# How to detect the spacetime curvature without rulers and clocks

## TL;DR

This paper shows that it is possible to determine whether a 4-dimensional spacetime is curved or flat solely through a finite set of measurements of causality relations between events, without using rulers or clocks.

## Contribution

It proves that non-conformally flat spacetimes can be distinguished from flat ones with only sixteen causal relation measurements, clarifying the finite measurement requirements for detecting curvature.

## Key findings

- Non-conformally flat spacetimes can be identified with 16 measurements.
- Causality relations suffice to determine spacetime flatness.
- Finite measurement sets can verify spacetime curvature.

## Abstract

We demonstrate how one can distinguish a curved 4-dimensional spacetime from a flat one, when it is possible, relying only on the causality relations between events. It is known that it is possible only for spacetimes that are not conformally flat. We prove that if a spacetime is not conformally flat, then its non-flatness can be verified by only a few (sixteen) measurements of causal relations. Therefore the results of this paper clarify what can be said about flatness or non-flatness of the spacetime after a finite number of measurements of causal relations.