Atom Interferometry Beside a Spin-Polarised Source: The Torsion Phase and Its Detectability

Atom interferometers measure phases with extraordinary precision, and sending atoms through a spin-polarised material is one of the few laboratory geometries in which the probe actually enters the region where Einstein-Cartan torsion exists. This paper computes the torsion phase for thermal atoms traversing a magnetised iron foil 10 micrometres thick at 1000 m per second. The polarised electron density of iron, 1.9e29 per cubic metre, sources a torsion of 6.24e-40 per metre through the Cartan equation; the corresponding spin energy shift is 1.23e-46 eV, and the phase accumulated in transit is 1.87e-39 radians. Against an averaged phase sensitivity of 1e-09 radians the Einstein-Cartan phase lies 29.7 orders of magnitude out of reach, and the measurement bounds any multiplier of the torsion coupling at 5.35e+29. Reaching a detectable phase in a single shot would require a polarised spin density of 1.02e+62 per cubic metre, far beyond any condensed matter. The result is a precise negative: atom interferometry through foils cannot test the minimal theory, and its torsion value lies in bounding much stronger axial couplings. Computed from stated assumptions, not measured.