[simiones]

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.

[oneshtein]

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

[simiones]

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.

[oneshtein]

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.

[simiones]

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