Abstract
We argue that quantum gravity theories should involve constructing a quantum theory on non-Cauchy hypersurfaces and suggest that the hypersurface direction should be the same as the direction of the effective non-gravitational force field at a point. We start we a short review of works which support this idea and then we foliate spacetime along a effective non-gravitational force field direction. Next we discuss the implication of this foliation on the expected properties of quantum gravity. We also discuss the vagueness caused by constructing any quantum theory when using non-Cauchy foliation.
Highlights
Obtaining a gravitational theory from microscopic objects or quantum fields is extremely important and challenging
Combining quantum mechanics with general relativity is problematic since time plays a different role within these two frameworks: whereas general relativity treats time as a dynamical variable, quantum theories use the Hamiltonian formalism which causes time to act as an independent parameter through which states evolve
We suggest to consider the symmetry breaking caused by an effective non-gravitational force field, and to use its direction as an independent parameter through which states evolve
Summary
Obtaining a gravitational theory from microscopic objects or quantum fields is extremely important and challenging. As we will show this idea is supported by several works which all single out the direction of a non-gravitational force in order to obtain different aspects of quantum gravity It is in agreement with holography and Verlinde’s suggestion. It uses the natural symmetry breaking caused by an effective non gravitational force field, it eliminates the problem of time in the ADM formalism. This foliation enables us to obtain the conditions which are needed in order to derive an effective (2+1)D gravitational theory instead of (3+1)D theory, with can be renormelized in the quantum limit. We discuss the vagueness caused by constructing any quantum theory when using non-Cauchy foliation, and discuss the implications on quantum gravity
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