General Covariance, Diffeomorphism Invariance, and Background Independence in 5 Dimensions

TL;DR

This paper examines how extending general relativity to five dimensions introduces interpretational issues, which can be resolved by relaxing certain foundational principles, potentially addressing major problems in quantum gravity.

Contribution

It analyzes five-dimensional generalizations of general relativity, showing that relaxing the GR-desideratum resolves interpretational problems and may help address quantum gravity challenges.

Findings

Interpretational troubles arise in 5D general relativity when strict GR principles are enforced.

Relaxing the GR-desideratum dissolves conceptual problems in 5D models.

Potential implications for solving the problem of time and quantum non-locality embedding.

Abstract

The paper considers the "GR-desideratum", that is, the way general relativity implements general covariance, diffeomorphism invariance, and background independence. Two cases are discussed where $5$-dimensional generalizations of general relativity run into interpretational troubles when the GR-desideratum is forced upon them. It is shown how the conceptual problems dissolve when such a desideratum is relaxed. In the end, it is suggested that a similar strategy might mitigate some major issues such as the problem of time or the embedding of quantum non-locality into relativistic spacetimes.