Hiding in the Mirror (30 page)

I have debated this very point on stage twice
with Brian Greene, who has worked as hard as anyone to popularize
and celebrate string theory. Brian earnestly and successfully
communicates the excitement of the theory in a way that can inspire
lay people. Brian is an honest popularizer and prefaces his remarks
about string theory with qualifications about its present
speculative and unproven state. However, he is so convincing and
enthusiastic that I have argued with him that when such things as
animations of strings within elementary particles are presented,
even if the intent is merely illustrative, it tends to give the
impression that string theory is a better defined construct than it
currently is, and also suggests it gives definite predictions about
the properties of observed elementary particles in four dimensions.
This is of course a subjective issue, and I know Brian disagrees
with me about this. Ultimately, from my perspective, this
enthusiasm is unwarranted at the present time, given what might be
described as the current impotence of the theory.

In order to dramatize my own concerns about the
dangers of conveying enthusiasm as truth, I have claimed that
string theory is in some sense the least successful great idea in
twentieth-century physics, a statement that
The
New York Times
kindly quoted out of context. At a recent event
celebrating Einstein, I pointed out that it is somewhat incongruous
to, on one hand, portray as tragic the past thirty years of
Einstein’s life, during which he worked on his own on an
unsuccessful unified field theory, while at the same time celebrate
at scientific meetings and in the popular media perhaps three
thousand man-years of full-time intellectual activity by a brigade
of some of the most talented young theoretical minds around the
world on a proposed unified theory that has thus far been largely
fruitless in its predictions, and has yet to be properly
understood. I believe both extreme viewpoints are inappropriate.
Einstein’s efforts were no more tragic than the recent string
program has been an unqualified success. Both are part of the search
for underlying order in the natural world that proceeds by fits and
starts, and is full of far more blind alleys than awakenings.

And I want to reiterate once again, perhaps
even more strongly, that these efforts, even if they do not produce
the results we wish, will not have been wasted. Ed Witten wrote me
a frank letter after I asked him to read a draft of this book. He
described how, when he was a student in the 1970s, he was obsessed
with trying to understand, on the basis of simple analytical
physical calculations, exactly why quarks are confined together. He
gave up, because he thought the problem was too hard. Now, almost
thirty years later, he is working on the problem again, this time
using the tools of string theory, and he feels he is making
progress. As he put it: “Being able to develop these models in the
last decade, fifteen years after giving up on quark confinement as
too hard, has been a lot of fun.” Moreover, after arguing that the
many developments I have discussed are evidence that our
understanding of string theory is reaching a deeper level, he
nevertheless emphasized that this most recent work, on using string
methods to attack quark confinement and not quantum gravity, as
originally intended, has “maybe been the most fun for me.”

One never knows where insights will come from,
or where they may lead. The pleasure of research is discovering the
unexpected. Ed’s poignant remark underscores that ultimately the
driving force behind all human inquiry is the satisfaction of the
quest itself. We may or may not be hardwired to long for hidden
realities, but we are most certainly hardwired to enjoy solving
puzzles, especially when their resolution is far from what one may
initially have expected.

I would also be less than candid if I did not
reveal that there is other, more personal evidence I now have that
the string effort has already borne some fruit. After
The New York Times
published my supposed statement
on the failures of string theory, I received a package in the mail
from California. Upon opening it, I found a fruit basket from John
Schwarz with a note, which read: “Dear Lawrence: Now maybe you
won’t feel it’s all been so fruitless.”

This finally brings me to David Gross, who has
played the most interesting sociological role in the story I have
told. You will recall that David was a student at Berkeley in the
1960s, the era of bootstrap models and dual string models as
applied to strongly interacting elementary particles. He thus
received his scientific grounding in theories that turned out to be
footnotes in scientific history. But it was ultimately his own work
on asymptotic freedom, for which he has shared the Nobel Prize,
that turned them into footnotes.

In another poetic example of the ironies of
scientific progress, over a decade later David became a key part of
the new string revolution, which reinstated the very ideas he had
earlier killed, but this time in a new context. His work on
heterotic strings, and the possibility of explaining all the
phenomenology of elementary particle physics in four dimensions via
an underlying theory in ten
and
twenty-six
dimensions, helped to create the fervor that motivated Witten’s
statement about the incursion of twentyfirst-century physics into
the twentieth century. But, as Ed Witten has admitted, these ideas
ultimately just produced a “rough draft” that has yet to ever go
beyond this stage. One might think that having witnessed the demise
of a similar rough draft in the 1970s that Gross might temper his
statements about the ultimate truth of the new string theory. But
it is an interesting facet of the human condition that
revolutionaries sometimes replicate certain features of the regimes
they set out to overthrow. In this case the former young rebel has
become something of a defender of the faith.

In many forums David has argued forcefully—and,
of course, brilliantly, because his is a powerful intellect—that
the theory is simply too beautiful
not
to
be true. As such, every new result tends to merely reinforce its
truth, even without the luxury of experiment. As I have described,
this attitude has been adopted by many of the younger researchers
in this field, who are, of course, strongly influenced by their
senior mentors, as well as the mathematical appeal of the
subject.

I do not mean to cast aspersion on David’s
scientific work, which has been impeccable and important. And as I
said, it is perfectly reasonable to expect those theorists who have
devoted decades to exploring a theory to be driven by an
expectation of its inherent validity. The problem, however, is that
this viewpoint strikes some, including me, as sounding like
religion more than science. At other times in this century, science
may have been able to more easily tolerate such confusion. Perhaps
I am oversensitive on this subject, but I have spent much of the
past several years fighting attacks on science, from the classroom
to the White House. The aim of both these sets of challenges has
been to replace the hard-won results of the scientific process with
ideological dogma. In the former case, where individuals have been
attempting to impugn a well-tested scientific theory that is the
foundation of all of modern biology, I have often been told that
science itself is merely another kind of religion. I believe that
nothing should be further from the truth, and anything that
confuses this issue is regressive. Still, the convergence of truth
and beauty, at least as we behold it, is a notion that is in some
sense central to almost everything I have discussed in this book.
Indeed, I began with a discussion of the mysterious fact that
nature and beautiful mathematics seem inextricably united. Recall
Bertrand Russell’s description of mathematics as possessing “not
only truth, but supreme beauty.” With that in mind it is, I
believe, generally appropriate to give the last word to a
mathematician whose work played a central role in the earliest
developments that I have described here. I refer to Hermann Weyl,
the brilliant mathematical physicist whose results originally
inspired Kaluza to ponder extra dimensions, and who first exposed
the fundamental symmetry of nature that we now call gauge
invariance, which is at the heart of the description of all the
known forces in nature, including gravity. Weyl was a student of
Hilbert, one of the fathers of higher-dimensional geometry, and, as
you may also recall, a competitor of Einstein’s on the road to
developing general relativity. And Weyl ended his career at the
Institute for Advanced Study at Princeton along with Einstein. So
it is, in fact, particularly appropriate to turn to Weyl for
enlightenment as we reach the end of our own journey through the
looking glass. Upon reflecting upon his work, which clearly touched
not only on mathematics but on the physical world, Weyl made a
profoundly insightful confession that appeared in his own obituary,
written by the physicist Freeman Dyson in 1956. Nothing I can think
of better captures the dilemma exemplified by our ongoing, and
remarkably timely, love affair with extra dimensions. Referring to
his research, Weyl admitted:

My work always tried to unite the true with the
beautiful, but when I had to choose one or the other, I usually
chose the beautiful. So it is that mathematicians, poets, writers,
and artists almost always choose beauty over truth. Scientists,
alas, do not have this luxury, and can only hope that we do not
have to make a choice.

Each of my books has been a tremendous learning
experience. I depend greatly both on previous authors with their
accumulated wisdom and on generous colleagues from a variety of
areas who help steer me in the right direction as I begin to
grapple with sometimes totally new subjects. Thinking about the
cultural and social legacy associated with the notion of extra
dimensions, I am enormously grateful to my Case colleague Henry
Adams, professor of art history and former curator at the Cleveland
Museum of Art. He and a student of his provided me with a wonderful
bibliography of twentieth-century artists whose work related to the
notion of a fourth dimension.

One of the most important books that I
initially turned to was Linda Dalrymple Henderson’s
The Fourth Dimension and Non-Euclidean Geometry in
Modern Art
, a wonderfully broad and complex
discussion of the notion of a fourth dimension in modern art. I owe
a great debt to her scholarship, which pointed me in the direction
of numerous important sources, and which has inevitably strongly
influenced my own thinking. I also owe thanks to several individuals
in the science fiction community, notably Charles Brown and several
other of my colleagues on the board of the Science Fiction
Experience in Seattle, who helped direct me to the appropriate
literature, in particular to the fiction and nonfiction work of Rudy
Rucker on the fourth dimension.

I want to thank the librarians at the Case
Western Reserve University for providing me with great assistance,
including a room to work and store books in, as I tried to devour
the appropriate literature and write in a quiet place away from my
office.

I thank numerous colleagues for discussions and
illuminations related to the physics and historical ideas discussed
here. I learned a great deal from the informative introduction in
the book
Modern Kaluza Klein Theory,
by Tom
Appelquist, Alan Chodos, and Peter Freund, as well as the
comprehensive two-volume opus
Superstring
Theory
by Michael Green, John Schwarz, and Edward Witten, and
the more recent two-volume work
String
Theory
by Joe Polchinski, as well as, of course, the numerous
papers in the literature so easily accessible thanks to the physics
Web archive created by Paul Ginsparg. I owe a personal great debt
to my Case colleague and friend Cyrus Taylor, who spent many hours
introducing me to the intricacies of string theory, and who
directed me to appropriate places in the literature. Gia Dvali
helped me first tackle large extra dimensions, and continues to
provoke my imagination. My friend and colleague Frank Wilczek has
shared many of his physics and philosophical insights with me over
the years, and I appreciate his willingness to provide feedback on
some of the issues I raised in the final chapters. Lastly, I want to
thank all of my colleagues who have looked at this manuscript and
provided comments and feedback. In particular, I want to thank
Glenn Starkman for general suggestions, and John Schwarz and Edward
Witten for carefully reading the sections on string theory and
making comments.

Finally, I want to thank once again my wife
Kate and daughter Lilli for putting up with and supporting me
through yet another book project, and for being joyful reminders
that physics is just one part of a fascinating world.

Alpha rays:
Rays made
up of the nuclei of helium, containing two neutrons and two
protons, which are produced in the radioactive decays of various
heavy nuclei.

Angular momentum:
A
twisting force imparts angular momentum to objects, causing them to
spin. Angular momentum is calculated as the product of the mass of
an object times its rotational speed.

Anomaly:
Due to quantum
mechanical effects, a symmetry of nature that appears in a
classical theory (such as electromagnetism) can be violated at the
quantum level. When this happens the symmetry is said to be
anomalous, and the quantum mechanical contribution that violates
the symmetry is said to be an anomaly. Several “anomalous
symmetries” are known to exist in nature. However, it is very
important that quantum mechanical effects do not spoil the gauge
and general covariance symmetries that are at the heart of the four
known forces in nature. Making sure this does not happen has played
a key role in efforts to develop string theories as candidate
theories for the natural world.
Antiparticles:
The laws of quantum mechanics and
special relativity together imply that every elementary particle in
nature must have an antiparticle, with equal mass and opposite
electric charge. Many antiparticles have been created in the
laboratory, and are used regularly in high-energy particle
accelerators that explore the nature of matter and energy at
fundamental scales. When particles and antiparticles collide, they
can annihilate, producing pure radiation. Some neutral particles
can be their own antiparticles.
Asymptotic
freedom:
The remarkable property of the strong interaction,
discovered in 1974, that the force between quarks becomes stronger
as you pull the quarks apart. This is the opposite behavior from
electromagnetism, which gets weaker as elementary charges are moved
far apart from each other. Asymptotic freedom is presumably related
to the fact that no observable isolated quarks exist in nature (a
phenomenon called confinement).
Beta rays:
Rays made up of electrons, which are produced in the radioactive
decays of various elementary particles and nuclei.

Black body radiation:
When a perfectly black solid, like the heating element on a stove,
is heated up, it emits a continuous set of colors of radiation,
changing from red hot to blue hot to white hot, for example. This
distribution of radiation uniquely determines the temperature of
the object, and was explained using the laws of quantum mechanics
early in the twentieth century.

Bootstrap model:
An
idea that achieved prominence in the 1960s in response to the
growing number of strongly interacting elementary particles, which
suggested that no elementary particles were truly fundamental, but
rather that all particles could be made up of other elementary
particles. It proposed instead that what
was
fundamental was the mathematical relationship
between particles that governed their interactions with each other.
Bootstrap models eventually led to the development of string
theories that attempted to describe the interactions of strongly
interacting elementary particles.

Bosons:
Elementary
particles in which the spin angular momentum is quantized, having a
value equal to an integer multiple of some fundamental quantum of
angular momentum.

Chirality:
Certain
objects, like our two hands, or the spiral structures that make up
DNA can be said to be left handed or right handed, i.e., mirror
images of each other. This property is called chirality. Elementary
particles with spin angular momentum can be chiral, in that they
can appear to be spinning in either a clockwise or a
counterclockwise direction about their spin axis. One type of
particle is called left handed, and the other right handed.
Theories that distinguish between left-and right-handed particles
are called chiral theories. The weak interaction is one such
example as, for example, only left-handed neutrinos appear to sense
the weak interaction. (As a result we do not even know if
right-handed neutrinos exist in nature.)

Cloud chamber:
A device
developed in the early part of the twentieth century that produces
observable tracks when charged elementary particles, such as the
particles in cosmic rays, traverse the chamber. When these
particles more through the chamber the gas vapor surrounding the
particles with which they collide condenses, producing a visible
vapor trail. Different particles produce qualitatively different
tracks.

Compactification:
In
theories with extra dimensions beyond the three space and one time
dimension of our experience, one has to explain why the other
dimensions are not observed. One solution involves compactification,
in which the extra dimensions are curled up into “balls” that are
so small that no experiment yet performed could detect their
existence. The process by which one goes from a higher-dimensional
theory to an effective four-dimensional theory is called
compactification, and trying to understand how this might occur is
one of the major challenges of string theory, and other
higher-dimensional theories.

Conformal invariance:
A
mathematical symmetry that encompasses not only the general
covariance that is at the basis of general relativity but extends
it to include so-called scale transformations. If the world were
conformally invariant, then the world would appear unchanged if I
doubled the size of all objects, their masses, etc. This is clearly
not the case, so conformal invariance is not a property of the real
world as we measure it. However, it is an underlying property of
string theories, and clearly one of the challengesof having string
theory touch base with the world that we observe is to find
mechanisms by which this symmetry is broken in our world.
Connection tensor:
A mathematical quantity that
encodes the geometric nature of space. The connection tensor in
particular explains how the length and orientation of a standard
ruler might be measured to change as it moved between nearby points
in a curved space. The connection tensor therefore encodes
information about the curvature of space.
Cosmic microwave background:
The afterglow of the
big bang, this radiation is a remnant from the earliest era of the
expansion, when the temperature was so high that matter and
radiation were in thermal equilibrium. Once the temperature had
cooled sufficiently (to about three thousand degrees above absolute
zero), protons and electrons began to be able to combine to form
neutral atoms, which decoupled from the radiation so that the
universe became transparent. The remnant radiation cooled as the
universe expanded, and is now at a temperature of about three
degrees above absolute zero.
Cosmic rays:
Energetic elementary particles of many different types that bombard
the earth regularly from space. They originate from locations as
close as our own sun, and as far away as the centers of distant
galaxies.
Dark Energy:
When we add up the
total amount of mass in the visible universe, and compare it to the
total energy needed to result in the flat universe (see
Flat universe
) that we appear to live in, there is a
factor of three too little mass to account for the flatness of space
on large scales. At the same time, the observed expansion of the
universe appears to be accelerating, which could only be the case
if empty space possessed energy (see
Vac-
uum energy
). The amount of energy needed to
result in the observed acceleration turns out to be precisely that
required to also account for a flat universe. We currently
understand very little about this “dark energy,” which resides in
empty space, and do not know if it is vacuum energy, or some other
kind of yet more exotic form of energy.

D-branes:
Multidimensional surfaces (generalizations of two-dimensional
membranes—hence the name) on which “open strings” that is, strings
that are not closed loops, and that propagate in higher dimensions,
can end. The “D” in D-branes does not refer to the dimensionality
of the brane, but rather to the specific boundary conditions that
are imposed at the end of the string as it merges with the brane.
D-branes are now understood to be very important objects within
string theory, though they were not known in the earliest
formulations of the theory.

Density fluctuations:
Observed stars, galaxies, planets (and ultimately people) initially
arose as very small inhomogeneities in the distribution of matter
and radiation in the early universe, which collapsed due to their
internal gravitational attraction. Regions where there was a very
small excess of matter, for example, compared to the background
value, would expand slightly more slowly than the background,
eventually becoming so much more dense than the background that
they decoupled from the expansion of the universe, and started to
collapse. We believe this is how all large-scale structures now
observable in the universe first formed. The question then becomes,
what caused these initial density fluctuations in the early
universe? We currently have reason to believe that they formed due
to the quantum mechanical effects at very early times, as a result
of inflation.

Electron:
An elementary
particle with negative electric charge that comprises the outer
parts of all atoms. Neutral atoms contain an equal number of
electrons and protons, with the latter existing within a dense
nucleus at the center of the atoms. As far as we know, the electron
is absolutely stable.

Equivalence principle:
The principle that all objects fall at the same rate in a
gravitational field. Einstein argued that this is equivalent to the
notion that in a local free-falling frame, the effects of gravity
will be unobservable. This principle formed a fundamental pillar of
his general theory of relativity, because it allowed him to present
a completely geometric description of gravity in which its effects
could be ascribed to the curvature of space.

Ether
(also
Aether
)
:
The hypothetical
substance that was believed for centuries to fill space and in which
it was believed that light waves propagated. In 1887 the physicist
Albert A. Michelson and his colleague, chemist Edward Morley,
demonstrated experimentally that the ether, as a medium in which
light traveled, did not exist. Later, in 1905, Einstein
demonstrated that the existence of such an ether was in fact
inconsistent with the laws of physics.

Event horizon:
A region
surrounding a black hole, from which classically nothing, even
light, can escape. As a result, once objects cross the event
horizon observers outside of the black hole lose all information as
to their future behavior.

False vacuum:
If we
describe the vacuum state as the lowest energy state in which a
system can exist (such as a region of empty space devoid of matter
or energy), a false vacuum occurs when the lowest energy state in
certain circumstances turns out not to remain the lowest energy
state as those circumstance change. Possible examples include when
the value of some external field, or the temperature of the system,
changes. The system may exist in this false vacuum state for a long
time, but it will eventually decay, by the rules of quantum
mechanics, into the new lower energy state, releasing energy in the
process.
Fermions:
Elementary particles in
which the spin angular momentum is quantized, having a value equal
to a half-integer multiple of some fundamental quantum of angular
momentum.
Flat universe:
General relativity
implies that space can curve in the presence of mass and energy. On
the largest scales, if light travels in straight lines, this
implies that the universe is spatially flat. A spatially flat
universe is infinite in extent, and, if dominated by matter, will
continue to expand forever, with the expansion rate slowing
asymptotically, but never quite falling to zero. We appear to live
in a flat universe, as far as we can tell, although not one
dominated by matter.

Gamma rays:
The most
energetic electromagnetic rays. The photons making up gamma rays
can have energies as great as or greater than the energy associated
with the rest mass of elementary particles such as electrons and
protons.

General covariance:
A
mathematical notion at the heart of Einstein’s general relativity
theory that implies that the laws of physics are independent of any
specific coordinate frame in which we choose to measure them. One of
the implications of this is that for an observer in free fall in a
gravitational field, the effects of gravity will appear to
disappear. Another is that an observer accelerating upward in an
elevator in empty space will experience a force pushing him toward
the floor that will be completely indistinguishable from the force
of gravity that he would experience if he was at rest in a
gravitational field.

Grand unification:
The
theoretical notion that the three nongravitational forces in
nature—the weak, electromagnetic, and strong forces—can actually be
unified in a single framework, and moreover, that at a very small
scale, perhaps fifteen orders of magnitude smaller than we can
measure today, all of these forces will appear to have the same
strength.

Grassmann variable:
A
mathematical quantity that has some properties of a normal number,
but nevertheless has some vastly different properties. For example,
when a Grassman number is multiplied by itself, it produces zero.
Two different Grassman variables,
A
and
B
, when multiplied together in one order,
say
AB
, equal the negative value when
multiplied in the other order, so that
AB
=
−
BA
. It turns out that these properties
mimic the quantum mechanical properties that govern the behavior of
fermions.
Graviton:
When one combines
quantum mechanics and relativity, all forces are conveyed by the
exchange of elementary particles, like the photon, the fundamental
quantum of electromagnetism. We call the hypothetical particle that
conveys gravitation the graviton. Individual gravitons have not yet
been measured because of the weakness of gravity, although we have
no reason not to believe they exist.