Is
String Theory Even Wrong?
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For
nearly 18 years now, most advanced mathematical work in theoretical particle
physics has centered on something known as string theory. This theory is
built on the idea that elementary particles are not point-like objects but
are the vibration modes of one-dimensional "string-like" entities.
This formulation hopes to do away with certain lingering problems in
fundamental particle physics and to offer the possibility of soon explaining all physical phenomena everything
from neutrinos to black holes with a single theory. Fifteen years ago Edward Witten of the Institute for Advanced Study made the
widely quoted claim that "string theory is a part of 21st-century
physics that fell by chance into the 20th century," so perhaps it is now time to
begin judging the success or failure of this new way of thinking about
particle physics.
The
strongest scientific argument in favor of string theory is that it appears to
contain a theory of gravity embedded within it and thus may provide a
solution to the thorny problem of reconciling Einstein's general relativity
with quantum mechanics and the rest of particle physics. There are, however,
two fundamental problems, which are hard to get around. First,
string theory predicts that the world has 10 space-time dimensions, in
serious disagreement with all the evidence of one's senses. Matching string
theory with reality requires that one postulate six unobserved spatial
dimensions of very small size wrapped up in one way or another. All the
predictions of the theory depend on how you do this, but there are an infinite
number of possible choices, and no one has any idea how to determine which is
correct. The
second concern is that even the part of string theory that is understood is
internally inconsistent. This aspect of the theory relies on a series
expansion, an infinite number of terms that one is supposed to sum together
to get a result. Whereas each of the terms in the series is probably finite,
their sum is almost certainly infinite. String theorists actually consider
this inconsistency to be a virtue, because otherwise they would have an
infinite number of consistent theories of gravity on their hands (one for
each way of wrapping up six dimensions), with no principle for choosing among
them. The "M" Word These
two problems have been around since the earliest work on string theory along
with the hope that they would somehow cancel each other out. Perhaps some
larger theory exists to which string theory is just an approximate solution
obtained by series expansion, and this larger theory will explain what's going
on with the six dimensions we can't see. The latest version of this vision
goes under the name of "M-theory," where the "M" is said
variously to stand for "Membrane," "Matrix,"
"Mother," "Meta," "Magic" or
"Mystery" although "Mythical" may be more appropriate,
given that nearly eight years of work on this idea have yet to lead to even a
good conjecture about what M-theory might be. The
reigning Standard Model of particle physics, which string theory attempts to
encompass, involves at its core certain geometrical concepts, namely the Dirac operator and gauge fields, which are among the
deepest and most powerful ideas in modern mathematics. In string theory, the Dirac operator and gauge fields are not fundamental: They
are artifacts of taking a low-energy limit. String theorists ask
mathematicians to believe in the existence of some wonderful new sort of
geometry that will eventually provide an explanation for M-theory. But
without a serious proposal for the underlying new geometry, this argument is
unconvincing. The
experimental situation is similarly bleak. It is best described by Wolfgang Pauli's famous phrase, "It's not even wrong."
String theory not only makes no predictions about physical phenomena at
experimentally accessible energies, it makes no precise predictions
whatsoever. Even if someone were to figure out tomorrow how to build an
accelerator capable of reaching the astronomically high energies at which
particles are no longer supposed to appear as points, string theorists would
be able to do no better than give qualitative guesses about what such a
machine might show. At the moment string theory cannot be falsified by any
conceivable experimental result.
There
is, however, one physical prediction that string theory does make: the value
of a quantity called the cosmological constant (a measure of the energy of
the vacuum). Recent observations of distant supernovae indicate that this
quantity is very small but not zero. A simple argument in string theory
indicates that the cosmological constant should be at least around 55 orders
of magnitude larger than the observed value. This is perhaps the most
incorrect experimental prediction ever made by any physical theory that
anyone has taken seriously. With
such a dramatic lack of experimental support, string theorists often attempt
to make an aesthetic argument, professing that the theory is strikingly
"elegant" or "beautiful." Because there is no well-defined
theory to judge, it's hard to know what to make of these assertions, and one
is reminded of another quotation from Pauli.
Annoyed by Werner Heisenberg's claims that, though lacking in some specifics,
he had a wonderful unified theory (he didn't), Pauli
sent letters to some of his physicist friends each containing a blank
rectangle and the text, "This is to show the world that I can paint like
Titian. Only technical details are missing." Because no one knows what
"M-theory" is, its beauty is that of Pauli's
painting. Even if a consistent M-theory can be found, it may very well turn
out to be something of great complexity and ugliness. What
exactly can be said for
string theory? In recent years, something called the Maldacena
conjecture has led to some success in using string theory as a tool in
understanding certain quantum field theories that don't include gravity.
Mathematically, string theory has covered a lot of ground over the past 18
years and has led to many impressive new results. The concept of "mirror
symmetry" has been very fruitful in algebraic geometry, and conformal
field theory has opened up a new, fascinating and very deep area of
mathematics. Unfortunately for physics, these mathematically interesting
parts of string theory do little to connect it with the real world. String
theory has, however, been spectacularly successful on one front public
relations. For example, it's been the subject of the best-selling popular
science book of the past couple years: The
Elegant Universe by Brian Greene, one of my colleagues at It's
easy enough to see why the general public is taken with string theory, but
one wonders why so many particle theorists are committed to working on it.
Sheldon Glashow, a string-theory skeptic and
Nobel-laureate physicist at Harvard, describes string theory as "the
only game in town." Why this is so perhaps has something to do with the
sociology of physics. During
much of the 20th century there were times when theoretical particle physics
was conducted quite successfully in a somewhat faddish manner. That is, there
was often only one game in town. Experimentalists regularly discovered new
and unexpected phenomena, each time leading to a flurry of theoretical
activity (and sometimes to Nobel prizes). This pattern ended in the mid-'70s
with the overwhelming experimental confirmation and widespread acceptance of
the Standard Model of particle physics. Since then, particle physics has been
a victim of its own success, with theoreticians looking for the next fad to
pursue and finding it in string theory. One
reason that only one new theory has blossomed is that graduate students, post-docs
and untenured junior faculty interested in speculative areas of mathematical
physics beyond the Standard Model are under tremendous pressures. For them,
the idea of starting to work on an untested new idea that may very well fail
looks a lot like a quick route to professional suicide. So some people who do
not believe in string theory work on it anyway. They may be intimidated by
the fact that certain leading string theorists are undeniably geniuses.
Another motivation is the natural desire to maintain a job, get grants, go to
conferences and generally have an intellectual community in which to
participate. Hence, few stray very far from the main line of inquiry. Affirmative Actions What
can be done to inject more diversity of thought into this great quest of
theoretical physics? Even granting that string theory is an idea that
deserves to be developed, how can people be encouraged to come up with
promising alternatives? I would argue that a good first step would be for
string theorists to acknowledge publicly the problems and cease their
tireless efforts to sell this questionable theory to secondary school
teachers, science reporters and program officers. The
development of competing approaches will require senior string theorists to
consider working on less popular ideas and begin encouraging their graduate
students and post-docs to do the same. Instead of trying to hire people
working on the latest string-theory fad, theory groups and funding agencies
could try to identify young mathematical physicists who are exploring
completely different avenues. (Pushing 45, I no longer qualify.) Finding ways
to support such people over the long term would give them a much-needed
chance to make progress. Although
I am skeptical of science writer John Horgan's
pessimistic notion that physics is reaching an end, the past 15 years of
research in particle theory make depressingly clear one form such an end
could take: a perpetual, well-promoted but never-successful investigation of
a theory that has no connection with the physical world. If only physicists
have the will to abandon a failed project and start looking for some new
ideas, this sad fate can be avoided. |
