Hiding in the Mirror (28 page)

The key problem associated with trying to
describe dark energy in terms of fundamental particle physics is
that the effect of dark energy is primarily felt at large scales.
On the scale of the solar system and smaller, for example, the
gravitational forces associated with matter (i.e., the sun and
planets) overwhelm the minuscule repulsive effect induced by a
small cosmological constant. But on the scale of clusters of
galaxies and larger, the repulsive force due to this energy of
empty space dominates. The problem is actually even more serious
than this. The focus of our efforts to understand the fundamental
laws of nature has involved examining phenomena at ever-smaller
scales. When we first began to explore the nature of atoms we
discovered the laws of quantum mechanics. Similarly, as we explored
the nature of the nucleus, we discovered the weak and strong
forces. If all of these get unified in some grand unified model, we
expect the new physics might appear on scales much smaller than
this. Even those models that place a string theory scale near the
electroweak scale predict that if new physics appears, it will be
on scales smaller than those that we have currently been able to
measure.

Indeed, we now realize precisely how it is
possible that new physics can emerge on ever-smaller scales without
impacting upon the wellunderstood explanations of how the universe
operates on larger scales. Quantum mechanics, for example, is
largely irrelevant when considering the motion of baseballs or
cannonballs, which is why Newton didn’t have to know about it when
he developed his classical laws of motion. But the problem with
trying to understand dark energy from a fundamental physics
perspective is that it appears to be a large-scale phenomenon,
relevant to the expansion of the entire universe. The actual amount
of energy associated with empty space in the room in which you are
reading this is incredibly small—so small, in fact, that it is hard
to imagine how any revision of the laws of physics that might
accommodate it would not also dramatically affect physics on all
higher-energy scales. This, in a nutshell, is the fundamental
problem that has bedeviled all attempts, including string theory
attempts, to resolve the cosmological constant problem on
fundamental grounds.

In this regard, a particularly creative and
novel use of the Braneworld idea was proposed by Gia Dvali—whose
name has already come up several times as one of the most active
and inventive young theorists in this area today. Dvali, with his
NYU colleagues Gabadadze and Porrati, examined in a series of
papers a possibility that was in some sense diametrically opposed
to the extra-dimensional scenarios that had been considered
previously.

They imagined an infinite-volume
extra-dimensional space in which gravity could propagate. They then
argued that if one were confined—as we presumably are—to a
four-dimensional brane, then under certain circumstances, for
relatively short (on a cosmic scale) distances and times, one might
actually measure the gravitational interaction between objects on
our brane to be that calculated by Newton and Einstein. However,
over long times and distances the gravitational fields could “leak”
into the extra dimension. The net effect would be to change the
nature of gravity at large distances and times, not small ones.

Not being ones to hedge their bets, Dvali and
colleagues pointed out that there were two different ways that this
kind of mechanism might address both the nature of the dark energy
that is apparently driving the observed accelerated expansion of
the universe, and the broader and more fundamental cosmological
constant problem. It would do this by getting rid of both of
them.

As far as the nature of dark energy is
concerned, one of the interesting implications of modifying gravity
at large scales is that one might modify Einstein’s equations in a
way that would produce accelerated expansion on sufficiently large
scales, even without any dark energy as a source. This is, of
course, very attractive, because dark energy isn’t.

Nevertheless, even if one were to get rid of
the need for dark energy, one still has to explain why its value
isn’t gigantic. Specifically, we would need to solve the
cosmological constant problem by explaining why quantum mechanics
doesn’t produce a vacuum energy that results in even greater
acceleration than we would observe today from these additional new
gravitational shenanigans at large distance. Here again, Dvali and
colleagues provided at least the germ of an interesting idea. If,
on the largest scales, gravity is really five-dimensional, and not
fourdimensional, then the relevant vacuum energy to which gravity
would be sensitive is the full vacuum energy in five dimensions. It
just might be possible to imagine symmetries, like supersymmetry,
that could be exact in five or higher dimensions, while broken in
our four-dimensional world. Such symmetries might imply that the
higher-dimensional vacuum energy was zero. Thus, even if there
existed a nonzero cosmological constant on our brane, it could be
that gravity on large scales would not “feel” this cosmological
constant. These ideas are fascinating, in part because they are so
heretical and counterintuitive. Unfortunately, however, they are
also quite provisional. There are a lot of “mights” in the
preceding paragraph, and no real model including all of these
features has been developed and explored. What is worse is that
this possibility may in fact have already been ruled out by
observations.

As Dvali and his colleagues have shown, the
presence of such infinitevolume extra dimensions is not completely
hidden. Because of the nature of general relativity, it turns out
that, in their models, the effect of five dimensions changes gravity
slightly on all scales, so there must be small corrections to the
Newtonian gravitational attraction between all objects, no matter
how small or close. However, very high-precision experiments that
have been conducted on our solar system would strongly constrain
the magnitude of any such possible corrections to the force between
the sun and the inner planets, for example. If one is an optimist,
one might hope that as these measurements improve, deviations will
be seen that imply that perhaps gravity on large scales really
is
leaking away. In any case, for the
moment the upper bounds on what is allowed come very close to the
level one might expect from such extra-dimensional effects, but
work remains to be done to verify this in detail. We are thus left
at present with the somewhat uncomfortable situation that
Braneworlds, for all of their hope and hype, haven’t yet
demonstrated what it takes to be compelling. Their major virtue at
this point in time is that some of their consequences are at least
in principle testable, via either cosmological observations or the
next generation of particle accelerators. Which brings us back at
long last to string theory, M-theory, and the Theory of Everything.
Ultimately we should recall that Braneworld ideas seem at best poor
approximations to reality, if string theory is correct. What the
notion of large or possibly infinite extra dimensions has done is
borrow some of the facets of string theory while ignoring the bulk
of the theory (forgive the pun), about which, as I have explained,
we currently only have the vaguest notions. It seems to me to be a
very big long shot that an apparently ad hoc choice of what to keep
and what to ignore will capture the essential physics of our
universe. To truly understand the origin and evolution of our
universe from its earliest moments, if M-theory really corresponds
to reality, we will almost certainly be required to understand that
theory better than we currently do. And as I have now stressed
several times, one of the most significant areas where string theory
has had no success thus far (amidst a long list), and where it may
ultimately rise or fall, is the attempt to understand the energy of
empty space. String theory never explained why the vacuum energy
should be precisely zero when we thought that was the case in the
1980s and 1990s, nor did it predict that it might be nonzero but
unbelievably tiny, as it would seem to be in order to explain
current cosmological observations. Braneworld proposals
notwithstanding, it is most likely that to understand why empty
space appears to gravitate the way it does will require a complete
theory that merges quantum mechanics and gravity. At present
M-theory/string theory is the only game in town, even if no one yet
knows what the rules are.

So, even as the nature of M-theory seems to be
increasingly elusive and the likelihood that a higher-dimensional
theory will clearly resolve other fundamental questions in particle
physics is becoming murky, some string theorists have now turned
their attention to this fundamental puzzle in the hopes that
cosmology might provide a beacon that has otherwise been lacking
that can illuminate these dark and hidden worlds. This has resulted
in yet another fascinating sociological metamorphosis of the
theory, with warts becoming beauty marks. The presence of dark
energy may have completely changed the landscape of modern
cosmology, but string theory was not to be outdone: It has produced
its own landscape.

Recall that one of the apparent vagaries of
string/M-theory is the fact that even if the underlying symmetry
structure and number of dimensions associated with the theory were
to become explicitly known, the fundamental nature of physics in
our three-dimensional space might nevertheless remain undetermined.
This is because in order to reduce the theory from ten or eleven
dimensions to four, one generally must compactify the extra
dimensions, or at least explain how they might be otherwise
unobservable in our space at the present time. For now, there is no
guiding mathematical principle that tells us which compactifications
are reasonable. The number of different corresponding possible
ground states of our universe corresponds roughly to the number of
inequivalent possible compactifications. With ten dimensions to
start with, and a host of Calabi-Yau possible compactification
manifolds, for example, it has been estimated that there may be
more than 10100 different possible inequivalent ground state
configurations that might describe viable four-dimensional
universes, and that might result from a single underlying M-theory.
When this was first realized, it looked like bad news for string
theory, because it meant that any hope of predictability might go
down the drain. Without any way to choose between different ground
states, each of which would represent a four-dimensional universe
that might have a different configuration of forces and underlying
symmetries and a completely different spectrum of elementary
particles, the long-sought uniqueness of string theory seemed
ephemeral at best. For some time this final step, compactification,
was frankly not emphasized in discussions heralding the beauty of
string theory.

But with an exceedingly small vacuum energy
apparently present in our universe, suddenly the terms have
changed. The plethora of possible ground states of the theory, and
the nonuniqueness of string-theoretic predictions, have become a
virtue, offering hope where none had appeared before. The source of
this sudden optimism stems from a calculation first performed by
physicist Steven Weinberg with collaborators Paul Shapiro and Hugo
Martel at the University of Texas, which in turn has its basis in
one of the most slippery ideas in twenty-first-century physics,
which is somewhat pompously called the “anthropic principle.”

The anthropic principle is deceivingly simple
to state and equally difficult to fully come to terms with. It is
based on the suggestion that some, or perhaps all, of the
fundamental constants in nature describing elementary particle
interactions are what they are because if they took on different
values, we wouldn’t be here to measure them.

When one first hears this, it sounds like either
a truism or a religious claim. But it is far from either. It does
not imply, as some fundamentalists have tried to argue, that
physics is on the verge of proving that the universe was created
specifically for humankind to live in. Rather, at its best, it
suggests that it is at least possible that, if the underlying
theory of the universe does not uniquely predict the nature of
particles and fields that can exist, then there may be no
fundamental dynamical reason why the universe we live in is the way
it is.

I should say at the outset that this idea goes
completely against the grain of the entire history of physics over
the past four hundred years. Generations of physicists have
believed that their job was to explain why the universe has to
behave the way it does, rather than why most possible universes
would behave differently. Nevertheless, in the back of the minds of
those physicists who have tried to derive new fundamental laws over
the years, the nagging question asked in public by Einstein early
in the past century has continued to burn a hole. As he put it,
using a religious metaphor: “Did God have any choice in the
creation of the Universe?” By posing this question, Einstein in
effect wondered whether there might be only one consistent set of
laws that could result in a workable universe. Could it be that, if
the electron was not 1/2000 of the mass of the proton, or if the
electromagnetic force was not forty orders of magnitude stronger
than gravity, the logical consistency of whatever underlying theory
governs the physical workings of the universe would fall to pieces?
Or, could one imagine a plethora of possible universes, each of
which had different values for these quantities, and each of which
could still form a logical and consistent whole? If the former is
true, a Theory of Everything has teeth. If the latter is true, then
physics is ultimately, as John Preskill at Caltech once put it to
me, an “environmental science,” with even the fundamental laws of
nature being determined by possible “environmental” accidents.