**Table of Contents**

*.......The Elegant Universe*

**THE ELEGANT UNIVERSE,****Brian Greene,**1999, 2003

```(annotated and with added

**bold highlights by Epsilon=One**)

**Chapter 12 - Beyond Strings: In Search of M-Theory**

Is the Ballpark in the Ballpark?

It depends. Although the mathematical formula associated with each diagram becomes very complicated as the number of loops grows, string theorists have recognized one basic and essential feature. Somewhat as the strength of a rope determines the likelihood that vigorous pulling and shaking will cause it to tear into two pieces, there is a number that determines the likelihood that quantum fluctuations will cause a single string to split into two strings, momentarily yielding a virtual pair. This number is known as the

We will shortly take up the question of determining the value of the string coupling constant within any of the five string theories, but first, what do we really mean by "small" or "large" when assessing its size? Well, the mathematics underlying string theory shows that the dividing line between "small" and "large" is the number 1, in the following sense. If the string coupling constant has a value less than 1, then—like multiple strikes of lightning—larger numbers of virtual string pairs are increasingly

This realization leads us to the next crucial question: What is the value of the string coupling constant (or, more precisely, what are the values of the string coupling constants in each of the five string theories)?

*string coupling constant*(more precisely, each of the five string theories has its own string coupling constant, as we will discuss shortly). The name is quite descriptive: The size of the string coupling constant describes how strongly the quantum jitters of three strings (the initial loop and the two virtual loops into which it splits) are related—how tightly, so to speak, they are*coupled*to one another. The calculational formalism shows that the larger the string coupling constant, the more likely it is that quantum jitters will cause an initial string to split apart (and subsequently rejoin); the smaller the string coupling constant, the less likely it is for such virtual strings to erupt momentarily into existence.We will shortly take up the question of determining the value of the string coupling constant within any of the five string theories, but first, what do we really mean by "small" or "large" when assessing its size? Well, the mathematics underlying string theory shows that the dividing line between "small" and "large" is the number 1, in the following sense. If the string coupling constant has a value less than 1, then—like multiple strikes of lightning—larger numbers of virtual string pairs are increasingly

*unlikely*to erupt momentarily into existence. If the coupling constant is 1 or greater, however, it is increasingly*likely*that ever-larger numbers of such virtual pairs will momentarily burst on the scene.**The upshot is that if the string coupling constant is less than 1, the loop diagram contributions be¬come ever smaller as the number of loops grows. This is just what is needed for the perturbative framework, since it indicates that we will get reasonably accurate results even if we ignore all processes except for those with just a few loops. But if the string coupling constant is not less than 1, the loop diagram contributions become more important as the number of loops increases. As in the case of a trinary star system, this invalidates a perturbative approach. The supposed ballpark approximation—the process with no loops—is***5**not*in the ballpark. (This discussion applies equally well to each of the five string theories—with the value of the string coupling constant in any given theory determining the efficacy of the perturbative approximation scheme.)This realization leads us to the next crucial question: What is the value of the string coupling constant (or, more precisely, what are the values of the string coupling constants in each of the five string theories)?

*At present, no one has been able to answer this question.*It is one of the most important unresolved issues in string theory. We can be sure that conclusions based on a perturbative framework are justified only if the string coupling constant is less than 1. Moreover, the precise value of the string coupling constant has a direct impact on the masses and charges carried by the various string vibrational patterns. Thus, we see that much physics hinges on the value of the string coupling constant. And so, let's take a closer look at why**the important question of its value—in any of the five string theories—remains unanswered.**

Table of Contents

*.......The Elegant Universe*