science and science fiction is most easily
blurred. And that is precisely where we now are in this narrative
of our ongoing love affair with extra dimensions. This is not to
suggest, however, that all ideas are equally attractive. Over the
past five years, hundreds, if not thousands, of scientific papers
have been written considering cosmological possibilities that might
be associated with Braneworld scenarios. One cannot do justice to
all of them, but the greatest justice I could probably do to many
of them is to not mention them here. Nevertheless, it is undeniable
that the mere fact that we might live on a three-brane in a
possibly infinite or large but compactified extradimensional space
dramatically has broadened the scope of cosmological investigation.
For example: What may have caused our three spatial dimensions to
have become potentially so much larger than the other extra
dimensions, and could the latter’s dynamic evolution have an impact
upon the cosmological evolution of our visible universe? What about
the possible existence of other nearby branes? In the earliest
moments of our big bang expansion, when the scale of our presently
observable universe was as small or smaller than the present size
of any compactified extra dimension, how could the presence of
significant other dimensions have affected both the origin and
evolution of our universe? And, how might our brane evolve
dynamically within the bulk space today, or, equivalently, how
might the changing nature of gravity on small or large scales in
extradimensional Braneworld scenarios have an impact upon current
measurements in observational cosmology?

The first question has been around in one form
or another since Kaluza and Klein first wrote down their ideas
involving compact extra dimensions, and, as I have argued earlier,
it is fair to say that no very good answer has yet been provided.
If one compactifies extra dimensions into some small radii,
r
, then the size of these radii leaves an
imprint on the remaining large dimensions via the existence of new
fields in nature, called moduli fields. String theory is replete with
such moduli fields. One can explore the dynamics of these fields and
it turns out that they tend to want to relax to a zero value,
which, in the higher dimensional picture, corresponds to the radii
of the extra dimensions going to infinity. To stop this runaway
expansion of dimensions, one generally has to introduce ad hoc
mechanisms, which is one of the reasons that the Randall-Sundrum
warped-extra-dimensional scenario, with its infinitely large extra
dimensions, was proposed. Nevertheless, there have been suggestions
that somehow the expansion of our three dimensions might arise at a
cost to the extra dimensions, with our dimensions expanding, while
the others perhaps contract. While this notion has some aesthetic
appeal, no otherwise attractive mechanism has been proposed to
generate a workable model. The next question, regarding the
possible existence of other branes, and their potential effects on
our own, is more intriguing. One particularly inventive proposal in
this regard actually explored the possibility that these “extra”
branes might actually
be
our own.

Shortly after the first Arkani-Hamed and
colleagues (ADD) proposal for large extra dimensions, these
authors, along with several others, proposed that our brane might
actually be folded over on itself many times, with different sheets
located less than a millimeter away in the extra compact dimension.
Since electromagnetic radiation and all nongravitational fields
propagate only along our brane and not out into this extra
dimension, these other regions would be invisible to us as long as
the “folds” in our brane occurred at distances along our brane so
far away that light has not yet had sufficient time since the big
bang to travel across such distances. Thus, the only effect of
these extra sheets would be their gravitational effects on us,
since gravity can cross into the bulk between them. But since these
extra sheets are really part of our brane, the laws of physics on
them are identical to our own. Thus, otherwise invisible gas,
stars, and galaxies could exist superimposed “on top” of our space.
The authors of papers on this topic have suggested that these
invisible objects might somehow comprise the dark matter that we
infer to dominate the mass of our galaxies, for example.

While this might be plausible in a science
fiction universe, it will not pass muster in the real universe. The
question of why these invisible stars and galaxies should tend to
cluster along with our own but why the material in them should
nevertheless spread out in halos around visible galaxies, was
unanswered. Indeed, there are a host of other issues that must be
addressed, including what mechanism might fold our brane and keep
it folded.

The problems that beset this idea are typical
of many Braneworld scenarios for cosmology. The freedom allowed by
extra dimensions introduces lots of exotic possibilities, but
almost every one of them involves a set of new cosmological
problems that must be dealt with in order to agree with
observations. Most important of all, though, is the fact that there
are often very plausible non-Braneworld approaches that address
many of the same cosmological issues these new scenarios propose to
deal with. For example, elementary particle physics now offers many
realistic candidates for dark matter along with natural mechanisms
to explain how it might have survived the earliest moments of the
hot big bang so that it might come to dominate the mass of the
universe today. Morever, particle physics provides very elegant
mechanisms for generating the density perturbations in the very
early universe that might ultimately collapse to form galaxies of
visible and dark matter. It is not clear that the additional
intellectual overhead associated with branes and extra dimensions
is needed to explain anything that we might otherwise explain
without it.

Another example involves an idea that has
become central to modern cosmology, inflation. Recall that in 1980
the physicist Alan Guth proposed that phase transitions in the
early universe could lead to periods of rapid early expansion. What
he also showed is that such periods would resolve two otherwise
completely inexplicable but central features of our universe,
including its remarkable isotropy (i.e., uniformity) on large
scales and the fact that the universe does not appear to be curved
on large scales. Moreover, it was subsequently demonstrated that
quantum mechanical processes during inflation could generate density
fluctuations that could in principle later gravitationally collapse
to produce the observed distribution of galaxies in the universe.
Recently the observation of small temperature fluctuations in the
cosmic microwave background radiation appears to be completely
consistent with this scenario. While such consistency cannot prove
inflation actually happened in the early universe, it is strongly
suggestive. Nevertheless, in spite of the beauty of the idea of
inflation, no particle physics models have been developed that
provide compelling or even particularly attractive mechanisms that
might underlie it. One might wonder therefore whether, in this
case, Braneworlds might come to the rescue. Within a year after
Arkani-Hamed and colleagues’ article, Gia Dvali and his
collaborator Henry Tye recognized that as two branes approach each
other, the residual moduli field in our dimension that results from
their separation in the extra dimension strongly resembles the kind
of field that previously had been proposed, ad hoc, to result in an
inflationary phase in the early universe. Furthermore, depending
upon the net energy associated with empty space on each of the
branes, there would be forces of either attraction or of repulsion
between the branes that might produce a period of inflation that
could in principle gently end as the two branes approached or
diverged from each other. While this picture has the advantage of
allowing an inflationary phase without the need to introduce
additional elementary particles and fields in the early universe, it
is not without its own weaknesses. The brane energies have to be
carefully adjusted for the scenario to work. More than this, it is
very difficult in these scenarios, once brane interaction energies
are converted into the matter and radiation necessary to produce
the early hot universe that was the precursor of the universe we
now observe, to stop most of the produced energy from instead being
transferred to invisible gravitational modes that would be radiated
off into the bulk and not on our brane.

Another imaginative tack has been to use
Braneworlds to almost completely avoid the outstanding issues
associated with inflationary universe models. Paul Steinhardt at
Princeton and Neil Turok at Cambridge have recently proposed using
a Braneworld scenario to allow a return to the “cyclic universe”
models that were in vogue before the success of the current big
bang picture. They have proposed a model called the ekpyrotic
universe. In the ekpyrotic universe the current period of
accelerated expansion observed in our space is related to the
separation of our brane and another one embedded in some higher
dimensions. Ultimately, however, these two branes will stop moving
apart and will begin to draw closer together. When this happens,
our universe will undergo a collapse and reheat again in a reverse
of the current big bang expansion. These two branes will eventually
cross through each other, producing a burst of energy that will
generate another big bang expansion that might proceed again for
billions of years as the two branes once again separate.
Ultimately, as the interaction energy between the branes begins to
dominate, our brane will once again experience an exponential
expansion just before the attraction between the branes once again
causes them to stop separating and repeat the whole process. The
interesting aspect of this model, and the part that has a certain
science fiction charm, is the fact that the period of inflationary
expansion that ultimately causes the universe to look flatter and
smoother happens near the end of each big bang expansion phase
instead of at the beginning. Thus, the reason our universe looks
isotropic is that in the cycle that preceded ours, before all
stars, galaxies, and civilizations in that expanding universe were
subsequently destroyed in a big crunch preceding our own big bang,
astronomers in that doomed universe would have measured their
universe to be undergoing an accelerated expansion, just as we are
measuring today.

As aesthetically pleasing as such an
oscillating universe with no beginning and no end might be,
however, in order for it to be viable one must ensure that the
isotropic, relatively uniform universe that supposedly results
during the final accelerating expansion in one phase can survive the
subsequent collapse and collision of the two branes to produce
isotropic conditions for the next big bang. It is not at all clear
that this is possible. In particular, one must make certain that
the two colliding branes are precisely aligned as they collide in
order for this picture to be viable. Of greater concern, perhaps,
is that if one asks what the natural period is for this oscillating
universe to go through each cycle, the timeframe is of the order of
the Planck time, about 10–43 seconds! In order to produce universes
that expand for at least ten billion years, the parameters of these
models must therefore be very carefully fine-tuned.

By now I hope you get the general flavor of the
dilemma. Braneworlds provide lots of new possibilities for
cosmology and the early universe, but nothing yet to write home
about, or at least, it seems to me, nothing that yet seems much
more attractive than the theories we already have. But there
remains hope, in the form of the one inexplicable, crazy facet of
modern cosmology that so far has resisted all efforts to even begin
to understand it: dark energy. The fact that empty space appears to
carry an energy that is large enough to dominate the expansion of
the universe today, yet is 120 orders of magnitude smaller than
what one would expect on the basis of conventional ideas associated
with the quantum physics of four dimensions, literally begs for
some out-of-this-world ideas to explain its existence.