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What has string theory really reached in quantum gravity?
As a researcher in a completely different direction, I have completely ignored string theory. This is my personal bet. It may have been a bad choice, but even in this case it would be too late for me to switch to string theory. So, about string theory I'm in the position of a layman, and in fact only interested in understanding what they have really reached. In this thread, the question is what has been reached in the domain of quantum gravity.  

For comparison, quantum gravity is not really a problem in ether theory. It reintroduces a fixed Newtonian background into the theory. This background gives translational invariance. There is also a non-degenerated Lagrange formalism, and, as a consequence, Noether conservation laws and a non-degenerated Hamilton formalism with local energy and momentum conservation laws. So, all the conceptual problems related with the failure to create all this in a background-free theory disappear. Even more important is that the gravitational field follows usual condensed matter equations like the continuity and Euler equations. With a conserved density and a well-defined velocity field it is easy to introduce a comoving lattice as a regularization. And this lattice regularization, which gets rid of the field-theoretic infinities, is in no way obliged to have a well-defined limit for arbitrary small distances, because it has an own right to exist, as a fundamental atomic ether theory. In other words, we know how to quantized classical condensed matter theories, so that in quantum ether theory all we have to do is to follow known prescriptions, and not a problem at all.

The situation with quantization of general relativity is, instead, quite horrible. There is no background, which in itself leads to a quantum variant of the hole problem, and it is not even clear how to define GR as a quantum field theory. The topology is not fixed, and for the quantum domain one cannot exclude topologies which cannot appear as solutions of the Einstein equations, which requires to consider a topological foam. Einstein causality, defined by the gravitational field, becomes uncertain, thus, essentially undefined and undefinable. Because of diffeomorphism invariance, the Hamilton formalism can be defined only in a degenerate, problematic form, which leads to the "problem of time". Given that all the things which cause the problems, in particular, diffeomorphism invariance, are highly valued as deep insights of GR, it is almost anathema to abandon them, so that quantum GR researchers appear trapped by the rigorous requirements of GR philosophy.  

The situation is much easier in string theory, where we have a fixed Minkowski background. Even if this background is some 10- or 11-dimensional one, it may be sufficient to solve at least most of the conceptual problems caused in GR by its background freedom.

What remains is, of course, the field-theoretic part of the problem, the non-renormalizability of GR. Here, the problem is more serious than in ether theory, because one cannot simply consider a lattice regularization as an in itself satisfactory theory - the very point of string theory is that it will be true for arbitrary small distances. So, one really needs a finite theory for arbitrary small distances here. On the other hand, it is quite plausible that the very idea of strings instead of point particles allows to get rid of some infinities. Nonetheless, it does not mean that a really finite theory for arbitrary small distances has been actually reached. So, this is the first question I would be interested to learn more about, in particular about the actual state: Is there a satisfactory field theory of gravity, without any infinities, based on string theory or not?

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What has string theory really reached in quantum gravity? - by Schmelzer - 05-15-2016, 01:05 PM

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