Preprint shows Newton's third law does not require active-passive gravitational mass equality

The paper re-examines the standard textbook claim that Newton's third law forces active gravitational mass to equal passive gravitational mass. By relaxing implicit assumptions about how forces transform under Galilean boosts, Giulini constructs consistent equations of motion where the two masses differ while total momentum is conserved. This decouples the usual route from Newtonian gravity to the weak equivalence principle that underpins general relativity. The analysis stays strictly within classical mechanics and does not invoke quantum or relativistic corrections.

Standard tests of the equivalence principle, such as Eötvös-type experiments and lunar laser ranging, constrain inertial-gravitational equality but have not separately bounded active versus passive distinctions. The preprint identifies potential signatures in three-body systems where active mass asymmetry could produce anomalous center-of-mass accelerations at levels below current solar-system ephemeris precision. Such effects would appear as small violations of momentum conservation in the Newtonian limit rather than geodesic deviation.

Connecting to broader gravity tests, the result aligns with proposals to search for equivalence-principle violations in strong-field regimes using binary pulsars and extreme-mass-ratio inspirals. If active-passive inequality exists, it would appear first in precision timing of compact-object systems rather than laboratory torsion balances. The paper supplies an extended appendix on the Galilean group action that clarifies which dynamical symmetries survive when the two masses are allowed to differ.