Non-Cauchy surface foliations and their expected connection to quantum gravity theories

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 with a short review of works which support this idea and then we foliate spacetime along an 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.