**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**

Beyond Strings: In Search of M-Theory

In his long search for a unified theory, Einstein reflected on whether "God could have made the Universe in a different way; that is, whether the necessity of logical simplicity leaves any freedom at all."

Establishing such inevitability in the structure of the universe would take us a long way toward coming to grips with some of the deepest questions of the ages. These questions emphasize the mystery surrounding who or what made the seemingly innumerable choices apparently required to design our universe. Inevitability answers these questions by erasing the options. Inevitability means that, in actuality, there are no choices. Inevitability declares that the universe could not have been different. As we will discuss in Chapter 14, nothing ensures that the universe is so tightly constructed. Nevertheless, the pursuit of such rigidity in the laws of nature lies at the heart of the unification program in modern physics.

By the late 1980s, it appeared to physicists that although string theory came close to providing a unique picture of the universe, it did not quite make the grade. There were two reasons for this. First, as briefly noted in Chapter 7, physicists found that there were actually

The second deviation from inevitability is more subtle. To fully appreciate it, you must recognize that all physical theories consist of two parts. The first part is the collection of fundamental ideas of the theory, which are usually expressed by mathematical equations. The second part of a theory comprises the solutions to its equations. Generally speaking, some equations have one and only one solution while others have more than one solution (possibly many more). (For a simple example, the equation "2 times a particular number equals 10" has one solution: 5. But the equation "0 times a particular number equals 0" has infinitely many solutions, since 0 times any number is 0.) And so, even if research leads to a unique theory with unique equations, it might be that inevitability is compromised because the equations have many different possible solutions. By the late 1980s, it appeared that this was the case with string theory. When physicists studied the equations of any one of the five string theories, they found that they

These deviations from inevitability might seem to be unfortunate fundamental characteristics of string thebry. But research since the mid-1990s has given us dramatic new hope that these features may be merely reflections of the way string theorists have been analyzing the theory. Briefly put, the equations of string theory are so complicated that no one knows their exact form. Physicists have managed to write down only approximate versions of the equations. It is these approximate equations that differ significantly from one string theory to the next. And it is these approximate equations, within the context of any one of the five string theories, that give rise to an abundance of solutions, a cornucopia of unwanted universes.

Since 1995 (the start of the second superstring revolution), there has been a growing body of evidence that the exact equations, whose precise form is still beyond our reach, may resolve these problems, thereby helping to give string theory the stamp of inevitability. In fact, it has already been established to the satisfaction of most string theorists that, when the exact equations are understood, they will show that all five string theories are actually intimately related. Like the appendages on a starfish, they are all part of one connected entity whose detailed properties are currently under intense investigation. Rather than having five distinct string theories, physicists are now convinced that there is

To explain these insights we must engage some of the most difficult, cutting-edge developments in string theory.

Nevertheless, as there are many seemingly separate pieces that we must develop and assemble, in this chapter it is especially easy to lose the forest for the trees. And so, if at any time in this chapter the discussion gets a little too involved and you feel compelled to rush on to black holes (Chapter 13) or cosmology (Chapter 14), take a quick glance back at the following section, which summarizes the key insights of the second superstring revolution.

**With this remark, Einstein articulated the nascent form of a view that is currently shared by many physicists: If there is a final theory of nature, one of the most convincing arguments in support of its particular form would be that the theory couldn't be otherwise. The ultimate theory should take the form that it does because it is the unique explanatory framework capable of describing the universe without running up against any internal inconsistencies or logical absurdities. Such a theory would declare that things are the way they are because they***1**have*to be that way. Any and all variations, no matter how small, lead to a theory that—like the phrase "This sentence is a lie"—sows the seeds of its own destruction.Establishing such inevitability in the structure of the universe would take us a long way toward coming to grips with some of the deepest questions of the ages. These questions emphasize the mystery surrounding who or what made the seemingly innumerable choices apparently required to design our universe. Inevitability answers these questions by erasing the options. Inevitability means that, in actuality, there are no choices. Inevitability declares that the universe could not have been different. As we will discuss in Chapter 14, nothing ensures that the universe is so tightly constructed. Nevertheless, the pursuit of such rigidity in the laws of nature lies at the heart of the unification program in modern physics.

By the late 1980s, it appeared to physicists that although string theory came close to providing a unique picture of the universe, it did not quite make the grade. There were two reasons for this. First, as briefly noted in Chapter 7, physicists found that there were actually

*five*different versions of string theory. You may recall that they are called the Type I, Type IIA, Type IIB, Heterotic O(32) (Heterotic-O, for short), and Heterotic E8 x E8 (Heterotic-E, for short) theories. They all share many basic features—their vibrational patterns determine the possible mass and force charges, they require a total of 10 spacetime dimensions, their curled-up dimensions must be in one of the Calabi-Yau shapes, etc.—and for this reason we have not emphasized their differences in previous chapters. Nevertheless, analyses in the 1980s showed that they do differ. You can read more about their properties in the endnotes, but it's enough to know that they differ in how they incorporate supersymmetry as well as in significant details of the vibrational patterns they support.**(Type I string theory, for example, has open strings with two loose ends in addition to the closed loops we have focused on.) This has been an embarrassment for string theorists because although it's impressive to have a serious proposal for the final unified theory, having five proposals takes significant wind from the sails of each.***2*The second deviation from inevitability is more subtle. To fully appreciate it, you must recognize that all physical theories consist of two parts. The first part is the collection of fundamental ideas of the theory, which are usually expressed by mathematical equations. The second part of a theory comprises the solutions to its equations. Generally speaking, some equations have one and only one solution while others have more than one solution (possibly many more). (For a simple example, the equation "2 times a particular number equals 10" has one solution: 5. But the equation "0 times a particular number equals 0" has infinitely many solutions, since 0 times any number is 0.) And so, even if research leads to a unique theory with unique equations, it might be that inevitability is compromised because the equations have many different possible solutions. By the late 1980s, it appeared that this was the case with string theory. When physicists studied the equations of any one of the five string theories, they found that they

*do*have many solutions—for example, many different possible ways to curl up the extra dimensions—with each solution corresponding to a universe with different properties. Most of these universes, although emerging as valid solutions to the equations of string theory, appear to be irrelevant to the world as we know it.These deviations from inevitability might seem to be unfortunate fundamental characteristics of string thebry. But research since the mid-1990s has given us dramatic new hope that these features may be merely reflections of the way string theorists have been analyzing the theory. Briefly put, the equations of string theory are so complicated that no one knows their exact form. Physicists have managed to write down only approximate versions of the equations. It is these approximate equations that differ significantly from one string theory to the next. And it is these approximate equations, within the context of any one of the five string theories, that give rise to an abundance of solutions, a cornucopia of unwanted universes.

Since 1995 (the start of the second superstring revolution), there has been a growing body of evidence that the exact equations, whose precise form is still beyond our reach, may resolve these problems, thereby helping to give string theory the stamp of inevitability. In fact, it has already been established to the satisfaction of most string theorists that, when the exact equations are understood, they will show that all five string theories are actually intimately related. Like the appendages on a starfish, they are all part of one connected entity whose detailed properties are currently under intense investigation. Rather than having five distinct string theories, physicists are now convinced that there is

*one*theory that sews all five into a unique theoretical framework. And like the clarity that emerges when hitherto hidden relationships are revealed, this union is providing a powerful new vantage point for understanding the universe according to string theory.To explain these insights we must engage some of the most difficult, cutting-edge developments in string theory.

**We must understand the nature of**the approximations used in studying string theory and their inherent limitations. We must gain some familiarity with the clever techniques—collectively called**—that physicists have invoked to circumvent some of these approximations. And then we must follow the subtle reasoning that makes use of these techniques to find the remarkable insights alluded to above. But don't worry. The really hard work has already been done by string theorists and we will content ourselves here with explaining their results.***dualities*Nevertheless, as there are many seemingly separate pieces that we must develop and assemble, in this chapter it is especially easy to lose the forest for the trees. And so, if at any time in this chapter the discussion gets a little too involved and you feel compelled to rush on to black holes (Chapter 13) or cosmology (Chapter 14), take a quick glance back at the following section, which summarizes the key insights of the second superstring revolution.

Table of Contents

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