Ether is a physical thing, while quantum field is a mathematical model of the physical thing. Don't mix physics and mathematics, please.

Nothing in quantum theory is understood at a level where we can say "this is a physical thing" vs "this is a mathematical abstraction of the physical thing", like we can say for classical physics. In classical physics, it's easy to say "masses and speeds and positions and forces are physical things, while energy or the Langrangian or the Hamiltonian are mathematical tools".

But in quantum physics, we have things like the Schrodinger equation (or the QFTs) where it's not clear. They don't appear to be physical, but we also have the Bell inequalities that suggest there can't be an objective physical layer beneath them either, so we are left with a conundrum.

I think a lot of people do believe that quantum fields are real physical things, and actually "more real" than the classical intuitions we have. In this view, the electron field or the electric field are what actually exists, and balls or water or ether are the abstractions.

Yes, this is the problem I'm talking about. We are not understanding physics at quantum level, so we are using mathematical model to describe reality, but it creates problem when we are starting to understand the physics.

Hydrodynamic quantum analogs are macroscopic objects with quantum behavior, which we can study. We can clearly see, with our own eyes, medium, particle, it pilot wave, and their interaction. For example, double slit experiment is not a mystery anymore: it just self-interference of pilot wave.

I know about the hydrodynamic analogues, and I've seen the double-slit experiment with the bouncing droplet. However, it is unfortunately not a very good model, as it requires changes in the wave to propagate at infinite speed in order to explain other experiments (the ones that fail Bell's inequalities). And that in turn causes many other problems as well. Not to mention, the pilot wave interpretation actually needs lots of work that no one has done yet to actually concur with QFT and the extraordinarily precise experiments that have confirmed the results there. So, it's a particularly problematic interpretation of quantum mechanics, despite having the neat hydrodynamic model.

Hydrodynamic model is not an interpretation or a theory - it's a model. Models are not perfect, but they are physical, they are real things in the real world, no need to prove anything, because they are the proof.

HQM exists, it demonstrates quantum behavior, it has the pilot wave. If QFT doesn't fit the real world, then it is bad for theory, not for the real world.

The hydrodynamic analogue of quantum mechanics has some behaviors of QM, but not all. It's a nice analogy, and it is a real physical system of course, but it is not how elementary particles behave.

If you construct a hydrodynamic experiment where two droplets are bounced on the same wave in different directions (analogous to two entangled particles moving in different directions), and then performed simultaneous measurements on them far away from each other, you would not see the same correlations between the measurements on the separate droplets that you see when doing this experiment with entangled particles.

However, if you perform your measurement on one side, and after enough time on the other, you would see the expected correlation: the measurement on droplet A modifies the pilot wave, and that modification is carried over to affect the behavior of droplet B after some time. In experiments on elementary particles though, this time is 0, or at least much less than distance/c, which is why we say that QM pilot wave theory is non-local.

> If you construct a hydrodynamic experiment where two droplets are bounced on the same wave in different directions (analogous to two entangled particles moving in different directions), and then performed simultaneous measurements on them far away from each other, you would not see the same correlations between the measurements on the separate droplets that you see when doing this experiment with entangled particles

Why not? And what "measurement" means for walking droplets, when we can see the whole situation just by looking at it?

Measurement means the same thing in classical and quantum mechanics: you interact with the system using a measurement apparatus. For the particular experiment I'm thinking of, you'd have to interact with the bouncing droplets to measure some property that is shared by both through their common pilot wave. Most likely this should be something like adding a wave filter and seeing if the droplet is dissolved or not, similar to a polarization filter for light. The key is to perform the two measurements in a way that should show some correlation, such as checking for polarization under non-orthogonal angles.

The reason why I'm certain that this experiment will not reproduce the quantum effect, even though I didn't perform it, is that classical wave polarization is a local phenomenon, it propagates at the speed of light (or much slower) from the location where the polarizer is added. Conversely, the kinds of correlations that have been observed between entangled particles are non-local: they can't be explained by the two particles exchanging information at speeds lower or equal to the speed of light. This is well established in experiments related to Bell's inequality. It is also well established in experiments that this doesn't hold true for classical systems.

I'm scratching my head about how to reproduce Bell inequality in macro, to see what's going on...

It's not very hard to perform Bell test-style experiments with macroscopic objects, the problem is that the Bell inequality actually holds for them. Many classical physics phenomena produce pairs of objects whose properties must be shared, analogous to quantum entanglement.

In fact, the inequality in Bell's theorem is based exactly on how classical statistics works: if you and I randomly choose to measure some aspect of each of a pair of "entangled" objects, and assuming the result of our measurement can only be +1 or -1, then on average the sum of our measurements will be less than or equal to 2. It turns out though that this logic doesn't work for entangled quantum objects.

And one small note here: based on everything we know, the key here is quantum entanglement, not scale. That is, if you could entangle two basketballs or planets for long enough to perform a Bell test on them, they would likely reproduce the particle results. However, this property of quantum systems is very hard to preserve for such a large system with so many ways of interacting with the environment and experiencing decoherence.

The problem with walking droplet is that they have no polarization. However, we can use a pair of walkers, which walk together, to try to see how they walk through a line of pillars at different angles. It should work and produce similar results to results produced by polarized filters with light.

Maybe, it will be possible to make two entangled pairs of walkers and then see what happens to them.

Aren't the waves in the walking droplet experiment transverse waves, that do have polarization? Polarization is a property of waves, not particles.