FDM as a physical substrate for the pilot wave, has this been examined

[mzhb]

TL;DR

Pilot wave theory requires a real physical wave field but leaves it unidentified. FDM is a real physical scalar field permeating all space, only detectable through influence. The math structures overlap. Has anyone formally looked at whether these are the same thing?

Pilot wave theory (de Broglie-Bohm) requires a real physical wave field permeating all of space to guide particle behaviour. The guidance equation is mathematically precise but the physical identity of the pilot wave has been left unspecified since 1927.
Fuzzy Dark Matter is an ultralight scalar quantum field permeating all of space, invisible, only detectable through gravitational influence on visible matter. The FDM field equation (Schrödinger-Poisson) and the pilot wave guidance equation both derive from a complex scalar field — polar decomposition into amplitude R and phase S, with guidance determined by the gradient of S.
The structural parallel seems significant. Has anyone formally examined whether FDM could be the physical substrate that pilot wave theory describes mathematically but leaves unidentified? Or is there a known reason this mapping doesn't work?
I've searched the literature and can't find this question addressed directly. I'm not a physicist — if this is obviously ruled out I'd genuinely like to know why.

 

[PeterDonis]

Fuzzy Dark Matter

Do you have a reference for this? Is this a dark matter hypothesis that appears in the literature?

 

[mzhb]

Do you have a reference for this? Is this a dark matter hypothesis that appears in the literature?

Yes — Fuzzy Dark Matter is an established dark matter hypothesis in the literature. It's also called ultralight dark matter or wave dark matter. The canonical reference is Hu, Barkana and Gruzinov 2000. A comprehensive recent review is Lam Hui's 2021 Annual Review of Astronomy and Astrophysics paper on ultralight dark matter. The Capanelli, Hu and McDonough 2025 paper on wave interference in self-interacting FDM is a recent example of active research in the area.
My question is specifically about whether FDM as a physical substrate for the pilot wave has been examined — not about FDM itself as a dark matter candidate.

 

[PeterDonis]

Hu, Barkana and Gruzinov 2000

This?

Lam Hui's 2021 Annual Review of Astronomy and Astrophysics paper on ultralight dark matter

This?

Capanelli, Hu and McDonough 2025 paper on wave interference in self-interacting FDM

This?

It's a lot easier if you provide links with references.

 

[PeterDonis]

whether FDM as a physical substrate for the pilot wave has been examined

What does "a physical substrate for the pilot wave" mean? The pilot wave is not a physical theory: it's an interpretation of quantum mechanics.

the physical substrate that pilot wave theory describes mathematically but leaves unidentified?

How does the pilot wave interpretation describe any "physical substrate" mathematically?

 

[mzhb]

Noted, here are the relevant links.

Hu, Barkana and Gruzinov 2000:
https://arxiv.org/abs/astro-ph/0003365
Lam Hui 2021:
https://arxiv.org/abs/2101.11735
Capanelli, Hu and McDonough 2025: https://arxiv.org/abs/2503.21865

 

[mzhb]

What does "a physical substrate for the pilot wave" mean? The pilot wave is not a physical theory: it's an interpretation of quantum mechanics.


How does the pilot wave interpretation describe any "physical substrate" mathematically?

That's a fair challenge. In de Broglie-Bohm theory the guidance equation determines particle trajectories from the wave function. The wave function is mathematically well defined but its ontological status — whether it represents a real physical field or just a calculational tool — is an open question even within Bohmian mechanics.

My question is whether FDM, as a real physical scalar field with similar mathematical structure, could serve as a physical realisation of that wave function. Specifically whether the polar decomposition of the FDM field equation produces dynamics analogous to the guidance equation.

I'm asking whether the mathematical correspondence exists and whether it's been examined. Not claiming pilot wave theory already posits a physical field.

 

[Demystifier]

@mzhb the pilot wave is not permeating space, if by space you mean the usual physical 3-dimensional space. The pilot wave lives in a different space, the multi-dimensional configuration space. Therefore your hypothesis cannot be right.

 

[mzhb]

@mzhb the pilot wave is not permeating space, if by space you mean the usual physical 3-dimensional space. The pilot wave lives in a different space, the multi-dimensional configuration space. Therefore your hypothesis cannot be right.

That's a fair and important point. Is there a formulation of Bohmian mechanics — perhaps field theoretic extensions — where the wave field does live in three dimensional space rather than configuration space?

 

[Demystifier]

That's a fair and important point. Is there a formulation of Bohmian mechanics ... where the wave field does live in three dimensional space rather than configuration space?

There is such a formulation, but it is very complicated.
https://arxiv.org/abs/1410.3676

 

[mzhb]

There is such a formulation, but it is very complicated.
https://arxiv.org/abs/1410.3676

Ok thank you

 

[PeterDonis]

My question is whether FDM, as a real physical scalar field with similar mathematical structure, could serve as a physical realisation of that wave function.

Okay, what does "a physical realisation of that wave function" mean? You still haven't answered that question.