Physicist: Light travels at different speeds in different materials. A particle that somehow “scouts the future” and then picks the fastest path to get where it’s going seems impossible. The time, T, that it takes to traverse a path is D/V, where D is the length of the path and V is the speed. By changing x you change the path, and the amount of time T it takes to move along that path. Waves (light, sound, water, whatever) propagate perpendicular to their wave crests.