Retarded Potential Gravitation

This paper presents a theoretical framework in flat spacetime that reproduces the principal solar-system predictions of general relativity (GR) using retarded potentials. By reinterpreting the acceleration term in Feynman’s retarded-potential formula as the relative acceleration between the source and the test particle, we introduce a “mass-field force” that arises from the motion of a test body through a background gravitational potential.The framework is built upon two fundamental postulates: (1) the acceleration in Newton’s Second Law is the relative acceleration between interacting bodies, and (2) the force F = ma is an independent force rather than a resultant force.

Using these postulates, we construct a four-force equilibrium involving centripetal force, mass-field force, gravitational force, and angular-momentum force. These postulates cannot be derived from more fundamental principles within the current framework; instead, they are introduced as working hypotheses. Their validity is justified a posteriori by the fact that they naturally lead to a four-force equilibrium whose integration yields an energy conservation equation identical in form to the effective potential equation in the weak-field limit of general relativity.

This approach reproduces Mercury’s perihelion precession and the deflection of light without invoking curved spacetime geometry. We show that the mass-field force term emerges naturally from standard weak-field derivations of GR, suggesting that the retarded-potential formalism and GR’s geometric description may represent two complementary ways of describing the same physics in the weak-field regime.