The Final Contradiction


The results described above constitute quite an achievement for one century, but it leaves us with one fundamental contradiction that still needs to be resolved. General relativity and quantum field theory are incompatible. Many theorical physicists are convinced that superstring theory will provide the answer. There have been major advances in our understanding of this subject, which I consider to constitute the ``second superstring revolution,'' during the past few years.
After presenting some more background, I will describe the recent developments and their implications.
There are various problems that arise when one attempts to combine general relativity and quantum field theory. The field theorist would point to the breakdown of the usual procedure for eliminating infinities from calculations of physical quantities. This procedure is called "renormalization", and when it fails the theory is said to be "non-renormalizable."
In such theories the short-distance behaviour of interactions is so singular that it is not possible to carry out meaningful calculations. By replacing point-like particles with one-dimensional extended strings, as the fundamental objects, superstring theory overcomes the problem of non-renormalizability.
An expert in general relativity might point to a different set of problems such as the issue of how to understand the causal structure of space-time when the geometry has quantum-mechanical excitations. There are also a host of problems associated to black holes such as the fundamental origin of their thermodynamic properties and their apparent incompatibility with quantum mechanics. The latter, if true, would mean that a modification in the basic structure of quantum mechanics is required.
In fact, superstring theory does not modify quantum mechanics; rather, it modifies general relativity. The relativist's set of issues cannot be addressed properly in the usual approach to quantum field theory (perturbation theory), but the recent discoveries are leading to non-perturbative understandings that should help in addressing them.
Most string theorists expect that the theory will provide satisfying resolutions of these problems without any revision in the basic structure of quantum mechanics. Indeed, there are indications that someday quantum mechanics will be viewed as an implication (or at least a necessary ingredient) of superstring theory.
When a new theoretical edifice is proposed, it is very desirable to identify distinctive testable experimental predictions. In the case of superstring theory there have been no detailed computations of the properties of elementary particles or the structure of the universe that are convincing, though many valiant attempts have been made.
In my opinion, success in such enterprises requires a better understanding of the theory than has been achieved as yet. It is very difficult to assess whether this level of understanding is just around the corner or whether it will take many decades and several more revolutions.
In the absence of this kind of confirmation, we can point to three qualitative "predictions" of superstring theory. The first is the existence of gravitation, approximated at low energies by general relativity. No other quantum theory can claim to have this property (and I suspect that no other ever will).
The second is the fact that superstring solutions generally include Yang--Mills gauge theories like those that make up the "standard model" of elementary particles.
The third general prediction is the existence of supersymmetry at low energies (the electroweak scale). Since supersymmetry is the major qualitiative prediction of superstring theory not already known to be true before the prediction, let us look at it a little more closely. (One could imagine that in some other civilization, the sequence of discoveries is different.)


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| Contents | Resolving Contradictions | Supersymmetry | A Brief History of Superstings |

| Basic Ideas of Superstring Theory | Superstring Revolution, part deux |