Hydrogen Hyperfine and 1S-2S Spectroscopy Bounds on Spin-Contact Torsion Terms

The hydrogen atom is the one laboratory system in which two spins — the electron's and the proton's — are guaranteed to overlap, held together in a single bound state whose spectrum is known to extreme precision. Einstein-Cartan torsion, which acts exactly where spins overlap, must therefore shift the hydrogen hyperfine interval by a definite amount. This paper computes that shift from the contact spin-spin energy density of the theory, using the ground-state wavefunction density at the proton, |psi(0)| squared = 2.15e+30 per cubic metre. The torsion shift is 6.96e-46 eV. The 21-centimetre hyperfine interval itself is 5.87e-06 eV and is measured to a relative precision of 1e-12, an absolute sensitivity of 5.87e-18 eV, so the shift lies 27.9 orders of magnitude beneath the measurement, and the comparison bounds any multiplier of the torsion contact coupling at 8.44e+27. The muonium hyperfine interval gives the weaker bound 2.69e+32, its relative precision being poorer. The paper also explains why the still more precise 1S-2S interval cannot help: the torsion shift is spin-dependent and displaces the hyperfine components in a pattern the spin-averaged 1S-2S line does not isolate at the relevant precision. Computed from stated assumptions, not measured.