A What’s the physical nature of the pilot wave?

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1. Apr 14, 2017

Maxwell's Demon

Within the context of the de Broglie-Bohm pilot-wave theory, can anyone explain what the pilot wave is in physical terms? I’m having a hard time understanding how, for example, the pilot wave influences the trajectory of a photon in the double-slit experiment. Are we dealing with electromagnetic potentials in a background field, which exert a force on the photon as it moves?

Shouldn’t there be a reasonably straight-forward way to alter the path of the photons by inducing another source of pilot waves, such as another photon source acting perpendicular to the path of the photons?

It seems like there should be some way to determine if the pilot wave is real by performing some kind of experiment like this to directly alter the shape of the pilot wave, and settle the question once and for all. But I can’t seem to find a phenomenological explanation of the pilot wave which would provide a practical means of interacting with it.

Does anyone have any insight on this?

2. Apr 14, 2017

Demystifier

Think of pilot wave $\psi(x,t)$ as something similar to the principal function $S(x,t)$ of Hamilton-Jacobi formulation of classical mechanics. If you are unfamiliar with classical Hamilton-Jacobi equation, try to learn (and ask questions) about that first.

3. Apr 14, 2017

Maxwell's Demon

Thanks - you're right; I've got a lot of studying to do before before I can understand this. I found a Wiki page that discusses the quantum potential, which seems to be the key term in the quantum Hamilton–Jacobi equation that determines the Bohmian trajectories of particles in the double-slit experiment (if I’m reading this right the action S reduces to the classical limit as the quantum potential goes to 0?):
https://en.wikipedia.org/wiki/Quantum_potential

That page describes the quantum potential in terms of “a self-organising process involving a basic underlying field” without discussing that underlying field explicitly, but I gather from other articles that this is a background quantum field in equilibrium.

It also mentions the Aharonov-Bohm effect: “Also the shift of the interference pattern which occurs in presence of a magnetic field in the Aharonov–Bohm effect could be explained as arising from the quantum potential.” (that statement linked to this paper: https://arxiv.org/pdf/quant-ph/0308039.pdf ) So a magnetic vector potential influences the quantum potential for a charged particle, but I don’t see a method for influencing the quantum potential of a photon.

And even if there’s a way to do that, it seems that it could just as readily be explained within the conventional interpretation of quantum theory, which isn’t helpful.

Surely there has to be some way to determine whether the pilot wave is physical. At the very least shouldn’t there be some technological method for moving around the interference pattern with some kind of external field generator, sort of like a powerful magnet distorts the image on a CRT monitor…because we already know that the magnetic vector potential and the scalar electric potential influence the wave function, right?

4. Apr 14, 2017

SlowThinker

5. Apr 14, 2017

Denis

DBB theory does not have an answer to your question. In dBB theory, the wave function describes some really existing field, that's all. A physical description of the nature of this field will be the job of some more fundamental theory.

Think of the wave function as describing, in a general way, the influence of all the environment (including all the classical parts) on a system. Whatever the external things which have influence, it would define how the actual state changes, given its actual configuration. The actual configuration is some $q\in Q$, the result is some velocity $\dot{q}= F(q,X)$. So, quite universal, one can assign to that unknown $X$ some function $\psi(q)$ on the configuration space, which defines how $X$ influences the resulting velocity if the configuration is $q$. So, this would be, in the most general form, a map $X \to F_X(q)$.

The dBB formula is a special, particular case of this, with $F_X(q) = \nabla \Im \ln \psi_X(q)$, a formula which guarantees that part of the Schrödinger equation will be a continuity equation for the probability flow. But it is, nonetheless, close enough to this most general case, to guess that it is not really the wave function $\psi(q)$ which is that part of reality which defines, via the guiding equation, the velocity, but that it is only a placeholder for some unknown entity $X$ which defines some effective $\psi(q)$ in some more fundamental theory.