Clock-Anisotropy Limits on Spatial Torsion from Hughes-Drever Experiments

Hughes-Drever experiments, which watch atomic and nuclear energy levels for a sidereal wobble as the laboratory rotates, are the classical test of whether space has a preferred direction. A spatial axial torsion background is exactly such a direction, coupled to spin. This paper converts representative modern clock-anisotropy sensitivities into bounds on the spatial components of a torsion background. An anomalous neutron spin energy bounded at 1e-25 eV corresponds to a torsion component below 5.07e-19 per metre; an electron bound at 1e-24 eV corresponds to 5.07e-18 per metre. Two scales frame these numbers. At the top, the torsion at the Aldred bound in neutron matter is 1.35e+16 per metre, 34.4 orders of magnitude above the neutron bound, so clock experiments audit a regime utterly disjoint from the dense-matter regime where torsion is strong. At the bottom, even a wholly spin-polarised Earth — an unphysical ceiling — would source only 1.08e-38 per metre, nineteen orders below the bound: no terrestrial source in any torsion theory with gravitational-strength coupling can produce a background these clocks could see, so a positive signal would have to be cosmological or non-gravitational in origin. Computed from stated assumptions, not measured.