A General Theory of Quantum Relativity

TL;DR

This paper proposes a background independent extension of quantum mechanics, integrating geometric structures to develop a general theory of quantum relativity that unifies quantum events with gravity and matter.

Contribution

It introduces a novel geometric framework involving symplectic form, dynamical metric, and almost complex structure to extend quantum theory without background dependence.

Findings

Space of quantum events becomes dynamical

Incorporates a three-way interplay of geometric structures

Provides a conceptual basis for quantum gravity

Abstract

The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical. These postulates remain compatible within a background independent extension of quantum theory with a local intrinsic time implying the relativity of the concept of a quantum event. In this extension the space of quantum events becomes dynamical and only individual quantum events make sense observationally. At the core of such a general theory of quantum relativity is the three-way interplay between the symplectic form, the dynamical metric and non-integrable almost complex structure of the space of quantum events. Such a formulation provides a missing conceptual ingredient in the search for a background independent quantum theory of gravity and matter. The crucial new technical element in our scheme derives from a set of recent mathematical results on certain infinite dimensional almost Kahler manifolds which replace the complex projective spaces of standard quantum mechanics.