Born's prophecy leaves no space for quantum gravity

TL;DR

The paper argues that spacetime is a redundant abstraction in physics, especially if momentum space has nontrivial geometry, which challenges traditional views in quantum gravity and suggests a need to reconsider the fundamental nature of spacetime.

Contribution

It highlights the implications of nontrivial momentum space geometry for the concept of spacetime and explores how this affects quantum gravity theories and the notion of locality.

Findings

Spacetime may be a redundant abstraction if momentum space is nontrivial.

Nontrivial momentum space geometry implies a relativity of spacetime locality.

Implications for emergent gravity, spacetime, and black hole holography.

Abstract

I stress that spacetime is a redundant abstraction, since describing the physical content of all so-called "space-time measurements" only requires timing (by a physical/material clock) of particle detections (at a physical/material detector). It is interesting then to establish which aspects of our current theories afford us the convenient abstraction of a spacetime. I emphasize the role played by the assumed triviality of the geometry of momentum space, which makes room for an observer-independent notion of locality. This is relevant for some recent studies of the quantum-gravity problem that stumbled upon hints of a nontrivial geometry of momentum space, something which had been strikingly envisaged for quantum gravity already in 1938 by Max Born. If indeed momentum space has nontrivial geometry then the abstraction of a spacetime becomes more evidently redundant and less convenient: one may still abstract a spacetime but only allowing for the possibility of a relativity of spacetime locality. I also provide some examples of how all this could affect our attitude toward the quantum-gravity problem, including some for the program of emergent gravity and emergent spacetime and an indication of triviality of the holographic description of black holes. And in order to give an illustrative example of possible logical path for the "disappearance of spacetime" I rely on formulas inspired by the $\kappa$-Poincar\'e framework.