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Comment by whatshisface | Hacker News Reader

There is a small problem with your explanation: refraction can happen with single photons, which means that the "minimum path length" rule continues even as the wave formulation breaks down. If you say "the photon travels along all paths at the same time, finally choosing one path to have 'really' gone down," then you have to explain how it was able to move faster than light to collapse down to the single point where you found it on your camera's sensor.

There is indeed a mystery here. In fact, since the only option I know of that eliminates spooky FTL signalng and spooky hidden (unobservable) mechanics has spooky alternate universes, I feel safe in concluding that at least one spooky thing has to be happening, even though we don't know which one it is.

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Thinking about photons is bad for you, especially if you are doing quantum-optics. It is almost always better to think about quantum fields, and in this case the quantumness adds nothing to the physics.

The "photon" is just a quantum of excitation of the optical medium (in this case the EM compled with the electromechanical state of matter in it). These exictations obey wave equations, just as classical waves do, and hence Snell's law.

It's true that you can also (almost) think of photons as point-particles travelling over every possible path in time-space and then do infinite-dimensional path-integrals. That point of view is important for a physicist to understand, but it is not needed to explain refraction.

I'd say the last model is necessary for explaining refraction, but not for describing it (where a simpler wave model suffices).

Huygens explained refraction using classical wave velocities only. Though I agree there is a similarity between his notion wave-sources everywhere and path integrals. (Which is odd since path-integrals are a very particle oriented way of thinking).

What Huygens' explanation leaves slightly mysterious, is why (beyond a mathematical coincidence) this result just happens to also give the minimum-time result. Path integrals explain that very nicely.

You're describing quantum mechanics, but the phenomena here are classical. There is no mystery with Fermat's law, even if you do not accept wave optics and want a theory of light particles. At each instant in time a light particle can determine how its trajectory will bend based on purely local information. The bending of light is determined by the local variation in the index of refraction. Snell's law is what you get if the index of refraction jumps discontinuously. This is analogous to how in classical mechanics the trajectory of a particle is determined by the local variation in the potential energy function (or more generally, the Lagrangian), and how a particle's trajectory has a kink if the potential energy has a discontinuous jump. The particle bounces back if the jump is too high, which corresponds to reflection of light.

Well, here's why I wanted to bring up QM: the principle of least time is really most at home in geometric optics where beams of light are arrows and everything is steady-state. In that view, things are indeed nonlocal: I can alter the arrows drawn for a beam of light going from A to B by doing something over at point C. Wave optics would understand this as interference, but if we insist that we want to keep the arrows then we have to introduce the path integrals.

Essentially, geometric optics lets us draw arrows and assert refraction, QM lets us draw arrows and derive refraction, but wave optics doesn't really involve arrows at all.

Things aren't nonlocal in geometrical optics though. Something happens at C at the instant in time when the particle is at C. You can start a ray at any point in any direction, and just follow a straight line until you hit something. Then you determine what happens next based on local information at that point, and you continue. Ordinary tennis balls have the same property that the path from A to B can be altered by putting a wall at C.

By the way, wave optics is already QM in some sense. Maxwell's equations are the analogue of the Schrödinger equation for light. Geometrical optics is the analogue of classical mechanics.

Look at Bohm's interpretation of quantum mechanics and subsequent formulations for quantum field theory.

Hidden variables are possible for quantum mechanics, they just necessitate that the Universe is fundamentally non-local, offering a possible explanation for quantum entanglement results.

Von Neumann's rejection of hidden variables was not an absolute one but a conditional one; if the universe is local, then hidden variables cannot be invoked to explain the weirdness of the quantum world. Non locality opens the door to hidden variables.

AIUI photons are an observational phenomenon, the photon isn't travelling any path, the probability distribution is occupying all possible paths, the observation collapses the wavefunction and makes it so we can find the photon in a general locality.

I think the physics of QM is too far displaced from our natural ideas of how mechanical things work to be able to reason about in the way we would like.

I’m not a fan, but DeBB/Pilot Wave interpretation is also compatible with the predictions of QM.

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