Construct an apparatus to directly operationalise spacetime torsion in TEGR

Construct a physical experimental apparatus that, within the teleparallel equivalent of general relativity (TEGR), directly correlates its readouts with the components of the spacetime torsion tensor, thereby providing a clear operationalisation of torsion comparable to the gravitational gradiometer’s operationalisation of curvature in general relativity. Specify the measurement principle, the coupling (e.g., to spinning test particles), and the calibration procedure that map device outputs to torsion components, and demonstrate how the apparatus distinguishes torsion effects from curvature effects under TEGR’s dynamics.

Background

The paper assesses whether torsion in the teleparallel equivalent of general relativity (TEGR) can be made as empirically and operationally tangible as curvature in general relativity (GR). Curvature in GR is operationalised via devices such as gravitational gradiometers, which provide a systematic readout correlated to curvature components. By contrast, although TEGR is dynamically equivalent to GR, torsion is not yet matched to a standard measurement device with an equally direct operational prescription.

The authors discuss potential routes to operationalise torsion, including leveraging relations between curvature and torsion (e.g., via Bianchi identities) and coupling to spinning test particles following ideas by Hehl (1971). However, they emphasise that a concrete design and construction of a device that correlates measured signals to torsion components remains to be provided. Developing such an apparatus would help close an operational gap between the two empirically equivalent theories and clarify the empirical grasp of torsion in TEGR.