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By Root 2100 0

gives you ten billion billion dollars and challenges you to purchase products that will cost—cancel, so to speak—all but 189 of the dollars, not a dollar more or less. Coming up with such an enormous yet precise expenditure, without being privy to the exact prices of the individual items, would severely tax the acumen of even the world's most expert shoppers. In string theory, where the currency is energy as opposed to money, approximate calculations have conclusively shown that analogous energy cancellations certainly can occur, but for reasons that will become increasingly clear in subsequent chapters, verifying the cancellations to such a high level of precision is generally beyond our theoretical ken at present. Even so, as indicated before, we shall see that many other properties of string theory that are less sensitive to these finest of details can be extracted and understood with confidence.

This takes us to the third consequence of the enormous value of the string tension. Strings can execute an infinite number of different vibrational patterns. For instance, in Figure 6.2 we showed the beginnings of a never-ending sequence of possibilities characterized by an ever greater number of peaks and troughs. Doesn't this mean that there would have to be a corresponding never-ending sequence of elementary particles, seemingly in conflict with the experimental situation summarized in Tables 1.1 and 1.2?

The answer is yes: If string theory is right, each of the infinitely many resonant patterns of string vibration should correspond to an elementary particle. An essential point, however, is that the high string tension ensures that all but a few of these vibrational patterns will correspond to extremely heavy particles (the few being the lowest-energy vibrations that have near-perfect cancellations with quantum string jitters). And again, the term "heavy" here means many times heavier than the Planck mass. As our most powerful particle accelerators can reach energies only on the order of a thousand times the proton mass, less than a millionth of a billionth of the Planck energy, we are very far from being able to search in the laboratory for any of these new particles predicted by string theory.

There are more indirect approaches by which we could search for them, though. For instance, the energies involved at the birth of the universe would have been high enough to produce these particles copiously. In general one would not expect them to survive to the present day, as such super-heavy particles are usually unstable, relinquishing their enormous mass by decaying into a cascade of ever lighter particles, ending with the familiar, relatively light particles in the world around us. However, it is possible that such a super-heavy vibrational string state—a relic from the big bang—did survive to the present. Finding such particles, as we discuss more fully in Chapter 9, would be a monumental discovery, to say the least.

Gravity and Quantum Mechanics in String Theory

The unified framework that string theory presents is compelling. But its real attraction is the ability to ameliorate the hostilities between the gravitational force and quantum mechanics. Recall that the problem in merging general relativity and quantum mechanics turns up when the central tenet of the former—that space and time constitute a smoothly curving geometrical structure—confronts the essential feature of the latter—that everything in the universe, including the fabric of space and time, undergoes quantum fluctuations that become increasingly turbulent when probed on smaller and smaller distance scales. On sub-Planck-scale distances, the quantum undulations are so violent that they destroy the notion of a smoothly curving geometrical space; this means that general relativity breaks down.

String theory softens the violent quantum undulations by "smearing" out the short-distance properties of space. There is a rough and a more precise answer to the question of what this really means and how it resolves the conflict. We discuss each in turn.

The Rough