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Fermat's principle of least time says that light always takes the fastest path to any point. So how can light know which is the fastest path without taking all the paths first?

Qmechanic
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user81026
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    Very good question! The answer is that light, in quantum mechanics, DOES take all possible paths. Well, at least it seems to do it if we formulate quantum mechanics in the path integral formalism. I think you might enjoy reading "QED: The strange theory of light and matter" by Richard Feynman. If you are mathematically up to it, look up "path integrals". Fermat will appear under a completely "new light" after that. – CuriousOne May 12 '15 at 09:19
  • Furthermore fastest path is not correct, extremal path is. And I guess for light this comes from the eikonal approximation of the wave equation and can be explained without QED. I am pretty sure this in done in Landau-Lifshitz II (Classical Field Theory). – Sebastian Riese May 12 '15 at 12:24
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    Possible duplicate: http://physics.stackexchange.com/q/59607/2451 and links therein. – Qmechanic May 12 '15 at 12:31
  • How can light know which is the fastest path without taking all the paths first? Because it does take all paths. Think of light as something like a seismic wave moving from A to B. It isn't just the houses on the AB line that shake. All the houses shake. – John Duffield May 12 '15 at 20:21
  • Related: https://physics.stackexchange.com/questions/375170/how-does-fermats-principle-of-least-time-follow-from-huygens-principle – Gavin R. Putland Aug 10 '18 at 08:01

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