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So even if you forget about the completely different interpretations of the wave function and the shape of droplets, there is a difference (well, many differences, but I chose this one) at the purely mathematical level. The equations governing the evolution of the wave function must be exactly linear and there can't be any debate about it because it's a matter of consistency. The equations governing the evolution of the shape of droplets are almost certainly nonlinear because there is no general constraint that would ban the nonlinearity, and they are therefore 99.999...% likely to occur. You may find situations and approximations in which the nonlinearities are small or the nonlinear equations emulate some linear ones for other reasons, but fundamentally they are very different.
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newolder wrote:Some of the problems associated with the de Broglie/Bohm “pilot wave” idea include the inability to treat spin correctly (for a component of spin in, say, the z direction would break the rotational symmetry of pilot waves) and the fact that the pilot waves must act superluminally and therefore contradict special relativity in order to yield an interference pattern.

Bohmian trajectories never cross the z=0 plane – the horizontal line in the middle of the picture, in this convention. A particle in the upper half stays in the upper half, and the same holds for the lower half. There's clearly no sense in which this correlation exists in quantum mechanics – or the real world – and this unphysical feature of Bohmian mechanics is also exploited by ESSW to show that the Bohmian paths are "surreal".

CdesignProponentsist wrote:

newolder wrote:Some of the problems associated with the de Broglie/Bohm “pilot wave” idea include the inability to treat spin correctly (for a component of spin in, say, the z direction would break the rotational symmetry of pilot waves) and the fact that the pilot waves must act superluminally and therefore contradict special relativity in order to yield an interference pattern.

I'm pretty sure I've heard somewhere that they don't in fact need to act superluminally. I could be wrong. If I find it I'll link it.

CdesignProponentsist wrote:I've been a fan of the pilot wave interpretation ever since hearing of it. It seems to match the behaviors all too closely to be entirely coincidence.

igorfrankensteen wrote:

CdesignProponentsist wrote:I've been a fan of the pilot wave interpretation ever since hearing of it. It seems to match the behaviors all too closely to be entirely coincidence.

I assume this is because waves behave like waves behave like waves. The dissimilarities with quanta, would be be likewise because waveparticles aren't caused through constant input of several sources of energy from outside, as the oil droplets are.

It is a very convenient illustration of wave behavior.

Ps, I enjoyed that just as the narrator says "the oil droplets almost never recombine," two of them do.

newolder wrote:The alternative (to superluminal) Bohmian view would be trajectories like this (from wiki):

To which Motl adds:

Bohmian trajectories never cross the z=0 plane – the horizontal line in the middle of the picture, in this convention. A particle in the upper half stays in the upper half, and the same holds for the lower half. There's clearly no sense in which this correlation exists in quantum mechanics – or the real world – and this unphysical feature of Bohmian mechanics is also exploited by ESSW to show that the Bohmian paths are "surreal".

DavidMcC wrote:...
Can yuou supply the wiki reference, newolder? ...

...
Bohmian mechanics, which is the most mature form of the de Broglie pilot wave theory does explain measurement through the mechanism of hidden variables (i.e. by saying that there is state in a quantum system which is hidden from us). However, it is also known that Bohmian mechanics needs to be nonlocal to make the hidden variable explanation work. Roughly this means that it implies faster-than-light signalling, which in turn makes it very hard to make sense of causality: in a universe where faster than light signalling can be done, effects can come before their causes. So my belief is that most physicists would say that Bohmian mechanics is not a good explanation.

newolder wrote:Bohmian mechanics implies superluminal communication (physics stack exchange).

Adapted pilot wave theory that does not require superluminal communication results in the "surreal" trajectories as shown in the image. (Motl)

...

PensivePenny wrote:I know this question is a little off topic, but can someone direct a quantum mechanics illiterati to something that can explain waves in a vacuum, specifically with regard to the double slit experiment? What medium is the wave being created in, if there is a single particle? Medium is how I see waves, though I can comprehend forces like magnetism, gravity etc causing waves too. What is the wave in the double slit experiment comprised of?

A link or search term would be appreciated.

DavidMcC wrote:

newolder wrote:Bohmian mechanics implies superluminal communication (physics stack exchange).

Adapted pilot wave theory that does not require superluminal communication results in the "surreal" trajectories as shown in the image. (Motl)

...

.... As has already been said. However, I am not sure that any of that is Bohm's own idea, or whether it is "fake" Bohmian theory, put up either due to misunderstanding or a deliberate attempt to discredit his ideas.

newolder wrote:...

Also, some problems with the theory are noted here.