Gravitational time dilation, free fall, and matter waves

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.