The Metric Gradient Force — A Flagship Test of Geometric Unity

Physical interactions can be divided into two classes according to their time-reversal properties: reversible geometric forces and irreversible dissipative forces. General relativity describes the former, while Newtonian mechanics and statistical physics describe the latter. How to experimentally distinguish these two kinds of forces remains an open question. This paper presents an operational experimental scheme to answer this question, based on a core corollary of the order parameter spacetime theory: the geometric force produced by an effective metric gradient in a condensed-matter system obeys exactly the same scaling behavior as the geodesic deflection caused by spatial curvature in general relativity. The acceleration is proportional to the square of the velocity and its sign is independent of the velocity direction, whereas dissipative forces are linear in velocity and odd under velocity reversal. This symmetry difference provides a universal criterion and the theoretical foundation for the self-calibration mechanism of the experiment. The scheme uses a ⁸⁷Rb Bose–Einstein condensate and a Feshbach resonance with a spatially inhomogeneous magnetic field to generate an inhomogeneous effective metric. By measuring the mean displacement of the atomic cloud for two opposite initial velocities, the contributions of all known dissipative and conservative forces are subtracted, leaving a clean geometric force signal. Five signal identification criteria and three independent scaling relations are systematically provided. For baseline parameters, the expected displacement is ~1.47 μm; with optimized detuning and suppressed systematics, it can reach ~4.1 μm with a combined signal-to-noise ratio of ~8σ. A positive result would demonstrate that the condensed-matter effective metric and the spacetime metric are projections of the same geometric structure, rather than mere analogies. A negative result would directly falsify Postulate 1 of the order parameter spacetime theory.