Fermat's principle is an outcome of constructive interference of waves. It works both for classical and quantummechanical descriptions. E.g. check https://phys.libretexts.org/Bookshelves/University_Physics/U...
reply> a ray of light has to know where it will ultimately end up before it can choose the direction to begin moving in
replyA ray of light doesn't know or choose because it has no agency, just like an apple doesn't know or decide to fall because of gravity. It's an anthropomorphization.
True, so the interference is the "computation"(heavy emphasis on quotes) which gives rise to the principle.
reply> a ray of light has to know where it will ultimately end up before it can choose the direction to begin moving in
replyI'm no physicists, so I guess I'll ask it: Why?
Also related, why do some ray of light then "see" a black hole yet decide to head into them anyways, if they saw it before they went in that direction? Seems like a dumb move :)
Its future isn't over there because it moves in that direction, instead it moves in that direction because its future lies over there.
replyRelatedly:
> [General Relativity] basically says that the reason you are sticking to the floor right now is that the shortest distance between today and tomorrow is through the center of the Earth.
https://physics.stackexchange.com/questions/250800/gr-and-my...