In de Broglie–Bohm theory, the pilot wave guides particles but is usually treated as an abstract object in configuration space.

I’m exploring whether the pilot wave can instead be understood as a real constraint structure that exists prior to measurement and determines what outcomes are possible.

From this view:

• In the double-slit experiment, what passes through both slits is the constraint structure, not a particle.

• Interference arises from how these constraints overlap.

• Measurement corresponds to a selection (locking-in) of one allowed outcome, not the revelation of a pre-existing classical fact.

My question:

Is there any principled reason the pilot wave cannot be treated as a real physical or geometric constraint, rather than a purely mathematical guide?

1 hour ago, Spyroe Theory said:

In de Broglie–Bohm theory, the pilot wave guides particles but is usually treated as an abstract object in configuration space.

I’m exploring whether the pilot wave can instead be understood as a real constraint structure that exists prior to measurement and determines what outcomes are possible.

From this view:

• In the double-slit experiment, what passes through both slits is the constraint structure, not a particle.

• Interference arises from how these constraints overlap.

• Measurement corresponds to a selection (locking-in) of one allowed outcome, not the revelation of a pre-existing classical fact.

My question:

Is there any principled reason the pilot wave cannot be treated as a real physical or geometric constraint, rather than a purely mathematical guide?

Lack of any evidence for its physical existence, I suppose. Pauli described the pilot wave concept as an "uncashable cheque", as it makes no observable predictions that distinguish it from regular QM. As it has no predictive value it seems to add nothing as a scientific model and can thus be dispensed with on the basis of Ockham's Razor.

Pilot wave is considered more an interpretation much like the Copenhagen interpretation under QM.

Its premise is more deterministic than probabilistic however the Copenhagen is what is considered more in alignment with QM.

There were numerous issues with pilot wave in so far as entanglement and hidden variables as one of the reasons as to why the Copenhagen interpretation became more accepted.

Personally I dont see any means where it would tighten constraints that are not already accomplished by statistical weighted average for most likely position of a particle. Perhaps looking at how each interpretation would work with Dirac Delta functions might provide some insight.

Edited Tuesday at 07:24 PM1 day by Mordred

In the De Broglie-Bohm theory the pilot wave is source of a so-called quantum potential, that must be added to all other potentials acting on the particle. This quantum potential produces infinite repulsion in places where \( R=\left|\psi\right|^{2} = 0 \) (interference), as its form is proportional to \( \frac{\nabla²R}{R} \).

You are using "configuration space" in a sense that is not familiar to me. "Configuration space" in mechanics usually refers to the set of all accessible positions.

I don't know what you mean by "a real constraint structure". Constraints in mechanics are obstructions to how the system can move (holonomic constraints), like a particle being forced to be at the tip of a rigid rod, etc.

Your vocabulary is a bit weird, and I at least do not understand what you mean.

The theory has its virtues, but makes calculations extremely awkward, not least the ones pointed out by @Mordred .

Besides Pauli's objections, Einstein also seems to have said that it goes against every physical intuition to conceive of something that acts on other physical entities, but cannot be acted upon.

John Bell was one of its most notorious advocates. He didn't say it must be correct. He said it must be studied.

</my two cents>

IMO there is the possibility that it's but a version of a more elegant idea that we haven't been able to fathom so far.

Among other things, point particles cannot carry irreducible representations of the relevant space-time groups, so it could be the case that there's a generalisation of it having to do with scalars, rather than point-like densities. That seems healthier in the context of field theory.

</>

Edited yesterday at 02:55 AM1 day by joigus
Latex editing

Thanks, that helps clarify where you’re coming from. I’m not trying to redefine the Bohmian formalism or replace the quantum potential. I’m using informal language to ask a more basic question about interpretation.

When I say “constraint,” I don’t mean a mechanical constraint like a rigid rod. I mean that the wavefunction already seems to shape what is allowed and what is forbidden before any measurement happens (for example, nodes where outcomes never appear). That feels more like a pre-existing structure than just a bookkeeping device.

By “configuration space,” I was just pointing to the usual issue that the wavefunction lives somewhere different from the particle we observe, which is part of why people find the pilot wave ontologically strange.

I agree Bohmian mechanics may not be the final story. My interest is whether its difficulties are a hint that the pilot wave is pointing toward a more intuitive underlying picture, rather than something that “acts but cannot be acted upon,” as Einstein worried.

This video is not too bad. I usually dont subscribe to videos other than lectures but this one isn't too bad.

David Bohm’s Pilot Wave Interpretation of Quantum Mechanics

Science News, Physics, Science, Philosophy, Philosophy of Science

She touches on the key points between the Copenhagen interpretation ( non locality in particle physics terms specifically aa applied to interactions). The issue this causes with Lorentz invariance. The 3 principle equations of the the theory.

Some details to add is that the Hamilton-Jacobi usage is nonlocal and non linear as opposed to the linearity of the Schrodinger equation.

The other key point is there is no testable means of showing its more or less accurate than the Copenhagen interpretation aka standard QM. It makes no predictions that will differ from those of QM.

The other issue being the non locality when it comes to QFT. There are papers available of course presenting possible solutions to this problem but it's still in the works so to speak.

This should help answer sone of your questions on our cross post lol.

41 minutes ago, Spyroe Theory said:

When I say “constraint,” I don’t mean a mechanical constraint like a rigid rod. I mean that the wavefunction already seems to shape what is allowed and what is forbidden before any measurement happens (for example, nodes where outcomes never appear). That feels more like a pre-existing structure than just a bookkeeping device.

By “configuration space,” I was just pointing to the usual issue that the wavefunction lives somewhere different from the particle we observe, which is part of why people find the pilot wave ontologically strange.

I would like you to consider the following. A wavefunction under QM and QFT as you are aware is a probability graph. All functions are graphs but not all graphs are functions.

Those wavefunctions do have relevant constraints. For example causality is a constraint with regards to time dependent wavefunctions. Example the Dirac equations or Klein Gordon, Schrodinger etc

Other constraints applied include conservation laws for probability wave functions applicable to closed groups.

From those constraints anything not allowed is not included in the probability wavefunction.

This is a very technical article describing boundary conditions as applicable to quantum mechanics included in the article is the Borne approximation or Borne condition.

"Quantum boundary conditions"

https://dottorato.fisica.uniba.it/wp-content/uploads/2018/03/tesiPhD-Garnero-compressed.pdf

all boundary conditions is a form of constraint. All finite groups are also constrained.

What many laymen or those not mathematically versed in physics often do not realize is every statement under physics is mathematically defined or described. This includes the axioms of a physics theory, group etc.

Simple example symmetry ie laws of physics must be the same regardless of reference frame in the Minkowskii group is mathematically defined via

\[\mu\cdot\nu=\nu\cdot\mu\]

Constraints and boundary conditions are also mathematically defined.

Edited yesterday at 04:34 AM1 day by Mordred

16 hours ago, Spyroe Theory said:

In de Broglie–Bohm theory, the pilot wave guides particles but is usually treated as an abstract object in configuration space.

I’m exploring whether the pilot wave can instead be understood as a real constraint structure that exists prior to measurement and determines what outcomes are possible.

From this view:

• In the double-slit experiment, what passes through both slits is the constraint structure, not a particle.

• Interference arises from how these constraints overlap.

• Measurement corresponds to a selection (locking-in) of one allowed outcome, not the revelation of a pre-existing classical fact.

My question:

Is there any principled reason the pilot wave cannot be treated as a real physical or geometric constraint, rather than a purely mathematical guide?

@joigus

You are using "configuration space" in a sense that is not familiar to me. "Configuration space" in mechanics usually refers to the set of all accessible positions.

I don't know what you mean by "a real constraint structure". Constraints in mechanics are obstructions to how the system can move (holonomic constraints), like a particle being forced to be at the tip of a rigid rod, etc.

Your vocabulary is a bit weird, and I at least do not understand what you mean.

I think you are referring to what are often called the 'equations of constitution' (the Physics) and the 'equations of compatibility' (often geometric).

A simple example from incompressible fluid mechanics would be

Bernoulli's equation (an equation of motion ie one connecting time and space) is an equation of constitution.

An equation of compatibility would be A1 V1 = A2 V2 where A is area and V is velocity.

For pilot waves various possible equations of constiitution have already been listed,

An equation of compatibility would need to modulate the amplitude of the pilot wave in such a way tha its amplitude is zero except in the vicinity of the particle.

Does this help ?

Sorry I'm having great trouble witth computers a the moment.

I was under the impression that a recent experiment has cast serious doubts on the viability of Bohmian mechanics:

https://www.nature.com/articles/s41586-025-09099-4

This is essentially a direct conflict between what BM predicts in that situation, and the observed outcome. What it means is that, if I understand the implications correctly (and I’m not sure that I do), the concept of “particle” that BM is constructed on does not correspond to particles in the real universe.

Edited 9 hours ago9 hr by Markus Hanke

Interesting study, hadn't seen that one before and your judgement on the paper is accurate. Another factor to consider is the particle spin itself. One known problem with the particle view is say the electron in the particle view it's angular momentum exceeds c. However in the QFT field excitation view this is resolved.

Im still digging into how the Pilot wave theory deals with that (assuming solutions have been presented) more for my own curiosity lol. If I do find some decent literature in that regard I will share here

4 hours ago, studiot said:

I think you are referring to what are often called the 'equations of constitution' (the Physics)

Aaah... This sounds more like it. Although I wouldn't call the various equations coming from the Schrödinger equation "constitutive equations". Constitutive equations in physics implement properties of the medium, while the Bohmian wave implements properties of the system under study in reaction to that medium. After all, they come from a simple change of variables in the Schrödinger equation. But maybe that's just a matter of words.

5 hours ago, Markus Hanke said:

I was under the impression that a recent experiment has cast serious doubts on the viability of Bohmian mechanics:

https://www.nature.com/articles/s41586-025-09099-4

4 hours ago, Mordred said:

Another factor to consider is the particle spin itself.

I'm not surprised that the theory in its form of particle + wave does not work. That point-like particles are inconsistent with relativity has been known for a long time. So long a time that the scientific community as a whole seems to have forgotten, as the whole business painfully ground to a halt during the first decades of the 20th century.

A topological scalar field consistent with local gauge invariance might do the required jobs. A point particle is hopeless.