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## Main Question or Discussion Point

Photons(light) follow the fermat's principle of least time...so do all elementary particles also follow fermat's principle of least time?..say electron,proton etc..

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Photons(light) follow the fermat's principle of least time...so do all elementary particles also follow fermat's principle of least time?..say electron,proton etc..

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Quantum mechanically, to find the probability of ending up at some point, you add up every possible path, weighing each path with a phase factor of [itex]e^{i S}[/itex], and square the result. For the most part, paths interfere destructively because they all have wildly different phase factors. But for paths where [tex]S[/tex] is an extremum (minimum, maximum, saddle point), you end up with a lot of paths with the same phase factor, and these constructively interfere. So as long as quantum effects aren't too strong, the most dominant contribution to the probability comes from that path where [tex]S[/tex] is an extremum. This is simply the classical solution to the Euler-Lagrange equations of motion.

Fermat's principle played an important role in de Broglie's development of his wave theory as well as to the principle of extremal action.

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Read up on path integrals if you like.

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