A Characterisation of the Weylian Structure of Space-Time by Means of Low Velocity Tests

TL;DR

This paper proposes a method to characterize Weylian space-time structures using low velocity particle tests, replacing high velocity light-based tests, and demonstrates that Perlick's standard clock exists only in Weyl spaces.

Contribution

It introduces low velocity particle tests as an alternative to light-based experiments for characterizing Weylian space-time structures, simplifying experimental procedures.

Findings

Low velocity tests can replace high velocity light-ray tests in space-time characterization.

Null-experiments with low velocity particles can verify the compatibility axiom.

Perlick's standard clock exists exclusively in Weyl spaces.

Abstract

The compatibility axiom in Ehlers, Pirani and Schild's (EPS) constructive axiomatics of the space-time geometry that uses light rays and freely falling particles with high velocity, is replaced by several constructions with low velocity particles only. For that purpose we describe in a space-time with a conformal structure and an arbitrary path structure the radial acceleration, a Coriolis acceleration and the zig-zag construction. Each of these quantities give effects whose requirement to vanish can be taken as alternative version of the compatibility axiom of EPS. The procedural advantage lies in the fact, that one can make null-experiments and that one only needs low velocity particles to test the compatibility axiom. We show in addition that Perlick's standard clock can exist in a Weyl space only.