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Couder experiments ( https://www.youtube.com/watch?feature=player_embedded&v=W9yWv5dqSKk and https://hekla.ipgp.fr/IMG/pdf/Couder-Fort_PRL_2006.pdf), published in 2006, state that by dropping silicon droplets into a vertically vibrated bath, we can observe the whole paths of these droplets and see how interference works out.

1) Wouldn't this violate the uncertainty principle that states that $\sigma_x$ or $\sigma_p$ can never be zero? The only way I could imagine is that $\sigma_p$ becomes infinite. Can any experiment produce the case where $\sigma_p$ is infintie quantum-theoretically? (and is this paper's conclusion - that $\sigma_p$ is infinite during the experiments?)

2) This experiment is macroscopic; but some people are saying that this in fact reveals much about quantum world, and I am curious how macroscopic observation be directly applicable to microscopic world.

3) We all know that photons behave differently; we cannot see photons until they hit the screen and we can only know their interference patterns. We have to try to measure them before they hit the screen, but then interference is destroyed both in reality and in theory. Does this experiment imply that there might be a way to see the whole path and the interference pattern of photons together?

4) The path taken by each droplet seems still probability issues - while we can see them, there is no way we can predict exactly where the droplet goes. Does this experiment in any way reopen the question like Einstein's dream of determinism?

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Related: physics.stackexchange.com/q/38858/2451 –  Qmechanic Oct 2 '12 at 4:22
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I'll just try to answer 1). My take is that, at least in some sense, there is no violation of the uncertainty principle, as the droplet's coordinate and momentum are not defined very well: the droplet interacts with its own wave, so, for example, momentum is distributed between the droplet and its wave, and it's difficult to define the droplet's coordinate, as the droplet influences its surroundings through its wave as well. You may tell me that the droplet is classical, so its coordinate and momentum should be determined independently of its wave. While such approach is certainly legitimate, when we are talking about the uncertainty principle, we should make an apples-to-apples comparison with microscopic interference, in which case we don't divide the particle and, say, its electromagnetic field. In quantum mechanics we tend to assume that wherever and whenever we detect some influence of the particle, we measure its coordinate with some precision, although, e.g., the effective radius of the Coulomb interaction is infinite. By the way, one of the reasons the Couder experiment seems interesting to me, it shows that some traditional mantras about quantum interference, while relatively consistent, may look absurd when applied to the pretty similar case of the Couder experiment.

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Just curious: As the effective radius of the Coulomb interaction is obviously infinite, how can we even measure anything about the particle then... Its radius would be infinite.....? –  user27515 Oct 3 '12 at 1:56
    
@user27515: As I said, traditional mantras are relatively consistent. Yes, you can find an electron anywhere, but at large distances the photon transferred between the electron and the detector will have a small momentum (corresponding to a large wavelength), so the coordinate uncertainty will be large, and the momentum uncertainty can be small. –  akhmeteli Oct 3 '12 at 2:25
    
I got it. Thanks. –  user27515 Oct 3 '12 at 2:37
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