On quantization and general relativity

TL;DR

This paper discusses the fundamental differences between general relativity and quantum mechanics, emphasizing the need to extend diffeomorphism invariance to include topology changes for a complete quantum gravity theory.

Contribution

It proposes extending the principle of diffeomorphism invariance to encompass topology changes, aiming to advance the understanding of quantum gravity.

Findings

Highlighting the difference in invariance principles between the theories

Proposing a new extension of diffeomorphism invariance

Suggesting a path towards a complete quantum gravity theory

Abstract

This note is to bring to the reader's attention the fact that general relativity and quantum mechanics differ from each other in one main aspect. General relativity is based on the diffeomorphism covariant formulation of the laws of physics while quantum mechanics is constructed such that its fundamental laws remain invariant to a change of topology. It is the goal of this paper to show that in order to obtain a complete description of quantum gravity one has to extend the principle of diffeomorphism invariance from general relativity in the sense of quantum mechanics i.e. the laws of physics must be covariant to a change in the topology of spacetime.