The Aldred Limit in the Laboratory: The Einstein-Cartan Spin-Torsion Correction at Terrestrial Densities

The Aldred Limit is the density rho_A = 9.72 x 10^54 g/cm^3 at which the Einstein-Cartan spin-torsion term balances the matter term of a spin fluid. This paper evaluates the limit at laboratory densities: the correction to a body's effective gravitational density is the fraction rho/rho_A of the whole, which for the densest stable laboratory material (osmium) is 2.32 x 10^-54. Scored against the published sensitivities of the torsion-balance, atom-interferometer, optical-clock, and spin instrument classes, the effect falls short by 25 to 49 orders of magnitude depending on channel; between separated bodies the torsion-mediated spin force is identically zero. Equivalence-principle tests are shown to be blind to the correction at leading order. The Aldred Limit has no laboratory phenomenology; its correction first reaches the resolution of the best fractional metrology at densities of order 10^37 g/cm^3.