There is the silicone oil droplet phenomena which is a classical version of the pilot wave, and it does reproduce some quantum behavior, including the double slit. That a pilot wave has been discovered (granted at macro scale) does make one reconsider.

https://youtu.be/WIyTZDHuarQ

It does not, really. The macroscopic realisation is not particularly surprising (although it is quite awesome and original). If you put a ball floating on top of a wave you will observe the predictions from a mathematical model of that system, which is exactly what the pilot wave theory is, and there is nothing surprising here. Moreover, the macroscopic model simulates something which by definition is an unobservable construction in the quantum model. It does not simulate any inherently quantum behavior (classical waves is a thing we already knew exists).

Nobody tells that walkers are simulate all quantum behavior and doing that correctly. However, they helps to understand some of quantum puzzles. For example, droplets have spin. Can you predict behavior of the classical droplet spin in compare to the puzzling quantum spin?

But you can do the same with classical setups that mimic some effects from the typical quantum mechanical formulations. Those classical experiments are indeed amusing and interesting, but they do not illuminate the "quantum puzzles", no matter whether they are modeled after pilot wave theory or after quantum mechanics. And very importantly, those amusing demonstrations do not scale! Sure, you can mimic with classical contraptions the pilot wave (or the wave function) of a single particle, but the nice intuitive demonstrations fail when you try to scale it up to more particles (or anything that would be exhibiting the interesting, nontrivial quantum behavior).

So, your prediction for walker droplet spin is that walkers, in kind of Stern and Gerlach experiment, will behave like classical magnets, not like quantum particles, right?

No, they would behave like a ball floating on top of a wave and given that there are waves involved there will also be interference patterns. There is nothing quantum here. Sure, in one particular way it looks like a quantum particle (to the extent of a cargo cult), but in all the important ways it does not (entanglement, computational power, generalisation to multiple particles).

I asking about outcome of Stern and Gerlach experiment. It's binary thing. Make public prediction, please.

Certainly, but then please first pose/define the question clearly. What do you call a macroscopic Stern-Gerlach experiment with balls floating on top of the waves of a fluid? It would be an amusing toy problem to work out if you define it for me. However, it does not change the main argument: there is nothing quantum in macroscopic experiments with water waves - interference does not imply "quantumness".

Lets define experiment as following (excuse me my bad English, please):

- vibrating bath with non-conductive, non-magnetic, non-paramagnetic, non-diamagnetic fluid;

- vibrating bath is wide enough to avoid excessive interference with reflected waves from bath sides;

- vibrating bath has regular pattern on top of fluid, without any irregularities in space of experiment;

- small charged droplets of fluid on top of bath;

- north and south poles of a magnet are placed horizontally, without touching of bath fluid or droplets, e.g. at sides of bath, OR over fluid, OR under bath;

- an apparatus creates droplets of same size with random spin in all 3 dimensions;

- droplets are forced to walk through the batch, starting at center line between north and south pole and following that line;

- without magnetic field applied, droplets must walk straight;

- an detectors to measure decline of droplet path from center line must be installed at end of magnetic pole.

I expect that, when magnetic field is applied, droplets will slide completely to left or completely to the right, like electrons in Stern-Gerlach experiment.

It's not a quantum experiment, of course, but it can provide insight on nature of quantum spin.

PS.

Sorry, droplets must be charged, not magnetic. Updated.

The main point of the Stern-Gerlach experiment was that the electrons hitting the screen were forming two distinct dots instead of a long spread out line, therefore proving that the angular momentum is quantised. In your example you will instead have simply a spread-out distribution because there is no quantisation of the angular momentum of your droplets.

The pilot wave usually refers to the spatial degrees of freedom, especially in these classical mock-ups with balls on top of waves. They do not properly addressed internal degrees of freedom like spin.

Unrelated to those macroscopic mock-ups, pilot wave theory actually has serious problems with the description of anything that is not a spatial degree of freedom.

You can still use pilot wave theory to describe the quantum behavior of the coordinates of a particle. But even then, the classical mock-ups we are discussing will not show anything inherently quantum - it will simply produce some interference patterns, that can be explained classically.

P.S. side note: An important part in the Stern-Gerlach experiment was that the magnetic field was not homogeneous, because it is the gradient of the field, not the field itself that causes the electrons to move.

IMHO, Stern-Gerlach experiment demonstrates interaction of magnet field with guiding wave mediated via particle, so I expect that magnet will steer particle-wave into same spots, thus will demonstrate «quantum» behavior of particle spin at macro level.

Without disrespect I insist that you are wrong about that. The spin degree of freedom is "internal", unrelated to the position of the particle. The pilot wave does not influence that spin, and if you have a big ball on top of a wave, that wave does not care about the angular momentum of the ball. The ball is big and classical, hence its angular momentum is (practically) not quantized.

The thread got a bit long, but if you are really interested in learning about this I would be happy to continue the discussion through email ([email protected]). You probably also need proof of some kind of qualification on my part - my online profile does prove that I work at a respected institute doing research on that topic.

As far as I know there is no analog of entanglement in these experiments. If someone has heard or read something in that regard, I'd be interested in a reference!

Nobody even tried to entangle two walkers. AFAIK, uncharged non-magnetic particle without any inclusions (e.g. bubbles) has spin and phase of vibration only. How to entangle them?

Moreover, spin is 3d, walker is 2d, phase is 1d, while our Universe is 3d. It's like studying of 2d/1d projection of 3d world.

> Which will lead to the conclusion that Special Relativity (which was extensively validated) is either wrong or incomplete.

Not necessarily. The simplest relativistic pilot wave theory requires only a preferred foliation of spacetime.

This is seemingly unappealing to most physicists, but recent work has shown that the wave function itself contains just such a structure, so the needed foliation is present in every interpretation of QM.

Did you saw double slit experiment reproduction in 2D macro?: https://www.youtube.com/watch?v=nsaUX48t0w8

Observer breaks interference pattern.