Should quantum theory change in the light of gravity?

TL;DR

This paper explores how the geometrical nature of spacetime influences quantum mechanics, questioning the necessity of unitarity and causality, and suggesting potential modifications to quantum theory in light of gravity and general covariance.

Contribution

It provides a detailed analysis of quantum theory's compatibility with spacetime geometry, proposing that causality may need to be abandoned and quantum theory modified for general covariance.

Findings

Quantum theory can have non-unitary evolution while maintaining a probabilistic interpretation.

Quantum field theory is only ultra weakly covariant with respect to background spacetime.

Causality may not be a fundamental principle in a quantum theory compatible with gravity.

Abstract

In this paper, we study implications of the geometrical nature of space- time for some of the basic tenets of quantum mechanics. That is, we study two different implications of the principle of general covariance; first we quantize a reparametrization invariant theory, the free particle in Minkowski spacetime and point out in detail where this theory fails (no- tably these comments appear to be missing in the literature). Second we study the covariance of quantum field theory and show how it connects to causality, the outcome of this study is that QFT is what we shall call ultra weakly covariant with respect to the background spacetime. Third, we treat the question of whether evolution in quantum theory (apart from the measurement act) needs to be unitary, it is easily shown that a per- fectly satisfying probabilistic interpretation exists which does not require unitary evolution. Fourth, we speculate on some modifications quantum theory should undergo in order for it to be generally covariant. The results in this paper hint at a profound change of the theory in which causality as a fundamental principle is abandonned.