BRIAN
GREENE
The Elegant Universe
Superstrings, Hidden Dimensions, and the
Quest for the Ultimate Theory
An excerpt
______________________
Calling
it a cover-up would be far too dramatic. But for more than half
a century — even in the midst of some of the greatest scientific
achievements in history — physicists have been quietly aware
of a dark cloud looming on a distant horizon. The problem is this:
There are two foundational pillars upon which modern physics rests.
One is Albert Einstein's general relativity, which provides a
theoretical framework for understanding the universe on the largest
of scales: stars, galaxies, clusters of galaxies, and beyond to
the immense expanse of the universe itself. The other is quantum
mechanics, which provides a theoretical framework for understanding
the universe on the smallest of scales: molecules, atoms, and
all the way down to subatomic particles like electrons and quarks.
Through years of research, physicists have experimentally confirmed
to almost unimaginable accuracy virtually all predictions made
by each of these theories. But these same theoretical tools inexorably
lead to another disturbing conclusion: As they are currently formulated,
general relativity and quantum mechanics cannot both be right.
The two theories underlying the tremendous progress of physics
during the last hundred years — progress that has explained
the expansion of the heavens and the fundamental structure of
matter — are mutually incompatible.
If you have not heard previously about this ferocious antagonism
you may be wondering why. The answer is not hard to come by. In
all but the most extreme situations, physicists study things that
are either small and light (like atoms and their constituents)
or things that are huge and heavy (like stars and galaxies), but
not both. This means that they need use only quantum mechanics
or only general relativity and can, with a furtive glance, shrug
off the barking admonition of the other. For fifty years this
approach has not been quite as blissful as ignorance, but it has
been pretty close.
But
the universe can be extreme. In the central depths of a black
hole an enormous mass is crushed to a minuscule size. At the moment
of the big bang the whole of the universe erupted from a microscopic
nugget whose size makes a grain of sand look colossal. These are
realms that are tiny and yet incredibly massive, therefore requiring
that both quantum mechanics and general relativity simultaneously
be brought to bear. For reasons that will become increasingly
clear as we proceed, the equations of general relativity and quantum
mechanics, when combined, begin to shake, rattle, and gush with
steam like a red-lined automobile. Put less figuratively, well-posed
physical questions elicit nonsensical answers from the unhappy
amalgam of these two theories. Even if you are willing to keep
the deep interior of a black hole and the beginning of the universe
shrouded in mystery, you can't help feeling that the hostility
between quantum mechanics and general relativity cries out for
a deeper level of understanding. Can it really be that the universe
at its most fundamental level is divided, requiring one set of
laws when things are large and a different, incompatible set when
things are small?
Superstring
theory, a young upstart compared with the venerable edifices of
quantum mechanics and general relativity, answers with a resounding
no. Intense research over the past decade by physicists and mathematicians
around the world has revealed that this new approach to describing
matter at its most fundamental level resolves the tension between
general relativity and quantum mechanics. In fact, superstring
theory shows more: Within this new framework, general relativity
and quantum mechanics require one another for the theory to make
sense. According to superstring theory, the marriage of the laws
of the large and the small is not only happy but inevitable.
That's
part of the good news. But superstring theory — string theory,
for short — takes this union one giant step further. For
three decades, Einstein sought a unified theory of physics, one
that would interweave all of nature's forces and material constituents
within a single theoretical tapestry. He failed. Now, at the dawn
of the new millennium, proponents of string theory claim that
the threads of this elusive unified tapestry finally have been
revealed. String theory has the potential to show that all of
the wondrous happenings in the universe — from the frantic
dance of subatomic quarks to the stately waltz of orbiting binary
stars, from the primordial fireball of the big bang to the majestic
swirl of heavenly galaxies — are reflections of one grand
physical principle, one master equation.
Because
these features of string theory require that we drastically change
our understanding of space, time, and matter, they will take some
time to get used to, to sink in at a comfortable level. But as
shall become clear, when seen in its proper context, string theory
emerges as a dramatic yet natural outgrowth of the revolutionary
discoveries of physics during the past hundred years. In fact,
we shall see that the conflict between general relativity and
quantum mechanics is actually not the first, but the third in
a sequence of pivotal conflicts encountered during the past century,
each of whose resolution has resulted in a stunning revision of
our understanding of the universe.
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The
Three Conflicts
The
first conflict, recognized as far back as the late 1800s, concerns
puzzling properties of the motion of light. Briefly put, according
to Isaac Newton's laws of motion, if you run fast enough you can
catch up with a departing beam of light, whereas according to
James Clerk Maxwell's laws of electromagnetism, you can't. As
we will discuss in Chapter 2, Einstein resolved this conflict
through his theory of special relativity, and in so doing completely
overturned our understanding of space and time. According to special
relativity, no longer can space and time be thought of as universal
concepts set in stone, experienced identically by everyone. Rather,
space and time emerged from Einstein's reworking as malleable
constructs whose form and appearance depend on one's state of
motion.
The
development of special relativity immediately set the stage for
the second conflict. One conclusion of Einstein's work is that
no object — in fact, no influence or disturbance of any sort
— can travel faster than the speed of light. But, as we shall
discuss in Chapter 3, Newton's experimentally successful and intuitively
pleasing universal theory of gravitation involves influences that
are transmitted over vast distances of space instantaneously.
It was Einstein, again, who stepped in and resolved the conflict
by offering a new conception of gravity with his 1915 general
theory of relativity. Just as special relativity overturned previous
conceptions of space and time, so too did general relativity.
Not only are space and time influenced by one's state of motion,
but they can warp and curve in response to the presence of matter
or energy. Such distortions to the fabric of space and time, as
we shall see, transmit the force of gravity from one place to
another. Space and time, therefore, can no longer to be thought
of as an inert backdrop on which the events of the universe play
themselves out; rather, through special and then general relativity,
they are intimate players in the events themselves.
Once
again the pattern repeated itself: The discovery of general relativity,
while resolving one conflict, led to another. Over the course
of the three decades beginning in 1900, physicists developed quantum
mechanics (discussed in Chapter 4) in response to a number of
glaring problems that arose when nineteenth-century conceptions
of physics were applied to the microscopic world. And as mentioned
above, the third and deepest conflict arises from the incompatibility
between quantum mechanics and general relativity. As we will see
in Chapter 5, the gently curving geometrical form of space emerging
from general relativity is at loggerheads with the frantic, roiling,
microscopic behavior of the universe implied by quantum mechanics.
As it was not until the mid-1980s that string theory offered a
resolution, this conflict is rightly called the central problem
of modern physics. Moreover, building on special and general relativity,
string theory requires its own severe revamping of our conceptions
of space and time. For example, most of us take for granted that
our universe has three spatial dimensions. But this is not so
according to string theory, which claims that our universe has
many more dimensions than meet the eye — dimensions that
are tightly curled into the folded fabric of the cosmos. So central
are these remarkable insights into the nature of space and time
that we shall use them as a guiding theme in all that follows.
String theory, in a real sense, is the story of space and time
since Einstein.
To
appreciate what string theory actually is, we need to take a step
back and briefly describe what we have learned during the last
century about the microscopic structure of the universe.
The Universe at Its Smallest: What We Know about Matter
The
ancient Greeks surmised that the stuff of the universe was made
up of tiny "uncuttable" ingredients that they called
atoms. Just as the enormous number of words in an alphabetic language
is built up from the wealth of combinations of a small number
of letters, they guessed that the vast range of material objects
might also result from combinations of a small number of distinct,
elementary building blocks. It was a prescient guess. More than
2,000 years later we still believe it to be true, although the
identity of the most fundamental units has gone through numerous
revisions. In the nineteenth century scientists showed that many
familiar substances such as oxygen and carbon had a smallest recognizable
constituent; following in the tradition laid down by the Greeks,
they called them atoms. The name stuck, but history has shown
it to be a misnomer, since atoms surely are "cuttable."
By the early 1930s the collective works of J. J. Thomson, Ernest
Rutherford, Niels Bohr, and James Chadwick had established the
solar system like atomic model with which most of us are familiar.
Far from being the most elementary material constituent, atoms
consist of a nucleus, containing protons and neutrons, that is
surrounded by a swarm of orbiting electrons.
For a while many physicists thought that protons, neutrons, and
electrons were the Greeks' "atoms." But in 1968 experimenters
at the Stanford Linear Accelerator Center, making use of the increased
capacity of technology to probe the microscopic depths of matter,
found that protons and neutrons are not fundamental, either. Instead
they showed that each consists of three smaller particles, called
quarks — a whimsical name taken from a passage in James Joyce's
Finnegan's Wake by the theoretical physicist Murray Gell-Mann,
who previously had surmised their existence. The experimenters
confirmed that quarks themselves come in two varieties, which
were named, a bit less creatively, up and down. A proton consists
of two up-quarks and a down-quark; a neutron consists of two down-quarks
and an up-quark.
Everything
you see in the terrestrial world and the heavens above appears
to be made from combinations of electrons, up-quarks, and down-quarks.
No experimental evidence indicates that any of these three particles
is built up from something smaller. But a great deal of evidence
indicates that the universe itself has additional particulate
ingredients. In the mid-1950s, Frederick Reines and Clyde Cowan
found conclusive experimental evidence for a fourth kind of fundamental
particle called a neutrino — a particle whose existence was
predicted in the early 1930s by Wolfgang Pauli. Neutrinos proved
very difficult to find because they are ghostly particles that
only rarely interact with other matter: an average-energy neutrino
can easily pass right through many trillion miles of lead without
the slightest effect on its motion. This should give you significant
relief, because right now as you read this, billions of neutrinos
ejected into space by the sun are passing through your body and
the earth as well, as part of their lonely journey through the
cosmos. In the late 1930s, another particle called a muon —
identical to an electron except that a muon is about 200 times
heavier — was discovered by physicists studying cosmic rays
(showers of particles that bombard earth from outer space). Because
there was nothing in the cosmic order, no unsolved puzzle, no
tailor-made niche, that necessitated the muon's existence, the
Nobel Prize-winning particle physicist Isidor Isaac Rabi greeted
the discovery of the muon with a less than enthusiastic "Who
ordered that?" Nevertheless, there it was. And more was to
follow.
Using
ever more powerful technology, physicists have continued to slam
bits of matter together with ever increasing energy, momentarily
recreating conditions unseen since the big bang. In the debris
they have searched for new fundamental ingredients to add to the
growing list of particles. Here is what they have found: four
more quarks — charm, strange, bottom, and top — and
another even heavier cousin of the electron, called a tau, as
well as two other particles with properties similar to the neutrino
(called the muon-neutrino and tau-neutrino to distinguish them
from the original neutrino, now called the electron-neutrino).
These particles are produced through high-energy collisions and
exist only ephemerally; they are not constituents of anything
we typically encounter. But even this is not quite the end of
the story. Each of these particles has an antiparticle partner
— a particle of identical mass but opposite in certain other
respects such as its electric charge (as well as its charges with
respect to other forces discussed below). For instance, the antiparticle
of an electron is called a positron — it has exactly the
same mass as an electron, but its electric charge is +1 whereas
the electric charge of the electron is -1. When in contact, matter
and antimatter can annihilate one another to produce pure energy
— that's why there is extremely little naturally occurring
antimatter in the world around us.
Physicists
have recognized a pattern among these particles, displayed in
Table 1.1. The matter particles neatly fall into three groups,
which are often called families. Each family contains two of the
quarks, an electron or one of its cousins, and one of the neutrino
species. The corresponding particle types across the three families
have identical properties except for their mass, which grows larger
in each successive family. The upshot is that physicists have
now probed the structure of matter to scales of about a billionth
of a billionth of a meter and shown that everything encountered
to date — whether it occurs naturally or is produced artificially
with giant atom-smashers — consists of some combination of
particles from these three families and their antimatter partners.
A
glance at Table 1.1 will no doubt leave you with an even stronger
sense of Rabi's bewilderment at the discovery of the muon. The
arrangement into families at least gives some semblance of order,
but innumerable "whys" leap to the fore. Why are there
so many fundamental particles, especially when it seems that the
great majority of things in the world around us need only electrons,
up-quarks, and down-quarks? Why are there three families? Why
not one family or four families or any other number? Why do the
particles have a seemingly random spread of masses — why,
for instance, does the tau weigh about 3,520 times as much as
an electron? Why does the top quark weigh about 40,200 times as
much an up-quark? These are such strange, seemingly random numbers.
Did they occur by chance, by some divine choice, or is there a
comprehensible scientific explanation for these fundamental features
of our universe?
______________________
The
Forces, or, Where's the Photon?
Things
only become more complicated when we consider the forces of nature.
The world around us is replete with means of exerting influence:
balls can be hit with bats, bungee enthusiasts can throw themselves
earthward from high platforms, magnets can keep superfast trains
suspended just above metallic tracks, Geiger counters can tick
in response to radioactive material, nuclear bombs can explode.
We can influence objects by vigorously pushing, pulling, or shaking
them; by hurling or firing other objects into them; by stretching,
twisting, or crushing them; or by freezing, heating, or burning
them. During the past hundred years physicists have accumulated
mounting evidence that all of these interactions between various
objects and materials, as well as any of the millions upon millions
of others encountered daily, can be reduced to combinations of
four fundamental forces. One of these is the gravitational force.
The other three are the electromagnetic force, the weak force,
and the strong force.
Gravity
is the most familiar of the forces, being responsible for keeping
us in orbit around the sun as well as for keeping our feet firmly
planted on earth. The mass of an object measures how much gravitational
force it can exert as well as feel. The electromagnetic force
is the next most familiar of the four. It is the force driving
all of the conveniences of modern life — lights, computers,
TVs, telephones — and underlies the awesome might of lightning
storms and the gentle touch of a human hand. Microscopically,
the electric charge of a particle plays the same role for the
electromagnetic force as mass does for gravity: it determines
how strongly the particle can exert as well as respond electromagnetically.
The
strong and the weak forces are less familiar because their strength
rapidly diminishes over all but subatomic distance scales; they
are the nuclear forces. This is why these two forces were discovered
only much more recently. The strong force is responsible for keeping
quarks "glued" together inside of protons and neutrons
and keeping protons and neutrons tightly crammed together inside
atomic nuclei. The weak force is best known as the force responsible
for the radioactive decay of substances such as uranium and cobalt.
During
the past century, physicists have found two features common to
all these forces. First, as we will discuss in Chapter 5, at a
microscopic level all the forces have an associated particle that
you can think of as being the smallest packet or bundle of the
force. If you fire a laser beam — an "electromagnetic
ray gun" — you are firing a stream of photons, the smallest
bundles of the electromagnetic force. Similarly, the smallest
constituents of weak and strong force fields are particles called
weak gauge bosons and gluons. (The name gluon is particularly
descriptive: You can think of gluons as the microscopic ingredient
in the strong glue holding atomic nuclei together.) By 1984 experimenters
had definitively established the existence and the detailed properties
of these three kinds of force particles, recorded in Table 1.2.
Physicists believe that the gravitational force also has an associated
particle — the graviton — but its existence has yet
to be confirmed experimentally.
The
second common feature of the forces is that just as mass determines
how gravity affects a particle, and electric charge determines
how the electromagnetic force affects it, particles are endowed
with certain amounts of "strong charge" and "weak
charge" that determine how they are affected by the strong
and weak forces. (These properties are detailed in the table in
the endnotes to this chapter.1) But as with particle masses, beyond
the fact that experimental physicists have carefully measured
these properties, no one has any explanation of why our universe
is composed of these particular particles, with these particular
masses and force charges.
Notwithstanding
their common features, an examination of the fundamental forces
themselves serves only to compound the questions. Why, for instance,
are there four fundamental forces? Why not five or three or perhaps
only one? Why do the forces have such different properties? Why
are the strong and weak forces confined to operate on microscopic
scales while gravity and the electromagnetic force have an unlimited
range of influence? And why is there such an enormous spread in
the intrinsic strength of these forces?
To
appreciate this last question, imagine holding an electron in
your left hand and another electron in your right hand and bringing
these two identical electrically charged particles close together.
Their mutual gravitational attraction will favor their getting
closer while their electromagnetic repulsion will try to drive
them apart. Which is stronger? There is no contest: The electromagnetic
repulsion is about a million billion billion billion billion (10
to the 42th) times stronger! If your right bicep represents the
strength of the gravitational force, then your left bicep would
have to extend beyond the edge of the known universe to represent
the strength of the electromagnetic force. The only reason the
electromagnetic force does not completely overwhelm gravity in
the world around us is that most things are composed of an equal
amount of positive and negative electric charges whose forces
cancel each other out. On the other hand, since gravity is always
attractive, there are no analogous cancellations — more stuff
means greater gravitational force. But fundamentally speaking,
gravity is an extremely feeble force. (This fact accounts for
the difficulty in experimentally confirming the existence of the
graviton. Searching for the smallest bundle of the feeblest force
is quite a challenge.) Experiments also have shown that the strong
force is about one hundred times as strong as the electromagnetic
force and about one hundred thousand times as strong as the weak
force. But where is the rationale — the raison d'etre —
for our universe having these features?
This
is not a question borne of idle philosophizing about why certain
details happen to be one way instead of another; the universe
would be a vastly different place if the properties of the matter
and force particles were even moderately changed. For example,
the existence of the stable nuclei forming the hundred or so elements
of the periodic table hinges delicately on the ratio between the
strengths of the strong and electromagnetic forces. The protons
crammed together in atomic nuclei all repel one another electromagnetically;
the strong force acting among their constituent quarks, thankfully,
overcomes this repulsion and tethers the protons tightly together.
But a rather small change in the relative strengths of these two
forces would easily disrupt the balance between them, and would
cause most atomic nuclei to disintegrate. Furthermore, were the
mass of the electron a few times greater than it is, electrons
and protons would tend to combine to form neutrons, gobbling up
the nuclei of hydrogen (the simplest element in the cosmos, with
a nucleus containing a single proton) and, again, disrupting the
production of more complex elements. Stars rely upon fusion between
stable nuclei and would not form with such alterations to fundamental
physics. The strength of the gravitational force also plays a
formative role. The crushing density of matter in a star's central
core powers its nuclear furnace and underlies the resulting blaze
of starlight. If the strength of the gravitational force were
increased, the stellar clump would bind more strongly, causing
a significant increase in the rate of nuclear reactions. But just
as a brilliant flare exhausts its fuel much faster than a slow-burning
candle, an increase in the nuclear reaction rate would cause stars
like the sun to burn out far more quickly, having a devastating
effect on the formation of life as we know it. On the other hand,
were the strength of the gravitational force significantly decreased,
matter would not clump together at all, thereby preventing the
formation of stars and galaxies.
We
could go on, but the idea is clear: the universe is the way it
is because the matter and the force particles have the properties
they do. But is there a scientific explanation for why they have
these properties?
String Theory: The Basic Idea
String
theory offers a powerful conceptual paradigm in which, for the
first time, a framework for answering these questions has emerged.
Let's first get the basic idea.
The particles in Table 1.1 are the "letters" of all
matter. Just like their linguistic counterparts, they appear to
have no further internal substructure. String theory proclaims
otherwise. According to string theory, if we could examine these
particles with even greater precision — a precision many
orders of magnitude beyond our present technological capacity
— we would find that each is not pointlike, but instead consists
of a tiny one-dimensional loop. Like an infinitely thin rubber
band, each particle contains a vibrating, oscillating, dancing
filament that physicists, lacking Gell-Mann's literary flair,
have named a string. In Figure 1.1 we illustrate this essential
idea of string theory by starting with an ordinary piece of matter,
an apple, and repeatedly magnifying its structure to reveal its
ingredients on ever smaller scales. String theory adds the new
microscopic layer of a vibrating loop to the previously known
progression from atoms through protons, neutrons, electrons and
quarks.2
Although
it is by no means obvious, we will see in Chapter 6 that this
simple replacement of point-particle material constituents with
strings resolves the incompatibility between quantum mechanics
and general relativity. String theory thereby unravels the central
Gordian knot of contemporary theoretical physics. This is a tremendous
achievement, but it is only part of the reason string theory has
generated such excitement.
______________________
String
Theory as the Unified Theory of Everything
In
Einstein's day, the strong and the weak forces had not yet been
discovered, but he found the existence of even two distinct forces
— gravity and electromagnetism — deeply troubling. Einstein
did not accept that nature is founded on such an extravagant design.
This launched his thirty-year voyage in search of the so-called
unified field theory that he hoped would show that these two forces
are really manifestations of one grand underlying principle. This
quixotic quest isolated Einstein from the mainstream of physics,
which, understandably, was far more excited about delving into
the newly emerging framework of quantum mechanics. He wrote to
a friend in the early 1940s, "I have become a lonely old
chap who is mainly known because he doesn't wear socks and who
is exhibited as a curiosity on special occasions."3
Einstein
was simply ahead of his time. More than half a century later,
his dream of a unified theory has become the Holy Grail of modern
physics. And a sizeable part of the physics and mathematics community
is becoming increasingly convinced that string theory may provide
the answer. From one principle — that everything at its most
microscopic level consists of combinations of vibrating strands
— string theory provides a single explanatory framework capable
of encompassing all forces and all matter.
String
theory proclaims, for instance, that the observed particle properties,
the data summarized in Tables 1.1 and 1.2, are a reflection of
the various ways in which a string can vibrate. Just as the strings
on a violin or on a piano have resonant frequencies at which they
prefer to vibrate — patterns that our ears sense as various
musical notes and their higher harmonics — the same holds
true for the loops of string theory. But we will see that, rather
than producing musical notes, each of the preferred patterns of
vibration of a string in string theory appears as a particle whose
mass and force charges are determined by the string's oscillatory
pattern. The electron is a string vibrating one way, the up-quark
is a string vibrating another way, and so on. Far from being a
collection of chaotic experimental facts, particle properties
in string theory are the manifestation of one and the same physical
feature: the resonant patterns of vibration — the music,
so to speak — of fundamental loops of string. The same idea
applies to the forces of nature as well. We will see that force
particles are also associated with particular patterns of string
vibration and hence everything, all matter and all forces, is
unified under the same rubric of microscopic string oscillations
— the "notes" that strings can play.
For
the first time in the history of physics we therefore have a framework
with the capacity to explain every fundamental feature upon which
the universe is constructed. For this reason string theory is
sometimes described as possibly being the "theory of everything"
(T.O.E.) or the "ultimate" or "final" theory.
These grandiose descriptive terms are meant to signify the deepest
possible theory of physics — a theory that underlies all
others, one that does not require or even allow for a deeper explanatory
base. In practice, many string theorists take a more down-to-earth
approach and think of a T.O.E. in the more limited sense of a
theory that can explain the properties of the fundamental particles
and the properties of the forces by which they interact and influence
one another. A staunch reductionist would claim that this is no
limitation at all, and that in principle absolutely everything,
from the big bang to daydreams, can be described in terms of underlying
microscopic physical processes involving the fundamental constituents
of matter. If you understand everything about the ingredients,
the reductionist argues, you understand everything.
The
reductionist philosophy easily ignites heated debate. Many find
it fatuous and downright repugnant to claim that the wonders of
life and the universe are mere reflections of microscopic particles
engaged in a pointless dance fully choreographed by the laws of
physics. Is it really the case that feelings of joy, sorrow, or
boredom are nothing but chemical reactions in the brain —
reactions between molecules and atoms that, even more microscopically,
are reactions between some of the particles in Table 1.1, which
are really just vibrating strings? In response to this line of
criticism, Nobel laureate Steven Weinberg cautions in Dreams of
a Final Theory,
At the other end of the spectrum are the opponents of reductionism
who are appalled by what they feel to be the bleakness of modern
science. To whatever extent they and their world can be reduced
to a matter of particles or fields and their interactions, they
feel diminished by that knowledge. . . . I would not try to answer
these critics with a pep talk about the beauties of modern science.
The reductionist worldview is chilling and impersonal. It has
to be accepted as it is, not because we like it, but because that
is the way the world works.4
Some agree with this stark view, some don't.
Others
have tried to argue that developments such as chaos theory tell
us that new kinds of laws come into play when the level of complexity
of a system increases. Understanding the behavior of an electron
or a quark is one thing; using this knowledge to understand the
behavior of a tornado is quite another. On this point, most agree.
But opinions diverge on whether the diverse and often unexpected
phenomena that can occur in systems more complex than individual
particles truly represent new physical principles at work, or
whether the principles involved are derivative, relying, albeit
in a terribly complicated way, on the physical principles governing
the enormously large number of elementary constituents. My own
feeling is that they do not represent new and independent laws
of physics. Although it would be hard to explain the properties
of a tornado in terms of the physics of electrons and quarks,
I see this as a matter of calculational impasse, not an indicator
of the need for new physical laws. But again, there are some who
disagree with this view.
What
is largely beyond question, and is of primary importance to the
journey described in this book, is that even if one accepts the
debatable reasoning of the staunch reductionist, principle is
one thing and practice quite another. Almost everyone agrees that
finding the T.O.E. would in no way mean that psychology, biology,
geology, chemistry, or even physics had been solved or in some
sense subsumed. The universe is such a wonderfully rich and complex
place that the discovery of the final theory, in the sense we
are describing here, would not spell the end of science. Quite
the contrary: The discovery of the T.O.E. — the ultimate
explanation of the universe at its most microscopic level, a theory
that does not rely on any deeper explanation — would provide
the firmest foundation on which to build our understanding of
the world. Its discovery would mark a beginning, not an end. The
ultimate theory would provide an unshakable pillar of coherence
forever assuring us that the universe is a comprehensible place.
______________________
The
State of String Theory
The
central concern of this book is to explain the workings of the
universe according to string theory, with a primary emphasis on
the implications that these results have for our understanding
of space and time. Unlike many other exposés of scientific
developments, the one given here does not address itself to a
theory that has been completely worked out, confirmed by vigorous
experimental tests, and fully accepted by the scientific community.
The reason for this, as we will discuss in subsequent chapters,
is that string theory is such a deep and sophisticated theoretical
structure that even with the impressive progress that has been
made over the last two decades, we still have far to go before
we can claim to have achieved full mastery.
And
so string theory should be viewed as a work in progress whose
partial completion has already revealed astonishing insights into
the nature of space, time, and matter. The harmonious union of
general relativity and quantum mechanics is a major success. Furthermore,
unlike any previous theory, string theory has the capacity to
answer primordial questions having to do with nature's most fundamental
constituents and forces. Of equal importance, although somewhat
harder to convey, is the remarkable elegance of both the answers
and the framework for answers that string theory proposes. For
instance, in string theory many aspects of nature that might appear
to be arbitrary technical details — such as the number of
distinct fundamental particle ingredients and their respective
properties — are found to arise from essential and tangible
aspects of the geometry of the universe. If string theory is right,
the microscopic fabric of our universe is a richly intertwined
multidimensional labyrinth within which the strings of the universe
endlessly twist and vibrate, rhythmically beating out the laws
of the cosmos. Far from being accidental details, the properties
of nature's basic building blocks are deeply entwined with the
fabric of space and time.
In
the final analysis, though, nothing is a substitute for definitive,
testable predictions that can determine whether string theory
has truly lifted the veil of mystery hiding the deepest truths
of our universe. It may be some time before our level of comprehension
has reached sufficient depth to achieve this aim, although, as
we will discuss in Chapter 9, experimental tests could provide
strong circumstantial support for string theory within the next
ten years or so. Moreover, in Chapter 13 we will see that string
theory has recently solved a central puzzle concerning black holes,
associated with the so-called Bekenstein-Hawking entropy, that
has stubbornly resisted resolution by more conventional means
for more than twenty-five years. This success has convinced many
that string theory is in the process of giving us our deepest
understanding of how the universe works.
Edward
Witten, one of the pioneers and leading experts in string theory,
summarizes the situation by saying that "string theory is
a part of twenty-first-century physics that fell by chance into
the twentieth century," an assessment first articulated by
the celebrated Italian physicist Danielle Amati.5 In a sense,
then, it is as if our forebears in the late nineteenth century
had been presented with a modern-day supercomputer, without the
operating instructions. Through inventive trial and error, hints
of the supercomputer's power would have become evident, but it
would have taken vigorous and prolonged effort to gain true mastery.
The hints of the computer's potential, like our glimpses of string
theory's explanatory power, would have provided extremely strong
motivation for obtaining complete facility. A similar motivation
today energizes a generation of theoretical physicists to pursue
a full and precise analytic understanding of string theory.
Witten's
remark and those of other experts in the field indicate that it
could be decades or even centuries before string theory is fully
developed and understood. This may well be true. In fact, the
mathematics of string theory is so complicated that, to date,
no one even knows the exact equations of the theory. Instead,
physicists know only approximations to these equations, and even
the approximate equations are so complicated that they as yet
have been only partially solved. Nevertheless, an inspiring set
of breakthroughs in the latter half of the 1990s — breakthroughs
that have answered theoretical questions of hitherto unimaginable
difficulty — may well indicate that complete quantitative
understanding of string theory is much closer than initially thought.
Physicists worldwide are developing powerful new techniques to
transcend the numerous approximate methods so far used, collectively
piecing together disparate elements of the string theory puzzle
at an exhilarating rate.
Surprisingly,
these developments are providing new vantage points for reinterpreting
some of the basic aspects of the theory that have been in place
for some time. For instance, a natural question that may have
occurred to you in looking at Figure 1.1 is, Why strings? Why
not little frisbee disks? Or microscopic bloblike nuggets? Or
a combination of all of these possibilities? As we shall see in
Chapter 12, the most recent insights show that these other kinds
of ingredients do have an important role in string theory, and
have revealed that string theory is actually part of an even grander
synthesis currently (and mysteriously) named M-theory. These latest
developments will be the subject of the final chapters of this
book.
Progress
in science proceeds in fits and starts. Some periods are filled
with great breakthroughs; at other times researchers experience
dry spells. Scientists put forward results, both theoretical and
experimental. The results are debated by the community, sometimes
they are discarded, sometimes they are modified, and sometimes
they provide inspirational jumping-off points for new and more
accurate ways of understanding the physical universe. In other
words, science proceeds along a zig-zag path toward what we hope
will be ultimate truth, a path that began with humanity's earliest
attempts to fathom the cosmos and whose end we cannot predict.
Whether string theory is an incidental rest stop along this path,
a landmark turning point, or in fact the final destination we
do not know. But the last two decades of research by hundreds
of dedicated physicists and mathematicians from numerous countries
have given us well-founded hope that we are on the right and possibly
final track.
It
is a telling testament of the rich and far-reaching nature of
string theory that even our present level of understanding has
allowed us to gain striking new insights into the workings of
the universe. A central thread in what follows will be those developments
that carry forward the revolution in our understanding of space
and time initiated by Einstein's special and general theories
of relativity. We will see that if string theory is correct, the
fabric of our universe has properties that would likely have dazzled
even Einstein.
Copyright
© 1999 Brian Greene. All rights reserved.