What are the problems in unifying relativity and QM?

What are the problems in unifying general theory of relativity and Quantum Mechanics?


Should we even try to unify them considering that relativity does not treat gravity as force but as curvature of spacetime?





Has Dirac's theory completely unified special theory of relativity and QM or is the unification still incomplete?|||QM is probablistic





GR is deterministic





Conceptually, things larger than an atom behave in a deterministic manner because the quantum effects average out to a smooth deterministic behavior. This works fine for things that are large and high energy/mass. But, breaks down for things that are small and high energy/mass. Which leaves a problem: What is the behavior of something like a black hole that is both small (QM applies) and massive (GR applies) is its behavior probabilistic or deterministic? Cannot be both.





Thus, comceptually for a theory to unite GR and QM the theory must smooth out the probabilistic behavior of QM enough that it fits with GR.|||Basically, general realtivity can't be renormalized which you need to do in order to quantize it using the second quantization procedures. We get away with it in quantum electrodynamics because you have two parameters - mass and charge - that can be redefined so as to cancel the two infinities that occur in the theory. But in GR, you have no parameters left free that way. The masses drop out and as my old thesis advisor said, "You can't renormalize one".|||Dunno about Dirac's thing, but I do know they're still looking for the theory of everything (TOE). That is, none of the prevailing theories (e.g., quantum loop, string, M, Horava) has as yet merged the macro with the micro. Some of them are works in progress however.





I think you missed a point on the curved space-time aspect of the GTOR. That is the source of the force of gravity. Gravity is still a force, which by definition is just a push or a pull. Gravity still does that; it's still a force under the curved space-time of the GTOR.





The so-called geodesic tensor in AE's GTOR equation simply says that acceleration due to gravity, g, is due to bent space and time. But it's still g (or the equivalent acceleration, which is what the equivalence principle was all about). And it still gives us W = mg the force of gravity or weight. In the graviton model, g is the field of gravitons. Gravitons have yet to be found, but bent space has been observed all over the cosmos.





You probably know about singularities and such when trying to apply the GTOR at the quantum level. The other major issue is that the GTOR and STOR are deterministic, while quanta are, well, jittery and probabilistic. Yet another is that quantum theories are granular, discontinuous because the basic units they apply to are quanta, little bits. One vain attempt at bringing the continuous function of the GTOR into the realm of the little bits, was to granulate space itself. That seems to be leading nowhere last I heard about it.