BOOK REVIEW
All Strung Out?
Joseph Polchinski
The Trouble with Physics: The Rise of String Theory, the Fall of
a Science, and What Comes Next. Lee Smolin. xxiv + 392 pp.
Houghton Mifflin, 2006. $26.
Not Even Wrong: The Failure of String Theory and the Search for
Unity in Physical Law. Peter Woit. xi + 291 pp. Basic
Books, 2006. $26.96.
The 1970s were an exhilarating time in particle physics. After
decades of effort, theoretical physicists had come to understand the
weak and strong nuclear forces and had combined them with the
electromagnetic force in the so-called Standard Model. Fresh from
this success, they turned to the problem of finding a unified
theory, a single principle that would account for all three of these
forces and the properties of the various subatomic particles. Some
investigators even sought to unify gravity with the other three
forces and to resolve the problems that arise when gravity is
combined with quantum theory.
The Standard Model is a quantum field theory, in which particles
behave as mathematical points, but a small group of theorists
explored the possibility that under enough magnification, particles
would prove to be oscillating loops or strands of
"string." Although this seemingly odd idea attracted
little attention at first, by 1984 it had become apparent that this
approach was able to solve some key problems that otherwise seemed
insurmountable. Rather suddenly, the attention of many of those
working on unification shifted to string theory, and there it has
stayed since.
Today, after more than 20 years of concentrated effort, what has
been accomplished? What has string theory predicted? Lee Smolin, in
The Trouble with Physics, and Peter Woit, in Not
Even Wrong, argue that string theory has largely failed.
What is worse, they contend, too many theorists continue to focus
their efforts on this idea, monopolizing valuable scientific
resources that should be shifted in more promising directions.
Smolin presents the rise and fall of string theory as a morality
play. He accurately captures the excitement that theorists felt at
the discovery of this unexpected and powerful new idea. But this
story, however grippingly told, is more a work of drama than of
history. Even the turning point, the first crack in the facade, is
based on a myth: Smolin claims that string theorists had predicted
that the energy of the vacuum—something often called dark
energy—could not be positive and that the surprising 1998
discovery of the accelerating expansion of the universe (which
implies the existence of positive dark energy) caused a hasty
retreat. There was, in fact, no such prediction. Although his book
is for the most part thoroughly referenced, Smolin cites no source
on this point. He quotes Edward Witten, but Witten made his comments
in a very different context—and three years after the
discovery of accelerating expansion. Indeed, the quotation is doubly
taken out of context, because at the same meeting at which Witten
spoke, his former student Eva Silverstein gave a solution to the
problem about which he was so pessimistic. This episode also goes to
show that, contrary to another myth, young string theorists are not
so intimidated by their elders.
As Smolin charts the fall of string theory, he presents further
misconceptions. For example, he asserts that a certain key idea of
string theory—something called Maldacena duality, the
conjectured equivalence between a string theory defined on one space
and a quantum field theory defined on the boundary of that
space—makes no precise mathematical statements. It certainly
does. These statements have been verified by a variety of methods,
including computer simulations. He also asserts that the evidence
supports only a weak form of this conjecture, without quantum
mechanics. In fact, Juan Maldacena's theory is fully quantum mechanical.
A crucial principle, according to Smolin, is background
independence—roughly speaking, consistency with Einstein's
insight that the shape of spacetime is dynamical—and Smolin
repeatedly criticizes string theory for not having this property.
Here he is mistaking an aspect of the mathematical language being
used for one of the physics being described. New physical theories
are often discovered using a mathematical language that is not the
most suitable for them. This mismatch is not surprising, because one
is trying to express something that is different from anything in
previous experience. For example, Einstein originally formulated
special relativity in language that now seems clumsy, and it was
mathematician Hermann Minkowski's introduction of four-vectors and
spacetime that made further progress possible.
In string theory it has always been clear that the physics is
background-independent even if the language being used is not, and
the search for more suitable language continues. Indeed, as Smolin
belatedly notes, Maldacena duality provides a solution to this
problem, one that is unexpected and powerful. That solution is still
not complete: One must pin down spacetime on the edges, but in the
middle it is free to twist and even tear as it will, and black holes
can form and then decay. This need to constrain the edges is
connected with a property known as the holographic principle, which
appears to be an essential feature of quantum gravity. Extending
this principle to spaces with the edges free will require a major
new insight. It is possible that the solution to this problem
already exists among the alternative approaches that Smolin favors.
But his principal candidate (loop quantum gravity) is, as yet, much
more background-dependent than the current form of string theory.
Much of Smolin's criticism of string theory deals with its lack of
mathematical rigor. But physics is not mathematics. Physicists work
by calculation, physical reasoning, modeling and cross-checking more
than by proof, and what they can understand is generally much
greater than what can be rigorously demonstrated. For example,
quantum field theory, which underlies the Standard Model and much
else in physics, is notoriously difficult to put on a rigorous
foundation. Indeed, much of the interest that mathematicians have in
physics, and in string theory in particular, arises not from its
rigor but from the opposite: Physicists by their methods can obtain
new results whose mathematical underpinning is not obvious. String
theorists have a strong sense that they are discovering something,
not inventing it. The process is sometimes messy, with unexpected
twists and turns (not least the strings themselves!), and rigor is
not the main tool.
Woit covers some of the same ground, although his interests are more
centered on particle physics and on the connection with mathematics
than on the nature of spacetime. His telling is more direct, but it
is rather stuffed with detail and jargon, and his criticisms of
string theory are simpler and somewhat repetitious.
A major point for Woit is that no one knows exactly what string
theory is, because it is specified only through an infinite
mathematical series whose sum is ill-defined. This assertion is
partly true: With new physical theories there is often a long period
between the first insight and the final mathematical form. For
quantum field theory, the state of affairs that Woit describes
lasted for half a century. In string theory the situation is much
better than he suggests, because for 10 years we have had tools
(dualities) that in many cases give us a precise definition of the
theory. These have led in turn to many new applications of string
theory, such as to the quantum mechanics of black holes, and there
are hints to a more complete understanding.
But what about the lack of predictions? This is the key question,
for Woit, for Smolin and for string theory. Why have the last 20
years been a time of unusually little contact between theory and
experiment? The problem is partly on the experimental side: The
Standard Model works too well. It takes great time, ingenuity and
resources to try to look beyond it, and often what is found is still
the Standard Model.
A second challenge was set forth by Max Planck more than a century
ago. When one combines the fundamental constants of special
relativity, general relativity and quantum mechanics, one finds that
they determine a distance scale at which these theories appear to
come together:the Planck length of 10^{-33} centimeters. To
put this number in perspective, one would have to magnify an atom a
billion times to make it the size of a coffee cup, andone would have
to magnify the Planck length a trillion trillion times to make it
the size of an atom. If we could probe the Planck length directly,
we would be able to see the strings and extra dimensions, or
whatever else is lurking there, and be done with it. But we'll never
be able to do that. So instead, we must look for indirect evidence.
And, as was the case with atomic theory, one cannot predict how long
such a leap will take.
Smolin addresses the problem of the Planck length ("It is a
lie," he says). Indeed, Planck's calculation applies to a
worst-case scenario. String theorists have identified at least half
a dozen ways that new physics might arise at accessible scales, and
Smolin points to another in the theories that he favors, but for
now, these are just possibilities. As far as experiment yet shows,
Planck's challenge stands.
Or it may be that string theory has already made a connection with
observation—one of immense significance. Positive dark energy
is the greatest experimental discovery of the past 30 years
regarding the basic laws of physics. Its existence came as a
surprise to almost everyone in physics and astronomy, except for a
small number, including, in particular, Steven Weinberg.
In the 1980s, Weinberg had been trying to solve the long-standing
puzzle of why the density of dark energy is not actually much
greater. He argued that if the underlying theory had multiple vacua
describing an enormous number of potential universes, it would not
only explain why the density of dark energy is not high, but would
also predict that it is not zero. Weinberg's reasoning was contrary
to all conventional wisdom, but remarkably his prediction was borne
out by observation a decade later.
The connection between string theory and dark energy is still a
subject of much controversy, and it may be that Weinberg got the
right answer for the wrong reason. However, it may well turn out
that he got the right answer for the right reason. If so, it will be
one of the great insights in the history of physics, and the
multivacuumproperty of string theory, seemingly one of its main
challenges, will, in fact, be just what nature requires.
A second unexpected connection comes from studies carried out using
the Relativistic Heavy Ion Collider, a particle accelerator at
Brookhaven National Laboratory. This machine smashes together nuclei
at high energy to produce a hot, strongly interacting plasma.
Physicists have found that some of the properties of this plasma are
better modeled (via duality) as a tiny black hole in a space with
extra dimensions than as the expected clump of elementary particles
in the usual four dimensions of spacetime. The prediction here is,
again, not a sharp one, and string-theory skeptics could take the
point of view that it is just a mathematical spinoff. However, one
of the repeated lessons of physics is unity—nature uses a
small number of principles in diverse ways. And so the quantum
gravity that is being used to understand the experiments at
Brookhaven is likely to be the same one that operates everywhere
else in the universe.
A further development over the past few years, as our understanding
has deepened, has been the extensive study of the experimental
consequences of specific kinds of string vacua. Many of these make
distinctive predictions for particle physics and cosmology. Most or
all of these may well be falsified by experiment (which is, after
all, the fate of most new models). The conclusive test of string
theory may still be far off. In the meantime, science proceeds
through many small steps.
A central question for both Smolin and Woit is why so many very good
scientists continue to work on an idea that has allegedly failed so
badly. Both books offer explanations in terms of the sociology of
science and the psychology of scientists. These forces do exist, and
it is worth reflecting on their possible negative effects, but such
influences are not as strong as these authors posit. String
theorists include mavericks and contrarians, strong-willed
individuals who have made major contributions—not just in
string theory but in other parts of physics as well. The borders
between string theory and other areas of physics are not closed, and
theorists would emigrate if they did not believe that they were
already stomping around the most promising territory.
In fact, the flow of intellectual talent has been in the other
direction: In recent years, leading scientists in particle
phenomenology, inflationary cosmology and other fields have found
ideas generated by string theory to be useful in their disciplines,
just as mathematicians have long done. Many have begun to work with
string theorists and have in turn contributed their perspectives to
the subject and expanded the view of how string theory relates to nature.
This convergence on an unproven idea is remarkable. Again, it is
worth taking a step back and reflecting on whether the net result is
the best way to move science forward, and in particular whether
young scientists are sufficiently encouraged to think about the big
questions of science in new ways. These are important
issues—and not simple ones. However, much of what Smolin and
Woit attribute to sociology is really an issue of scientific judgment.
In the end, these books fail to capture much of the spirit and logic
of string theory. For that, either Brian Greene's The Elegant
Universe (first published in 1999)or Leonard Susskind's The
Cosmic Landscape (2005) does a better job.
The interested reader might also look to particle phenomenologist
Lisa Randall's Warped Passages (2005) and
cosmologistAlexander Vilenkin's Many Worlds in One (2006)
for accounts by two scientists from other fields who have seen a
growing closeness between string theory and their ideas about how
the cosmos is put together.