Equivalence-Principle Tests with Spin-Polarised Test Bodies

The equivalence principle — that all bodies fall alike — has been tested to one part in 1e15, but almost always with unpolarised matter. Spin changes the question: in theories where torsion propagates, a spin-polarised body carries an axial charge that an unpolarised body lacks, and a polarised source's torsion field would pull the two bodies differently, violating the equivalence principle in a spin-dependent channel that ordinary tests never address. This paper computes both sides of that channel. In Einstein-Cartan theory the predicted differential acceleration is exactly zero, for the same reason as in the torsion-balance analysis: torsion does not leave the source matter, so a falling body, polarised or not, feels only the metric. For propagating extensions, a polarised test body of 10 grams carrying 1e23 polarised spins, falling toward an Earth whose crustal electrons are taken to have a geomagnetically aligned fraction giving a net source charge of 1e42 spins, converts the Eotvos bounds into coupling limits: eta below 1e-13 (laboratory) bounds the axial coupling at g squared over 4 pi below 1.26e-40, and eta below 1e-15 (space-mission class) bounds it at 1.26e-42 — about five orders of magnitude above the electron's gravitational coupling of 1.75e-45 at the laboratory level, and three orders at the space level. Spin-equivalence tests are thereby identified as the closest approach to gravitational-strength spin couplings among force experiments. Computed from stated assumptions, not measured.