The Fabric of the Cosmos: Space, Time, and the Texture of Reality (45 page)

With the description I've given so far, it might seem baffling that any physicist would resist the allure of string theory. Here, finally, is a theory that promises to realize Einstein's dream and more; a theory that could quell the hostility between quantum mechanics and general relativity; a theory with the capacity to unify all matter and all forces by describing everything in terms of vibrating strings; a theory that suggests an ultramicroscopic realm in which familiar space and time might be as quaint as a rotary telephone; a theory, in short, that promises to take our understanding of the universe to a whole new level. But bear in mind that no one has ever seen a string and, except for some maverick ideas discussed in the next chapter, it is likely that even if string theory is right, no one ever will. Strings are so small that a direct observation would be tantamount to reading the text on this page from a distance of 100 light-years: it would require resolving power nearly a billion billion times finer than our current technology allows. Some scientists argue vociferously that a theory so removed from direct empirical testing lies in the realm of philosophy or theology, but not physics.

I find this view shortsighted, or, at the very least, premature. While we may never have technology capable of seeing strings directly, the history of science is replete with theories that were tested experimentally through indirect means.
¹³
String theory isn't modest. Its goals and promises are big. And that's exciting and useful, because if a theory is to be
the
theory of our universe, it must match the real world not just in the broad-brush outline discussed so far, but also in minute detail. As we'll now discuss, therein lie potential tests.

During the 1960s and 1970s, particle physicists made great strides in understanding the quantum structure of matter and the nongravitational forces that govern its behavior. The framework to which they were finally led by experimental results and theoretical insights is called the
standard
model
of particle physics and is based on quantum mechanics, the matter particles in Table 12.1, and the force particles in Table 12.2 (ignoring the graviton, since the standard model does not incorporate gravity, and including the Higgs particle, which is not listed in the tables), all viewed as point particles. The standard model is able to explain essentially all data produced by the world's atom smashers, and over the years its inventors have been deservedly lauded with the highest of honors. Even so, the standard model has significant limitations. We've already discussed how it, and every other approach prior to string theory, failed to merge gravity and quantum mechanics. But there are other shortcomings as well.

The standard model failed to explain
why
the forces are transmitted by the precise list of particles in Table 12.2 and
why
matter is composed of the precise list of particles in Table 12.1. Why are there three families of matter particles and why does each family have the particles it does? Why not two families or just one? Why does the electron have three times the electric charge of the down-quark? Why does the muon weigh 23.4 times as much as the up-quark, and why does the top-quark weigh about 350,000 times as much as an electron? Why is the universe constructed with this range of seemingly random numbers? The standard model takes the particles in Tables 12.1 and 12.2 (again, ignoring the graviton) as
input,
then makes impressively accurate predictions for how the particles will interact and influence each other. But the standard model can't explain the input—the particles and their properties—any more than your calculator can explain the numbers you input the last time you used it.

Puzzling over the properties of these particles is not an academic question of why this or that esoteric detail happens to be one way or another. Over the last century, scientists have realized that the universe has the familiar features of common experience only because the particles in Tables 12.1 and 12.2 have precisely the properties they do. Even fairly minor changes to the masses or electric charges of some of the particles would, for example, make them unable to engage in the nuclear processes that power stars. And without stars, the universe would be a completely different place. Thus, the detailed features of the elementary particles are entwined with what many view as the deepest question in all of science:
Why do the elementary particles have just the right properties to
allow nuclear processes to happen, stars to light up, planets to form around
stars, and on at least one such planet, life to exist?

The standard model can't offer any insight into this question since the particle properties are part of its required input. The theory won't start to chug along and produce results until the particle properties are specified. But string theory is different. In string theory, particle properties are
determined
by string vibrational patterns and so the theory holds the promise of providing an explanation.

To understand string theory's new explanatory framework, we need to have a better feel for how string vibrations produce particle properties, so let's consider the simplest property of a particle, its mass.

From E = mc
²
, we know that mass and energy are interchangeable; like dollars and euros, they are convertible currencies (but unlike monetary currencies, they have a fixed exchange rate, given by the speed of light times itself, c
²
). Our survival depends on Einstein's equation, since the sun's life-sustaining heat and light are generated by the conversion of 4.3 million tons of matter into energy every second; one day, nuclear reactors on earth may emulate the sun by safely harnessing Einstein's equation to provide humanity with an essentially limitless supply of energy.

In these examples, energy is produced from mass. But Einstein's equation works perfectly well in reverse—the direction in which mass is produced from energy—and that's the direction in which string theory uses Einstein's equation. The
mass
of a particle in string theory is nothing but the
energy
of its vibrating string. For instance, the explanation string theory offers for why one particle is heavier than another is that the string constituting the heavier particle is vibrating faster and more furiously than the string constituting the lighter particle. Faster and more furious vibration means higher energy, and higher energy translates, via Einstein's equation, into greater mass. Conversely, the lighter a particle is, the slower and less frenetic is the corresponding string vibration; a massless particle like a photon or a graviton corresponds to a string executing the most placid and gentle vibrational pattern that it possibly can.
^34
14

Other properties of a particle, such as its electric charge and its spin, are encoded through more subtle features of the string's vibrations. Compared with mass, these features are harder to describe nonmathematically, but they follow the same basic idea: the vibrational pattern is the particle's fingerprint; all the properties that we use to distinguish one particle from another are determined by the vibrational pattern of the particle's string.

In the early 1970s, when physicists analyzed the vibrational patterns arising in the first incarnation of string theory—the
bosonic string theory—
to determine the kinds of particle properties the theory predicted, they hit a snag. Every vibrational pattern in the bosonic string theory had a whole-number amount of spin: spin-0, spin-1, spin-2, and so on. This was a problem, because although the messenger particles have spin values of this sort, particles of matter (like electrons and quarks) don't. They have a fractional amount of spin, spin-½. In 1971, Pierre Ramond of the University of Florida set out to remedy this deficiency; in short order, he found a way to modify the equations of the bosonic string theory to allow for half-integer vibrational patterns as well.

In fact, on closer inspection, Ramond's research, together with results found by Schwarz and his collaborator André Neveu and later insights of Ferdinando Gliozzi, Joël Scherk, and David Olive, revealed a perfect balance—a novel symmetry—between the vibrational patterns with different spins in the modified string theory. These researchers found that the new vibrational patterns arose in pairs whose spin values differed by half a unit. For every vibrational pattern with spin-½ there was an associated vibrational pattern with spin-0. For every vibrational pattern of spin-1, there was an associated vibrational pattern of spin-½, and so on. The relationship between integer and half-integer spin values was named
supersymmetry,
and with these results the
supersymmetric string theory,
or
superstring theory,
was born. Nearly a decade later, when Schwarz and Green showed that all the potential anomalies that threatened string theory canceled each other out, they were actually working in the framework of superstring theory, and so the revolution their paper ignited in 1984 is more appropriately called the first
superstring
revolution. (In what follows, we will often refer to strings and to string theory, but that's just a shorthand; we always mean superstrings and superstring theory.)

With this background, we can now state what it would mean for string theory to reach beyond broad-brush features and explain the universe in detail. It comes down to this: among the vibrational patterns that strings can execute, there must be patterns whose properties agree with those of the known particle species. The theory has vibrational patterns with spin-½, but it must have spin-½ vibrational patterns that match precisely the known matter particles, as summarized in Table 12.1. The theory has spin-1 vibrational patterns, but it must have spin-1 vibrational patterns that match
precisely
the known messenger particles, as summarized in Table 12.2. Finally, if experiments do indeed discover spin-0 particles, such as are predicted for Higgs fields, string theory must yield vibrational patterns that match
precisely
the properties of these particles as well. In short, for string theory to be viable, its vibrational patterns must yield and explain the particles of the standard model.

Here, then, is string theory's grand opportunity. If string theory is right, there
is
an explanation for the particle properties that experimenters have measured, and it's to be found in the resonant vibrational patterns that strings can execute. If the properties of these vibrational patterns match the particle properties in Tables 12.1 and 12.2, I think that would convince even the diehard skeptics of string theory's veracity, whether or not anyone had directly seen the extended structure of a string itself. And beyond establishing itself as the long-sought unified theory, with such a match between theory and experimental data, string theory would provide the first fundamental explanation for why the universe is the way it is.

So how does string theory fare on this critical test?

Well, at first blush, string theory fails. For starters, there are an infinite number of different string vibrational patterns, with the first few of an endless series schematically illustrated in Figure 12.4. Yet Tables 12.1 and 12.2 contain only a finite list of particles, and so from the get-go we appear to have a vast mismatch between string theory and the real world. What's more, when we analyze mathematically the possible energies—and hence masses—of these vibrational patterns, we come upon another significant mismatch between theory and observation. The masses of the permissible string vibrational patterns bear no resemblance to the experimentally measured particle masses recorded in Tables 12.1 and 12.2. It's not hard to see why.

Since the early days of string theory, researchers have realized that the stiffness of a string is inversely proportional to its length (its length squared, to be more precise): while long strings are easy to bend, the shorter the string the more rigid it becomes. In 1974, when Schwarz and Scherk proposed decreasing the size of strings so that they'd embody a gravitational force of the right strength, they therefore also proposed increasing the tension of the strings—all the way, it turns out, to about a thousand trillion trillion trillion (10
³⁹
) tons, about 100000000000000000000000000000000000000000 (10
⁴¹
) times the tension on an average piano string. Now, if you imagine bending a tiny, extremely stiff string into one of the increasingly elaborate patterns in Figure 12.4, you'll realize that the more peaks and troughs there are, the more energy you'll have to exert. Conversely, once a string is vibrating in such an elaborate pattern, it embodies a huge amount of energy. Thus, all but the simplest string vibrational patterns are highly energetic and hence, via E = mc
²
, correspond to particles with huge masses.

Figure 12.4 The first few examples of string vibrational patterns.

And by huge, I really mean huge. Calculations show that the masses of the string vibrations follow a series analogous to musical harmonics: they are all multiples of a fundamental mass, the
Planck mass,
much as overtones are all multiples of a fundamental frequency or tone. By the standards of particle physics, the Planck mass is colossal—it is some 10 billion billion (10
¹⁹
) times the mass of a proton, roughly the mass of a dust mote or a bacterium. Thus, the possible masses of string vibrations are 0 times the Planck mass, 1 times the Planck mass, 2 times the Planck mass, 3 times the Planck mass, and so on, showing that the masses of all but the 0-mass string vibrations are gargantuan.
¹⁵

As you can see, some of the particles in Tables 12.1 and 12.2 are indeed massless, but most aren't. And the nonzero masses in the tables are farther from the Planck mass than the Sultan of Brunei is from needing a loan. Thus, we see clearly that the known particle masses do not fit the pattern advanced by string theory. Does this mean that string theory is ruled out? You might think so, but it doesn't. Having an endless list of vibrational patterns whose masses become ever more remote from those of known particles is a challenge the theory must overcome. Years of research have revealed promising strategies for doing so.

As a start, note that experiments with the known particle species have taught us that heavy particles tend to be unstable; typically, heavy particles disintegrate quickly into a shower of lower-mass particles, ultimately generating the lightest and most familiar species in Tables 12.1 and 12.2. (For instance, the top-quark disintegrates in about 10
^-24
seconds.) We expect this lesson to hold true for the "superheavy" string vibrational patterns, and that would explain why, even if they were copiously produced in the hot, early universe, few if any would have survived until today. Even if string theory is right, our only chance to see the superheavy vibrational patterns would be to produce them through high-energy collisions in particle accelerators. However, as current accelerators can reach only energies equivalent to roughly 1,000 times the mass of a proton, they are far too feeble to excite any but string theory's most placid vibrational patterns. Thus, string theory's prediction of a tower of particles with masses starting some million billion times greater than that achievable with today's technology is not in conflict with observations.

This explanation also makes clear that contact between string theory and particle physics will involve only the lowest-energy—the massless— string vibrations, since the others are way beyond what we can reach with today's technology. But what of the fact that most of the particles in Tables 12.1 and 12.2 are not massless? It's an important issue, but less troubling than it might at first appear. Since the Planck mass is huge, even the most massive particle known, the top-quark, weighs in at only .0000000000000000116 (about 10
^-17
) times the Planck mass. As for the electron, it weighs in at .0000000000000000000000034 (about 10
^-23
) times the Planck mass. So, to a first approximation
—valid
to better than 1
part in 10
¹⁷
—all the particles in Tables 12.1 and 12.2 do have masses equal to zero times the Planck mass (much as most earthlings' wealth, to a first approximation, is 0 times that of the Sultan of Brunei), just as "predicted" by string theory. Our goal is to better this approximation and show that string theory explains the tiny deviations from 0 times the Planck mass characteristic of the particles in Tables 12.1 and 12.2. But massless vibrational patterns are not as grossly at odds with the data as you might have initially thought.

This is encouraging, but detailed scrutiny reveals yet further challenges. Using the equations of superstring theory, physicists have listed every massless string vibrational pattern. One entry is the spin-2 graviton, and that's the great success which launched the whole subject; it ensures that gravity is a part of quantum string theory. But the calculations also show that there are
many
more massless spin-1 vibrational patterns than there are particles in Table 12.2, and there are
many
more massless spin
¹
/2 vibrational patterns than there are particles in Table 12.1. Moreover, the list of spin-½ vibrational patterns shows no trace of any repetitive groupings like the family structure of Table 12.1. With a less cursory inspection, then, it seems increasingly difficult to see how string vibrations will align with the known particle species.

Thus, by the mid-1980s, while there were reasons to be excited about superstring theory, there were also reasons to be skeptical. Undeniably, superstring theory presented a bold step toward unification. By providing the first consistent approach for merging gravity and quantum mechanics, it did for physics what Roger Bannister did for the four-minute mile: it showed the seemingly impossible to be possible. Superstring theory established definitively that we could break through the seemingly impenetrable barrier separating the two pillars of twentieth-century physics.

Yet, in trying to go further and show that superstring theory could explain the detailed features of matter and nature's forces, physicists encountered difficulties. This led the skeptics to proclaim that superstring theory, despite all its potential for unification, was merely a mathematical structure with no direct relevance for the physical universe.

Even with the problems just discussed, at the top of the skeptics' list of superstring theory's shortcomings was a feature I've yet to introduce. Superstring theory does indeed provide a successful merger of gravity and quantum mechanics, one that is free of the mathematical inconsistencies that plagued all previous attempts. However, strange as it may sound, in the early years after its discovery, physicists found that the equations of superstring theory do
not
have these enviable properties if the universe has three spatial dimensions. Instead, the equations of superstring theory are mathematically consistent only if the universe has
nine
spatial dimensions, or, including the time dimension, they work only in a universe with
ten
spacetime dimensions!

In comparison to this bizarre-sounding claim, the difficulty in making a detailed alignment between string vibrational patterns and known particle species seems like a secondary issue. Superstring theory requires the existence of
six
dimensions of space that no one has ever seen. That's not a fine point
—that's
a problem.

Or is it?

Theoretical discoveries made during the early decades of the twentieth century, long before string theory came on the scene, suggested that extra dimensions need not be a problem at all. And, with a late-twentieth-century updating, physicists showed that these extra dimensions have the capacity to bridge the gap between string theory's vibrational patterns and the elementary particles experimenters have discovered.

This is one of the theory's most gratifying developments; let's see how it works.