Hiding in the Mirror (20 page)

It turned out, however, that by introducing
those weird Grassmann quantities into the picture, one could in
fact circumvent the famous Coleman-Mandula theorem and instead have
such a symmetry interchanging bosons and fermions in a single
physical description of the natural world. Moreover, such an
extended symmetry—or “supersymmetry,” as it became known—ultimately
seemed to be an essential part of theories of strings that
contained both fermions and bosons.

Now, interestingly enough, it wasn’t until the
1970s that anyone explored the idea of applying supersymmetry
beyond dual strings (i.e., twodimensional objects moving around in
ten or twenty-six dimensions) and to our good old four-dimensional
universe with elementary particles such as quarks and photons. In
1974, Julius Wess and Bruno Zumino wrote a pivotal paper in which
they extended the relation that had held on twodimensional strings
to our four-dimensional spacetime time consisting of fermions and
bosons.

The history of supersymmetry is a somewhat
convoluted one, primarily because it appeared in several different
places in the literature as a mathematical idea in search of a
physical application. Such ideas tend to lie dormant until
circumstances arise that cause physicists to latch onto them. Once
they do, there tends to be an explosion of activity, as theorists
smell new opportunities like sharks smell blood.

Recall that in 1974, following the discovery a
year earlier that QCD as the theory of the strong force, we
appeared to have had for the first time a full quantum mechanical
understanding of all the nongravitational forces in nature.
Prompted by this development, Sheldon Glashow and Howard Georgi
made the first proposal that same year to unify these forces in a
grand unified theory.

Glashow and Georgi had written down a simple
extension of the existing theories that not only appeared to unify
these three nongravitational forces using a simple mathematical
framework, but also nicely classified all of the known elementary
particles at the same time.

On the surface, it might seem like folly to try
and unify three forces whose intrinsic strengths are so different.
The electric force beween quarks is tens of thousands of times less
powerful than the strong force between quarks within a proton, for
example. However, the beauty of asymptotic freedom was that it
demonstrated that the strong force gets weaker as you measure it on
smaller scales. Perhaps on some very small scale the strengths of
all the forces might become similar.

Just such a calculation was first performed by
Georgi and Weinberg, along with physicist Helen Quinn; it
demonstrated that the quantum dynamics of the known forces was such
that the difference in their strengths should indeed diminish if
one examined nature on ever-smaller scales, with the strong force
becoming weaker and the electromagnetic force stronger, for
example. If one extrapolated to much smaller scales the known
behavior at scales one could measure in the laboratory and assumed
this behavior persisted without any fundamentally new physical
phenomena entering in to change the results along the way, then on
a scale approximately one million billion times smaller than the
size of the proton, the three known forces would have approximately
the same strength. What better signature of possible unification
could one expect?

Everything now pointed to a simple unification
of the strong, weak, and electromagnetic interactions, which, I
believe, Glashow dubbed “grand unification.” Moreover, this theory
was not merely a convenient form of taxonomy but actually made new
predictions. The boldest was that the basic building block of all
matter, the proton, might not be stable, but could decay within a
period of time that, while far longer than the current age of the
universe, might nevertheless be measurable. A host of huge
experiments was soon underway to attempt such a measurement. As
Glashow put it: “Diamonds are not forever!”

As I have already described, the theoretical
exuberance associated with the development of GUTs, following on
the flush of success in explaining the electroweak and strong
forces, was contagious. The response of the physics community
followed a standard trend. Strings were largely forgotten, except
by an earnest few, and there was a stampede to explore the
possibilities of a new Theory of “Almost” Everything. Suddenly
physicists were boldly extrapolating known physics onto scales of
energy, space, and time that had previously been unimaginable.
These theories promised not just to explain the known forces, but
also to answer longstanding puzzles such as how matter in the
universe originated and whether matter is absolutely stable.
Physicists were now seriously discussing questions associated with
the earliest moments of the big bang, and experimentalists were
building detectors to explore possible new phenomena on scales a
million billion times smaller than the size of a proton!

Of course, following the first flush of romantic
love invariably comes the recognition that the object of one’s
affections is not quite perfect. So it was with grand unification.
As I have indicated, one of its key predictions was that the proton
should not be absolutely stable, but should decay after a lifetime
of about 1030 years. This is comfortably older than the current age
of the universe (by a factor of about a hundred billion billion),
so we don’t have to sell our diamond rings for a loss quite yet.
However, long as it is, it was within the reach of larger
experiments, with tanks of thousands of tons of water containing
enough protons so that one might expect, given the laws of
probability, to find a few decaying each year. (With an average
lifetime of 1030 years, this means that if one assembles 1030
protons in one place, on average, one will decay each year.)

Unhappily, alas, while these beautiful
experiments have been launched, we have yet to witness the decay of
a single proton. This failure has ruled out the GUT of Glashow and
Georgi, although, as you can imagine, theorists have proposed other
possibilities that still make the cut. Another experimental problem
has arisen, however, for even the simplest GUTs. Since 1974 the
strength of the weak and strong forces has been measured with
greater precision. Taking account of the new, more precise values,
and examining theoretically what should happen as one probes on
ever smaller scales, one finds that the different strengths of the
three forces would not converge precisely together at a single
scale, as seemed possible within the earlier, less accurate
estimates. Does this mean that grand unification is ultimately
untenable? Not at all. For, even as many physicists at the time
suggested, making an assumption that no new physics might enter in
to change the scaling behavior of the fundamental forces as they
evolve over fifteen orders of magnitude in size, from the proton
size to the presumed scale of grand unification, was a remarkably
conservative supposition. To come up such a vast “desert,” as it
became known, and to encounter no new or interesting physics, would
at the very least defy a well-established historical tradition in
the field. But what could be the source of such new scaling
behavior? It turned out that another problem, this time a
theoretical one associated with the possible existence of grand
unification, pointed the way. The hierarchy problem, as it has
become known, can be simply stated: Why are the energy (and mass
and length) scales at which grand unification might occur, and the
scale of the masses of the known elementary particles, so
different? In another way of putting it, if grand unification indeed
occurs at a scale a million billion times smaller than the size of
the proton, why does nature choose to produce such a dramatic
difference in scales? Now, one perfectly good answer might simply
be the same answer that parents give their children when they keep
nagging them with the question, “Why?” The answer? “Because!”

Indeed, it could be just an accident of nature
that we would have to live with, except that within the framework
of the standard model of elementary particle physics, as it was
formulated in 1974, such an accident should not happen! For, it
turns out that when calculating the effects of virtual
particles—the same objects that allow such good predictions for
quantum electrodynamics, and also produce such nonsensical
predictions for the energy of empty space—such a hierarchy would be
unstable. By unstable I mean that one can show that the virtual
particles associated with the GUT can affect the measured value of
some elementary particle masses at the weak scale, just as virtual
particles in QED affect the magnitude of the spacing between energy
levels in hydrogen atoms in a way that can be both calculated and
measured. However, unlike the case in QED, where the corrections
are extremely small, it turns out that the effect of virtual
particles at a very high GUT-scale energy can be large enough so as
to actually cause the masses of all the known particles to be
raised up to this scale. The only way this can be avoided in
general within the standard model would be if some very careful
fine-tuning of parameters at the highenergy scale occurred, so that
various large numbers would cancel out each other to high
precision, leaving a remainder that might be fifteen to thirty
orders of magnitude smaller. There are no known mechanisms in
physics to make such cancellations occur in any natural way.
Indeed, this particular feature of the hierarchy problem is known
as a “naturalness” problem. Now, as I like to say, unnatural acts
probably don’t seem unnatural at the time to those engaged in them.
But naturalness in this sense has a well-defined meaning: It is
“unnatural” to have a huge hierarchy between the masses of everyday
particles and the mass scale associated with grand unification if
quantum mechanical corrections to the former due to the latter
might be large.

This problem has not been fully resolved, and
it continues to present a tremendous challenge to theorists as they
attempt to build models of reality. In fact, the vast difference in
scales between the proton size and the scale at which grand
unification might occur is itself dwarfed by another larger
hierarchy. The predicted GUT energy scale is, in fact, several
orders of magnitude smaller still than the energy scale where
quantum mechanical effects in gravity should become important, and
where, presumably the gravitational force might unify with the
other forces. This latter scale, as I have mentioned, is called the
Planck mass, and it is the ultimate bogeyman in physics. Once
again, we can ask the question: Why is the Planck energy scale so
vastly different than the scales of all the known elementary
particles?

A glimmer of hope regarding these conundrums
was elaborated by a number of authors, ultimately receiving widest
impact in 1981 in a paper by Edward Witten, who had just moved to
Princeton University on his way ultimately to the Institute for
Advanced Study in Princeton, where he is now one of the most highly
regarded and accomplished mathematical physicists and string
theorists in the world.

The hope appeared in the form of supersymmetry.
Following 1974 a growing number of physicists began to get
interested in the possible implications of space-time supersymmetry
in nature beyond its utility solely for dual string models.

In order to understand the reasons for this
interest, I should briefly present the key feature of supersymmetry
as a symmetry of space-time. By connecting bosons and fermions,
supersymmetry requires that for every boson in nature, there be a
fermionic partner of exactly the same mass, electric charge, and so
on.

However, in the world as we know it, this is
manifestly not the case!

No “superpartners,” as they are called, of
ordinary elementary particles have ever been seen. There is no
evidence for a bosonic version of the electron, or for a fermionic
version of the photon. Why on earth, then, would any physicist in
her right mind suggest that such a symmetry might be appropriate to
our understanding of nature? Well, an optimistic physicist, of whom
there have been many in recent years, would counter this argument
by insisting that it is not that we haven’t discovered all the
particles predicted by supersymmetry, but rather that we have
discovered precisely half of the particles! Isn’t that
progress?

This is not a completely facetious argument,
because it turns out there are many symmetries in nature that are
not manifest at first sight. For example, as I have already
described, the laws of electromagnetism, which govern much of what
we experience on a daily basis, do not distinguish between left and
right. Yet, when I look out the window I can clearly distinguish
the landscape to the left of me, where there happens to be a
mountain at the moment, from the landscape to the right of me,
where there doesn’t happen to be one.

This is an example of what physicists call
“spontaneous symmetry breaking,” but it could just as justifiably be
called an environmental accident. Namely, while an underlying law
of nature may possess some symmetry, like left–right symmetry, that
symmetry need not be manifest in the particular circumstances in
which we find ourselves, such as me sitting in my office.

This may sound almost trivial, but the
recognition that spontaneous symmetry breaking can occur in nature,
along with an investigation of the physical implications of this
possibility, have played a central role in many of the fundamental
developments in a host of areas of physics over the past four
decades. They certainly influenced the formulation of the
electroweak theory by Glashow, Salam, and Weinberg. In that theory
a fundamental symmetry relates certain facets of the weak force,
and the electric force—namely, the two different forces turn out to
be based in part on different mathematical realizations of a single
theory. However, due to an accident of our circumstances—which, as
we shall see momentarily, one can quantitatively and precisely
probe—it turns out that environmental factors cause the weak force
to end up looking much weaker than the electromagnetic force. This
happens because it turns out that due to differing interactions
with a background field that is postulated to exist today throughout
space, one of the particles that conveys the weak force (as its
cousin, the massless photon, conveys the electromagnetic force)
ends up behaving differently than the photon. In particular, the
interactions of this “weak photon” with the background field make
the “weak photon” behave like a very massive particle, almost a
hundred times as massive as the proton. This particle acts like a
marble being dragged in the mud, while a photon is like a marble
rolling on a smooth surface: The two marbles may be intrinsically
identical, but they behave very differently due to the accidental
circumstances in which they find themselves. As a result, since the
weak force is thus conveyed by an apparently massive particle,
while the massless photon conveys the electromagnetic force, from
our perspective the two forces look quite different. This
phenomenon is quite reminiscent of a much more familiar one on
earth. We distinguish “north” from all the other directions because
of a background magnetic field that makes our compasses point in
that direction. However, if the earth had no magnetic field, there
would be no such fundamental way to distinguish north from
east.