Dancing Drops and De Broglie’s Pilot Wave

Just watched a Youtube video from Veritasium showing silicone oil droplets dancing on a vibrating surface of the same liquid.

Analogies are made between droplets guided by standing waves and quantum mechanics.  Much of this is universal to any wave phenomenon.  QM involves waves, depends crucially on the idea of waves, so it’s no surprise there are matches to be found between quantum phenomena and acoustics, mechanics, etc.   The match-up seems especially strong when de Broglie’s idea of Pilot Waves, or his earlier more comprehensive Theory of the Double Solution, is considered.

Pilot wave, or de Broglie’s original Theory of the Double Solution from which PW descended, is a no-go for me. I was fascinated with this idea long ago, in grad school. But it didn’t survive.

For one, it does a poor job dealing with multiple identical particles. Two electrons need two pilot waves. Just what is it that’s doing the waving? In the demo with the dancing drops, it’s the surface of the water or oil, a single “universal” shared entity filling space, with one wavefunction – height above the average surface. Attempts to make Pilot Wave quantum mechanics work like that fail. It’s inherent in the math of QM that each particle needs its own wave.

Then there’s metaphysical garbage to be collected. Suppose an electron goes flying along then whack! Right into a piece of metal. There’s be a circular pilot wave escorting it along until the electron stops – does the pilot wave suddenly stop? All at once? Does the part of it near the electron suddenly stop along with the electron while the outer parts continue? Is there an outward ring of sudden-slowing of the PW, expanding at the speed of light? Are there 10^hundreds of ’empty’ pilot waves fluttering through every point of space from all the electrons which suddenly changed motion or were cancelled out of existence by positrons?

Real QM doesn’t have an answer to such questions because we just throw away the wavefunction, and write a new one for the electron in its new home. This is unsatisfying to Human minds, but it’s what works. Reality is weird.

Finally, pilot wave theory is deterministics, and “realistic” in the sense of EPR paradoxes and Bell Theorem. PW will obey Bell’s inequalities. Reality, as measured by experiments since the 1990s, does not. Entanglement is real, and is described by Hilbert space mathematics of the sort that lets you fly past Bell’s limitations. PW just can’t do that.

So goodbye Pilot Wave, and I won’t waste time on meaningless fluff like Many Worlds. Interpretations based on subtleties of statistics don’t generalize or explain Delayed Choice experiments, and other interpretations… I could write a book. Copenhagen is empty, philosophically unsatisfying, but truly nothing better has come along. Copenhagen works for the practical everyday physicist or electronics engineer.

Hmm, I wasn’t expecting to write a short philosophy of physics essay on YT today, but there you go.


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