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[personal profile] jack
Does anyone understand pilot wave theory even a little bit?

Prodded by several recent articles, I've been trying to follow what it says, and am still quite unsure of the realities.

The analogy usually presented is, if you have a small oil drop on the surface of water, and the water container is subject to a regular pattern of vibration, the water forms standing waves in shapes affected by the edges of the container and any obstructions in the surface of the water. And the oil drop tends to move across the surface of the water following the paths in those waves.

If you look solely at the oil drop, you can't tell which of two equal paths it would follow, but you can predict it will take one of them with equal probability, and predict its motion probabilistically. And if you couldn't see the standing water waves, you could deduce something in that shape exists.

You can even get some analogies for weird quantum behaviour like the an electron passing through two parallel slits and experiencing interference with itself: the water waves form possible channels for the oil drop, and the oil drop goes through one slit or the other, but ends up only at certain places on the far side.

However, the analogy to actual quantum physics is still unclear to me. Not whether it's true, but even what people are suggesting might happen.

Are people suggesting there's some underlying medium like the water? In that case, isn't there some propagation speed? The water waves exist in a steady state once all the obstructions are set up, but they don't respond to changes instantly. If the water trough were miles long, the oil drop would set off following water wave paths that existed at the point it passes through, not the paths corresponding to the obstructions that are going to be in place when the oil drop passes through them.

And yet, as I understand it, no-one expects a propagation delay in quantum experiments. People keep checking it out, but there never is: it always acts like an electron propagates just like it is itself a wave.

I agree, if there WERE some delay, if you changed the slits at this time, and got one result, and changed them at another time, and got another result, that would be massive, massive, evidence of something, possibly of something like pilot wave theory. But AFAIK proponents of pilot wave theory aren't advocating looking for such delays, and don't expect to find any.

Contrariwise, if this is just an analogy, and the quantum equivalent of the water waves (equivalent to the wave function in other interpretations of quantum mechanics) propagates at "infinite" speed, then... that is undetectable, indistinguishable from other interpretations of quantum mechanics. But it raises red-flag philosophical questions about what "infinite speed" means when all the intuition from special (or general) relativity indicates that all physical phenomena are local, and are influenced only by physics of nearby things, and "the same time" is a human illusion like the earth being stationary. Even if you don't expect to detect the pilot wave, can you write down what it should be in a universe where physics is local? Does that in fact provide a way to make QM deterministic and independent of observers, even if you change the reference frame? Because it doesn't sound like it will work.

FWIW, those are very superficial objections, I don't understand what it's saying enough to actually evaluate in depth. But I don't understand why these don't show up on lists of "common objections and rebuttals". Common objections have confident rebuttals in several places, and I've *seen* articles about them, but not understood well enough. Can anyone explain better?


I do agree, the idea that QM equations are an emergent property of something else, ideally a statistical interpretation of a deterministic underlying reality, would be very nice in clearing up a lot of confusion. But AFAIK, the closest candidate to that is Many Worlds, which doesn't appeal to many people who want to get away from QM unpleasantness.