Operational verification of the existence of a spacetime manifold

TL;DR

This paper proposes an operational, theory-independent protocol for experimentally verifying the existence and properties of a spacetime manifold, including its dimension and topology, without assuming its prior existence.

Contribution

It introduces a novel gedanken-experiment protocol that establishes the observability of spacetime's manifold structure respecting diffeomorphism symmetry, and discusses criteria for spacetime emergence.

Findings

Protocol can determine spacetime dimension and topology with current precision

Establishes the manifold structure without assuming its prior existence

Respects the underlying diffeomorphism symmetry

Abstract

We argue that there exists an operational way to establish the observability of the notions of space and time. Specifically, we propose a theory-independent protocol for a gedanken-experiment, whose outcome is a signal establishing the observability of the spacetime manifold, without a priori assuming its existence. The experimental signal contains the information about the dimension and the topology of spacetime (with the currently achievable precision), and establishes its manifold structure, while respecting its underlying diffeomorphism symmetry. We also introduce and discuss appropriate criteria for the concept of emergence of spacetime, which any tentative theoretical model of physics must satisfy in order to claim that spacetime does emerge from some more fundamental concepts.