Theos-Talk Archives (August 2003 Message tt00147)

American Scientist, March-April 2002 v90 i2 p110(3) 
Is string theory even wrong? (Macroscope). Peter Woit.

Full Text: COPYRIGHT 2002 Sigma Xi, The Scientific
Research Society 

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 Columbia. The National Science Foundation is
funding a series of NOVA programs based on his
accessible and inspiring book. What is more, the
Institute for Theoretical Physics at the University of
California, Santa Barbara, organized last spring a
conference to train high school teachers in string
theory so that they can teach it to their students.
And The New York Times and other popular publications
regularly run articles on the latest developments in
string theory. 

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, postdocs 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 postdocs 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. 

Peter Woit, a faculty member in the Department of
Mathematics of Columbia University, received a Ph.D.
in theoretical physics from Princeton University in
1985. He held postdoctoral appointments at the State
University of New York at Stony Brook and at the
Mathematical Sciences Research Institute in Berkeley,
California, before moving to Columbia in 1989. 


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