Neutron Spin Rotation in Polarised Matter as a Direct Torsion Measurement

Of all laboratory probes, a polarised neutron beam is the most literal torsion meter available: the neutron carries spin one half, travels slowly enough to spend real time inside a target, and its spin direction can be read out with high precision after the traversal. This paper computes the spin rotation that Einstein-Cartan torsion produces in two standard targets. In a magnetised iron stack one centimetre thick, where the polarised electron density of 1.9e29 per cubic metre sources a torsion of 6.24e-40 per metre, a thermal neutron at 2200 m per second rotates by 8.50e-37 radians. In a polarised helium-3 cell three bar and ten centimetres long, the rotation is 6.20e-39 radians. Against a spin-rotation sensitivity of 1e-07 radians, the iron signal falls short by 29.1 orders of magnitude and the helium signal by 31.2 orders; a null measurement bounds any multiplier of the torsion coupling at 1.18e+29. The paper also shows why the neutron's famous sensitivity to tiny energy shifts does not rescue the measurement: the torsion energy shift in iron is 1.23e-46 eV, beneath even neutron resonance spectroscopy by twenty orders. Computed from stated assumptions, not measured.