I've always thought that the reason we had trouble unifying Quantum mechanics and General relativity is:
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Quantum mechanics is defined "on" space time and time doesn't vary because of energy. Time is considered a constant (or more like an independent variable.) Whereas GR states that energy bends spacetime and that time is not a constant (or it varies).
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The second thing is that energy is not Globally conserved. While in Quantum mechanics everything is based on energy conservation. And hence, both are not completely compatible.
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There might be some mathematical incompatibilities like re-normalization which doesn't work for GR. I don't know why though.
Then how does string theory solve these problems? Isn't the theory just an Idea that string exist and their vibrational state determines the type of particle. Then how does it relate to time being considered as a variable, energy conservation problems and space time curvatures?
How does it try to unite GR with QM?
Best Answer
This is an answer by an experimental particle physicist who saw theoretical models developed to fit the particle data from Regge theory and the Fermi interactions ending finally to the present standard model which unifies all three interactions involving elementary particles.
Thus unification of all four forces becomes the holy grail for a theory of everything (TOE) and that is where quantization of gravity comes in.
Effective quantization of gravity is used in cosmological models. Effective because it is only valid over some range of scales , and not generally.
String theories are a good candidate for particle physics , because they contain in the symmetries of the vibrating strings all the group structure of the standard model, which can thus be embedded in a string theory, with the particles being vibrational levels of the universal string. In a sense the whole standard model is a verification of the string model, except that theorists have not managed to propose one unique string theory model, to be tested with new data in accelerator physics. There have been some phenomenological models with large extra dimensions which have not been seen, though they are sought, at the LHC. A second attraction, for particle physics, of string theories, is that they can also accommodate supersymmetry which seems to be necessary theoretically for the standard model . Andas a bonus the successes of the Regge theory can also be incorporated.
Thus the fact that string theories have a spin two elementary particle which can accommodate the graviton ,i.e. encompass quantization of gravity, makes that an attractive candidate for a TOE once a specific model is built from all the thousand possible string theories.
At the moment the other candidates offered for quantization of gravity cannot embed the standard model of particle physics , and thus are not candidates for a TOE .
Well, one would have to study how string theories work, after all. The general statement is that gravity can be accommodated in a string theory.