What waves in a double slit experiment is the "hidden subquantic medium"

[Asympotically_fat]

This is a post from from the orginal thread that I had started to reply to. It seems to me there is a bit of a misunderstanding going on:

@mpc755

Yes, de Broglie agreed with Bohm in terms of the “subquantic medium”. However, Bohm considered the wave-function wave to be the pilot-wave. This is what de Broglie disagreed with when he said, “to render impossible the adoption of the pilot-wave theory.”

NON-LINEAR WAVE MECHANICS
A CAUSAL INTERPRETATION
by
LOUIS DE BROGLIE

"During the summer of 1951, there came to my attention, much to my surprise, a paper by David Bohm which appeared subsequently in The Physical Review [3]. In this paper Bohm went back to my theory of the pilot-wave, considering the W wave as a physical reality He made a certain number of interesting remarks on the subject, and in particular, he indicated the broad outline of a theory of measurement that seemed to answer the objections Pauli had made to my approach in 1927.3 My first reaction on reading Bohm’s work was to reiterate, in a communication to the Comptes rendus de VAcademic des Sciences [4], the objections, insurmountable in my opinion, that seemed to render impossible any attribution of physical reality to the W wave, and consequently, to render impossible the adoption of the pilot-wave theory."*

de Broglie says it is impossible to attribute physical reality to the wave-function wave.

There are two waves in de Broglie’s double solution theory. There is the wave-function wave which is statistical, non-physical and is used to determine the probabilistic results of experiments. There is also a physical wave in the hidden subquantic medium which guides the particle.

Bohmian mechanics: one wave.

de Broglie’s double solution theory : two waves. One mathematical. One physial.

You posted that quote earlier, but as I pointed out he must’ve changed his mind and posted a paper to show that point.

The wavefunction is not a physical wave in any interpretation that I am aware of and certainly not in Bohmian mechanics. The problem with interpreting it as a wave is that the function in a classical wave equation describing a physical wave would be a real-valued function u(x,y,z,t), whereas the wavefunction of a two-particle system (for example) in position space is a complex-valued function Ψ(x[sub]1[/sub],x[sub]2[/sub],y[sub]1[/sub],y[sub]2[/sub],z[sub]1[/sub],z[sub]2[/sub],t), which looks nothing like something that could describe a physical wave.

The physical wave in Bohmian mechanics is the pilot-wave, which is precisely the same wave that de Broglie talks about in his paper on double-solution. Note he describes the same Hamilton-Jacobi equation and continuity equation as described here. Similiarly the wavefunction can be derived from Bohmian mechanics, but importantly it is statistical in nature.

I.e. “Double solution theory” is just de Broglie’s own term for de Broglie-Bohm theory.