STRING THEORY AS A UNIFIED THEORY OF PHYSICS

String theory is an excellent candidate for a unified theory of all forces in nature. It is also a rather impressive prototype of a complete theory of physics. In string theory all forces are truly unified in a deep and significant way. In fact, all the particles are unified. String theory is a quantum theory, and, because it includes gravitation, it is a quantum theory of gravity. Viewed from this perspective, and recalling the failure of Einstein?s gravity to yield a quantum theory, one may conclude that in string theory all other interactions are necessary for the consistency of the quantum gravitational sector! While it may be difficult to measure the effects of quantum gravity directly, a theory of quantum gravity such as string theory may have testable predictions concerning the other interactions.

Why is string theory a truly unified theory? The reason is simple and goes to the heart of the theory. In string theory, each particle is identified as a particular vibrational mode of an elementary microscopic string. A musical analogy is very apt. Just as a violin string can vibrate in different modes and each mode corresponds to a different sound, the modes of vibration of a fundamental string can be recognized as the different particles we know.

One of the vibrational states of strings is the graviton, the quantum of the gravitational field. Since there is just one type of string, and all particles arise from string vibrations, all particles are naturally incorporated into a single theory. When we think in string theory of a decay process α → β + γ, where an elementary particle α decays into particles β and γ, we imagine a single string vibrating in such a way that it is identified as particle α that breaks into two strings that vibrate in ways that identify them as particles β and γ.

Since strings may turn out to be extremely tiny, it may be difficult to observe directly the string-like nature of particles.

Are we sure that string theory is a good quantum theory of gravity? There is no complete certainty yet, but the evidence is very good. Indeed, the problems of incalculability or lack of predictability that occur when one tries to quantize Einstein?s theory do not seem to appear in string theory.

For a theory as ambitious as string theory, a certain degree of uniqueness is clearly desirable. It would be somewhat disappointing to have several consistent candidates for a theory of all interactions. The first sign that string theory is rather unique is that it does not have adjustable dimensionless parameters. As we mentioned before, the Standard Model of particle physics has about twenty parameters that must be adjusted to some precise values. A theory with adjustable dimensionless parameters is not really unique. When the parameters are set to different values one obtains different theories with potentially different predictions. String theory has one dimensionful parameter, the string length l s. Its value can be roughly imagined as the typical size of strings.

Another intriguing sign of the uniqueness of string theory is the fact that the dimensionality of spacetime is fixed. Our physical spacetime is four-dimensional, with one time dimension and three space dimensions. In the Standard Model this information is used to build the theory, it is not derived. In string theory, on the other hand, the number of spacetime dimensions emerges from a calculation. The answer is not four, but rather ten. Some of these dimensions may hide from plain view if they curl up into a space that is small enough to escape detection in experiments done with low energies. If string theory is correct, some mechanism must ensure that the observable dimensionality of spacetime is four.

The lack of adjustable dimensionless parameters is a sign of the uniqueness of string theory: it means that the theory cannot be deformed or changed continuously by changing these parameters. But there could be other theories that cannot be reached by continuous deformations. So how many string theories are there?

Let us begin by noting two broad subdivisions. There are open strings, and there are closed strings. Open strings have two endpoints, while closed strings have no endpoints. One can consider theories with only closed strings, and theories with both open and closed strings. Since open strings generally can close to form closed strings, we do not consider theories with only open strings. The second subdivision is between bosonic string theories and superstring theories. Bosonic strings live in 26 dimensions, and all of their vibrations represent bosons. Since they lack fermions, bosonic string theories are not realistic. They are, however, much simpler than the superstrings, and most of the important concepts in string theory can be explained in the context of bosonic strings. The superstrings live in ten-dimensional spacetime, and their spectrum of states includes bosons and fermions. In fact, these two sets of particles are related by supersymmetry. Supersymmetry is therefore an important ingredient in string theory. All realistic models of string theory are built from superstrings. In all string theories the graviton appears as a vibrational mode of closed strings. In string theory gravity is unavoidable.

By the mid 1980s five ten-dimensional superstring theories were known to exist. In the years that followed, many interrelations between these theories were found. Moreover, another theory was discovered by taking a certain strong coupling limit of one of the superstrings. This theory is eleven-dimensional and has been dubbed M-theory, for lack of a better name.

It has now become clear that the five superstrings and M-theory are only facets or different limits of a single unique theory! At present, this unique theory remains fairly mysterious. The less promising bosonic string theories appear to be unrelated to the superstring web of theories but this understanding could change in the future.

All in all, we see that string theory is a truly unified and possibly unique theory. It is a candidate for a unified theory of physics, a theory Albert Einstein tried to find ever since his discovery of general relativity. Einstein would have been surprised, or perhaps disturbed, by the prominent role that quantum mechanics plays in string theory. But string theory appears to be a worthy successor of general relativity. It is almost certain that string theory will give rise to a new conception of spacetime. The prominence of quantum mechanics in string theory would have not surprised Paul Dirac. His writings on quantization suggest that he felt that deep quantum theories arise from the quantization of classical physics. This is precisely what happens in string theory. This book will explain in detail how string theory, at least in its simplest form, is nothing but the quantum mechanics of classical relativistic strings.

Date: 2016-06-12; view: 209