Gravitational time dilation, free fall, and matter waves

TL;DR

This paper explains gravitational free fall using matter wave behavior and clock rate differences in gravitational fields, providing a new wave-based perspective without relying on geodesic motion.

Contribution

It introduces a wave-based explanation for gravitational free fall, avoiding the traditional geodesic postulate and using elementary algebra.

Findings

Matter waves turn towards regions of smaller gravitational potential.

Clocks run slower in smaller gravitational potentials, influencing wave behavior.

The approach explains free fall qualitatively and quantitatively.

Abstract

We demonstrate that a de Broglie wave of a particle in a gravitational field turns towards the region of a smaller gravitational potential, causing the particle to fall. This turning is caused by clocks running slower in the smaller potential. We use the analogy of ocean waves that are slower in shallower water and turn towards beaches. This approach explains the free fall qualitatively and quantitatively without postulating motion along geodesics and with only elementary algebra.