Optomechanical Force Noise and the Detectability of a Torsion-Induced Vacuum Force

This paper examines whether cryogenic optomechanical force sensitivity is sufficient to resolve vacuum forces at micrometre separations and limit an additional torsion-related component. The system considered is a picogram-scale cryogenic optomechanical resonator at 10 millikelvin, and the observable is thermal force noise, Casimir force magnitude and integration time. Evaluating the ordinary behaviour of the system and the spin-torsion contribution under explicit assumptions about polarisation and uniformity, and inverting the comparison at the stated laboratory precision, gives a quantitative bound rather than a qualitative assertion of smallness. The computed record is: force_noise_N_per_sqrtHz = 5.891e-20; casimir_force_N = 1.300e-11; integration_s_for_casimir_snr1 = 2.053e-17; mass_kg = 1.000e-12; temperature_K = 0.01. The torsion-related contribution is far below the level that would alter the ordinary behaviour of the system at current precision, and the value that would have produced a visible residual is stated so that future improvements can be assessed against it directly. No new measurement is reported. This study is simulated and computed from stated assumptions, not measured.