We demonstrate that the de Broglie wave of a particle in a gravitational field turns toward the region of lower 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 toward beaches. This approach implies that the motion is along a geodesic and explains the free fall qualitatively and quantitatively with only elementary algebra.

中文翻译：

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引力时间膨胀，自由落体和物质波动

我们证明了引力场中粒子的德布罗意波转向较低的引力区域，从而导致粒子掉落。这种转折是由时钟在较小电势下运行速度较慢引起的。我们以在浅水处较慢并转向海滩的海浪为类比。这种方法意味着运动是沿着测地线进行的，并且仅使用基本代数就可以定性和定量地解释自由落体。