There are these popular experiments with droplets having wave-particle duality, e.g. here is Veritasium video with 2.3M views, great webpage with materials and videos, a lecture by Couder.

Among others, they claim to recreate:

  1. Interference in particle statistics of double-slit experiment (PRL 2006) - corpuscle travels one path, but its "pilot wave" travels all paths - affecting trajectory of corpuscle (measured by detectors).

  2. Unpredictable tunneling (PRL 2009) due to complicated state of the field ("memory"), depending on the history - they observe exponential drop of probability to cross a barrier with its width.

  3. Landau orbit quantization (PNAS 2010) - using rotation and Coriolis force as analog of magnetic field and Lorentz force (Michael Berry 1980). The intuition is that the clock has to find a resonance with the field to make it a standing wave (e.g. described by Schrödinger's equation).

  4. Zeeman-like level splitting (PRL 2012) - quantized orbits split proportionally to applied rotation speed (with sign).

  5. Double quantization in harmonic potential (Nature 2014) - of separately both radius (instead of standard: energy) and angular momentum. E.g. n=2 state switches between m=2 oval and m=0 lemniscate of 0 angular momentum.

  6. Recreating eigenstate form statistics of a walker's trajectories (PRE 2013).

They connect these experiments with de Broglie-Bohm interpretation, e.g. supported by measurement of average trajectories in double-slit experiment (Science 2011).

While in Couder's experiments oscillations are due to external periodic force, for quantum physics they would need e.g. intrinsic oscillations of particles - called de Broglie's clock or Zitterbewegung - separate stack.

I wanted to ask about the issues of using its intuitions to understand quantum mechanical analogous?


marked as duplicate by knzhou, ZeroTheHero, Jon Custer, Buzz, John Rennie newtonian-mechanics Jan 4 at 7:57

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  • $\begingroup$ Wanting to understand recreating eigenstate from statistics of trajectories, it is worth to look at MERW: en.wikipedia.org/wiki/Maximal_entropy_random_walk . It shows that standard random walk/diffusion often uses only approximation of the maximal entropy principle, required by statistical physics models - doing it right, Maximal Entropy Random Walk turns out to lead to stationary probability distribution exactly like for quantum ground state - with strong localization property. $\endgroup$ – Jarek Duda Feb 28 '18 at 6:12

I think there's a straightforward issue: it can not be an analogue for entanglement, which is an example of superposition in the multi-particle case. If you have multiple droplets, they will not be guided by a wave analoguous to the wave function on configuration space, but by a real physical wave in 3D.

  • $\begingroup$ Indeed performing Madelung transformation for single particle we get continuity equation plus Hamilton-Jacobi equation with additional hbar-order interaction with the particle. However, analogously doing it for multiple particles would need much more complex separate fields - while here everything is done with just a single shared field. So the main question is: what are the arguments for the need of separate pilot fields for multiple particles? $\endgroup$ – Jarek Duda Feb 16 '18 at 11:44
  • $\begingroup$ Be careful, the pilot fields are not necessarily separated in the multiple particle case. In fact, if they were, there would be no entanglement. You can have states like $\psi(\vec{x}_1,\vec{x}_2)=\phi_1(\vec{x}_1)\phi_2(\vec{x}_2)+\phi_2(\vec{x}_1)\phi_1(\vec{x}_2)$ which don't factor in a product of one-particle states. The argument is simply that we can make those states or those states exist in nature. It's as simple as that. $\endgroup$ – Raskolnikov Feb 16 '18 at 16:03
  • $\begingroup$ Sure, the "simplest" example is helium atom, where in fact the two electrons are highly anti-correlated. However, in quantization of walking droplets trajectories, they are usually also highly anti-correlated. To get real counterexample, you need inseparable two-particle state with essentially different behavior than for walkers? And while walker's single wavefield definitely cannot reconstruct all quantum phenomena (e.g. spin direction required for EPR/Bell violation?), it brings some interesting intuitions - is it right to take these intuitions to QM? $\endgroup$ – Jarek Duda Feb 16 '18 at 16:18
  • $\begingroup$ this answer is not a proof but an intuition. a (dis)proof would have to be mathematical. agreed the multiparticle case for pilot wave hydrodynamics seems not yet to have been analyzed much in the literature so far and could be tricky. there is a sense in which QM sch. eqn. is itself a wave superposition for so called "non interacting particles" but this is apparently rarely pointed out anywhere. btw, historically, difficulty of interpreting the multiparticle case by QM founders/ pioneers is one of the original rationales for rejection of local/ classical theories for QM. $\endgroup$ – vzn Feb 16 '18 at 16:25

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