10 or 11 Dimensions? Phenomenological Conundrum. Drunken Risibility.


It is not the fact that we are living in a ten-dimensional world which forces string theory to a ten-dimensional description. It is that perturbative string theories are only anomaly-free in ten dimensions; and they contain gravitons only in a ten-dimensional formulation. The resulting question, how the four-dimensional spacetime of phenomenology comes off from ten-dimensional perturbative string theories (or its eleven-dimensional non-perturbative extension: the mysterious M theory), led to the compactification idea and to the braneworld scenarios.

It is not the fact that empirical indications for supersymmetry were found, that forces consistent string theories to include supersymmetry. Without supersymmetry, string theory has no fermions and no chirality, but there are tachyons which make the vacuum instable; and supersymmetry has certain conceptual advantages: it leads very probably to the finiteness of the perturbation series, thereby avoiding the problem of non-renormalizability which haunted all former attempts at a quantization of gravity; and there is a close relation between supersymmetry and Poincaré invariance which seems reasonable for quantum gravity. But it is clear that not all conceptual advantages are necessarily part of nature – as the example of the elegant, but unsuccessful Grand Unified Theories demonstrates.

Apart from its ten (or eleven) dimensions and the inclusion of supersymmetry – both have more or less the character of only conceptually, but not empirically motivated ad-hoc assumptions – string theory consists of a rather careful adaptation of the mathematical and model-theoretical apparatus of perturbative quantum field theory to the quantized, one-dimensionally extended, oscillating string (and, finally, of a minimal extension of its methods into the non-perturbative regime for which the declarations of intent exceed by far the conceptual successes). Without any empirical data transcending the context of our established theories, there remains for string theory only the minimal conceptual integration of basic parts of the phenomenology already reproduced by these established theories. And a significant component of this phenomenology, namely the phenomenology of gravitation, was already used up in the selection of string theory as an interesting approach to quantum gravity. Only, because string theory – containing gravitons as string states – reproduces in a certain way the phenomenology of gravitation, it is taken seriously.

But consistency requirements, the minimal inclusion of basic phenomenological constraints, and the careful extension of the model-theoretical basis of quantum field theory are not sufficient to establish an adequate theory of quantum gravity. Shouldn’t the landscape scenario of string theory be understood as a clear indication, not only of fundamental problems with the reproduction of the gauge invariances of the standard model of quantum field theory (and the corresponding phenomenology), but of much more severe conceptual problems? Almost all attempts at a solution of the immanent and transcendental problems of string theory seem to end in the ambiguity and contingency of the multitude of scenarios of the string landscape. That no physically motivated basic principle is known for string theory and its model-theoretical procedures might be seen as a problem which possibly could be overcome in future developments. But, what about the use of a static background spacetime in string theory which falls short of the fundamental insights of general relativity and which therefore seems to be completely unacceptable for a theory of quantum gravity?

At least since the change of context (and strategy) from hadron physics to quantum gravity, the development of string theory was dominated by immanent problems which led with their attempted solutions deeper. The result of this successively increasing self- referentiality is a more and more enhanced decoupling from phenomenological boundary conditions and necessities. The contact with the empirical does not increase, but gets weaker and weaker. The result of this process is a labyrinthic mathematical structure with a completely unclear physical relevance

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