A Transactional Wave Model of Gravitational Time Dilation and Geodesic Motion

In this paper, we develop a localized wave-mechanical model of gravitational acceleration and geodesic motion, building on the time-symmetrical emitter-absorber framework of the Transactional Interpretation of Quantum Mechanics and the wave-particle energy-transfer model developed by Watts and Mead [1]. The central proposal is that a global network of emitters and absorbers establishes a background temporal reference, while localized, high-density standing-wave configurations, interpreted here as matter, introduce a spatially varying phase lag into that reference. This phase lag appears macroscopically as gravitational time dilation. We then ask whether the resulting clock-rate gradient can be treated as an optical medium through which quantum wave fronts propagate. Using the Schwarzschild gravitational clock-rate profile as the target macroscopic limit, we define an effective temporal refractive index and show that wave fronts traversing this index gradient bend toward regions of slower proper time by the same mechanism that bends light in a gradient-index optical medium. In this formulation, geodesic motion is not introduced as a separate force law at the quantum scale. It emerges as the path of phase stationarity and earliest constructive interference in a spatially varying temporal medium. The model is intended as a mathematical and physical analogue, not as a replacement for general relativity. Its purpose is to provide a concrete wave-based interpretation of why light and matter follow the same gravitational trajectories, consistent with the Equivalence Principle, while remaining compatible in spirit with a transactional account of quantum energy transfer.