On the Motion of Matter in Spacetime

TL;DR

This paper questions the traditional geodesic hypothesis in gravity theories with scalar fields, proposing a refined approach using a torsion-based connection, and explores its implications for planetary motion and timekeeping.

Contribution

It introduces a reformulation of Brans-Dicke theory with a dynamically determined torsion connection, challenging the conventional geodesic assumption in scalar-tensor gravity theories.

Findings

Perihelion shift calculations differ under the new hypothesis.

Timekeeping methods may require refinement if scalar fields influence matter.

The proposed model impacts the understanding of matter motion in alternative gravity theories.

Abstract

We argue that the geodesic hypothesis based on auto-parallels of the Levi-Civita connection may need refinement in theories of gravity with additional scalar fields. This argument is illustrated with a re-formulation of the Brans-Dicke theory in terms of a spacetime connection with torsion determined dynamically in terms of the gradient of the Brans-Dicke scalar field. The perihelion shift in the orbit of Mercury is calculated on the alternative hypothesis that its world-line is an auto-parallel of such a connection. If scalar fields couple significantly to matter and spinless test particles move on such world-lines, current time keeping methods based on the conventional geodesic hypothesis may need refinement.