On Poincar\'e gauge theory of gravity, its equations of motion, and Gravity Probe B

TL;DR

This paper reviews Poincaré gauge theory of gravity, its equations of motion, and the implications for detecting spacetime torsion, concluding that current experiments like Gravity Probe B do not provide evidence for torsion.

Contribution

It clarifies the theoretical framework of Poincaré gauge gravity and demonstrates that torsion couples only to elementary particle spin, not orbital angular momentum, challenging previous experimental claims.

Findings

Torsion couples only to particle spin, not orbital angular momentum.

Gravity Probe B and similar experiments do not detect spacetime torsion.

The energy-momentum law in Poincaré gauge gravity is consistent across models.

Abstract

Ever since E.Cartan in the 1920s enriched the geometric framework of general relativity (GR) by introducing a {\it torsion} of spacetime, the question arose whether one could find a measurement technique for detecting the presence of a torsion field. Mao et al.(2007) claimed that the rotating quartz balls in the gyroscopes of the Gravity Probe B experiment, falling freely on an orbit around the Earth, should "feel" the torsion. Similarly, March et al.(2011) argue with the precession of the Moon and the Mercury and extend later their considerations to the Lageos satellite.--- A consistent theory of gravity with torsion emerged during the early 1960's as gauge theory of the Poincar\'e group. This Poincar\'e gauge theory of gravity incorporates as simplest viable cases the Einstein-Cartan(-Sciama-Kibble) theory (EC), the teleparallel equivalent GR|| of GR, and GR itself. So far, PG and, in particular, the existence of torsion have {\it not} been experimentally confirmed. However, PG is to be considered as the standard theory of gravity with torsion because of its very convincing gauge structure.--- Since the early 1970s up to today, different groups have shown more or less independently that torsion couples only to the {\it elementary particle spin} and under no circumstances to the orbital angular momentum of test particles. This is established knowledge and we reconfirm this conclusion by discussing the energy-momentum law of PG, which has same form for all versions of PG. Therefore, we conclude that, unfortunately, the investigations of Mao et al. and March et al. do not yield any information on torsion.