Testing the Metric Gradient Force Prediction of the Order Parameter Spacetime Theory with Cold-Atom Stern-Gerlach Experimental Data

The metric gradient force is the only purely geometric force term in the irreversible equation of motion of the Order Parameter Spacetime Theory. Its acceleration is proportional to the square of the velocity and independent of the velocity direction, making it exclusively distinguishable from all known dissipative forces (which are odd functions of velocity). We perform the first direct test of this prediction using Stern-Gerlach experimental data of Feshbach molecules from a ⁸⁷Rb Bose-Einstein condensate published by the MPQ group in 2003. By extracting the center-of-mass position data of the molecular cloud at 16 time slices from Figure 4 of the experiment, we find that the molecular cloud exhibits simple harmonic oscillation in a 100 G/cm magnetic field gradient, with an oscillation frequency of 56 Hz and an amplitude of 0.68 mm. Comparing the experimental acceleration with the theoretically predicted metric gradient force a_eff = (1/2)·(∂ ln g_ii/∂x)·ẋ², we verify the a ∝ v² scaling relation and deduce an order-parameter-space metric gradient ∂ ln g_ii/∂x ≈ 3.4 × 10³ m⁻¹. The left and right limits of the molecular cloud oscillation are approximately symmetric about the equilibrium position (deviation from center ≈ 0.68 mm), consistent with the prediction of the metric gradient force as an even function of velocity. The 2004 BEC-BCS crossover experiment by the Innsbruck group and the 2003 ⁶Li Fermi gas experiment by the ENS group provide qualitative support for this conclusion. Combined with previous tests of the theory in the cosmological weak-field (BAO and full-shape) and strong-field black hole (EHT) regimes, the Order Parameter Spacetime Theory has now passed observational tests across scales from microscopic cold-atom physics to macroscopic cosmology.