The Pilot Wave Interpretation of Quantum Mechanics

Continuing the discussion from The Meaning of "Random":

Is that right @PdotdQ? What about the oil droplet analogues of quantum mechanics, which show a non-local wave coupled with a particle, in a classical system can mimic QM?

Yves Couder, Emmanuel Fort, and coworkers recently discovered that a millimetric droplet sustained on the surface of a vibrating fluid bath may self-propel through a resonant interaction with its own wave field. This article reviews experimental evidence indicating that the walking droplets exhibit certain features previously thought to be exclusive to the microscopic, quantum realm. It then reviews theoretical descriptions of this hydrodynamic pilot-wave system that yield insight into the origins of its quantum-like behavior. Quantization arises from the dynamic constraint imposed on the droplet by its pilot-wave field, and multimodal statistics appear to be a feature of chaotic pilot-wave dynamics. I attempt to assess the potential and limitations of this hydrodynamic system as a quantum analog. This fluid system is compared to quantum pilot-wave theories, shown to be markedly different from Bohmian mechanics and more closely related to de Broglie’s original conception of quantum dynamics, his double-solution theory, and its relatively recent extensions through researchers in stochastic electrodynamics.

These experiments, for example, can replicate a hydrogen atoms orbits, thin slit interference, non-specular reflection, couplets, and more. This page has a great summary: Also there are great videos online:

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As I understand it, all that these experiments can show is that nonlocal hidden variable theories can replicate standard QM. This is at the level of mathematical equivalence: any computation that I can do with standard QM can also be made using oil droplets.

The main point that they cannot show is whether in reality there exists an analog to their “surface of a vibrating fluid bath”. It is well and good to show that the standard QM and pilot-wave QM are mathematically equivalent. But unless they can show that these pilot waves are real physical entities, then this mathematical equivalence is just a calculational tool: pilot-wave mathematics can be used as an aid to solve QM calculations.

The pilot-wave proponents will level the same charge against me: I cannot show that the wavefunction collapse picture is the ontologically correct view of quantum mechanics. Until I can do so, my standard QM is just a calculational tool to solve pilot-wave equations.

In the end, it is a matter of choice whether you want to give up nonlocality or determinism. Giving up nonlocality in the pilot-wave interpretation entails a preferred observer frame (the technical term is a preferred foliation of space time, or a preferred choice of a time axis). As a relativist, I found this absolutely abhorrent.

@dga471 is the quantum mechanic, while I work mostly on classical stuff, so he probably can tell you more about this.


Except there are no nonlocal variables in classical mechanics, right? So this shows that local variables can mimic nonlocal variables when waves are involved.

I think the point of this is that you don’t have to choose. You could just have local determinism, with an unobservable pilot wave.

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I don’t think that is the correct interpretation of these experiments. If this is true then it will run contrary to Bell’s theorem. @dga471 I think you need to help me on this.

Here is my wild guess:
There is an assumption in the oil droplet experiment that the sound speed in the vibrating medium is fast compared to anything in the system. Only in this limit can it reproduce QM phenomena.


I don’t think that is correct. If you don’t chose, you can’t know - (system is in two states at same time). If you do chose, system collapses instantaneously and you are either right or wrong.

Knowing the internal state is different than determinism. I’m not sure this is in conflict.

Regarding Bells inequality, it appears to be consistent with a sub light speed pilot wave. I’ll dig up the paper on it @PdotdQ.

Here’s the latest on Bell’s inequality.

Bear in mind that for these oil/water drop experiments, sub-light is not good enough. As I mentioned in my previous post, if they are in the limit where the sound speed is fast, they can mimic nonlocal interactions classically.

I’m not talking about the classic analogue here. Bell’s inequality violations do not imply nonlocality that propogates faster that light, it seems.

Okay, I need to see the context for this statement, because there are a lot in this sentence that could/could not be true depending on the context. There are many Bell inequalities and I don’t know which one(s) you are referring to, and there are also subtleties in what one defines as nonlocality.

If the claim is just that Bell’s inequality violation does not imply nonlocal hidden variable, this is a trivial statement, as orthodox QM is not a nonlocal hidden variable theory.

5 posts were split to a new topic: J Mac Bets a Physicist

So here is the context in my mind. What is your assessment of this paper?

Are Hidden-Variable Theories for Pilot-Wave Systems Possible ?
Louis Vervoort, 05.04.2018

Abstract: Recently it was shown that certain fluid-mechanical ‘pilot-wave’ systems can strikingly mimic a range of quantum properties, including single particle diffraction and interference, quantization of angular momentum etc. How far does this analogy go? The ultimate test of (apparent) quantumness of such systems is a Bell-test. Here the premises of the Bell inequality are re-investigated for particles accompanied by a pilot-wave, or more generally by a resonant ‘background’ field. We find that two of these premises, namely outcome independence and measurement independence, may not be generally valid when such a background is present. Under this assumption the Bell inequality is possibly (but not necessarily) violated. A class of hydrodynamic Bell experiments is proposed that could test this claim. Such a Bell test on fluid systems could provide a wealth of new insights on the different loopholes for Bell’s theorem. Finally, it is shown that certain properties of background-based theories can be illustrated in Ising spin- lattices.

Ok, let me read the paper. Let’s ping @dga471 also, as he is an actual quantum physicist.

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I read this, and I am clueless. Can the smart young physicists explain it to us?

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Sorry for responding so late - have been very busy in the lab lately. @PdotdQ is right that I do work with quantum mechanics, but most of the type we do is pretty bread and butter atomic physics stuff; this sort of foundational tests of QM is its own field which I’m not an expert in. That being said, I do have some long-standing interest in Bell test experiments, so I’m looking forward to read this paper more carefully.

(However, I was not previously aware of the water droplets experiments. I mostly only keep up with experimental tests of Bell inequalities. My impression is that such experiments are only interesting classical analogues of quantum situations - perhaps useful for simulating a theoretical idea but not telling us anything about the fundamental nature of QM itself. But maybe I’m wrong :sweat_smile:)

On a first glance, though, it seems that a linchpin of this new theory is that it violates measurement independence (MI), which in many experiments is interpreted as freedom-of-choice - whether our experimental settings (e.g. chosen detector orientations of Alice and Bob) are truly random and uncorrelated. (This is explained in page 5.)

My first reflex upon reading this is to think about the recent work performed to close this loophole - most spectacularly, in my opinion, the recent experiments performed by the groups of Anton Zeilinger and David Kaiser, where the detector settings were determined by distant astronomical sources, such that if there were any correlations, they would have to have been produced several billion years ago. (The ultimate goal is to stretch this to the moment of the Big Bang itself - then the only loophole would be superdeterminism, which undermines the basis of all science itself.)

However, it seems that in this new paper, the authors claim that their “background field” results in a pilot wave that produces correlations which are not destroyed by choosing random detector settings (page 16). They claim that “one simply needs to assume that the switching does not totally disrupt the structure in the pilot-wave…” and then mention the droplet experiment, which I need to read more closely. I suppose this claim, if true, makes the theory immune from experiments such as the one above. That’s the point that I’m interested in.


There are several YouTube videos surmising that there ARE non-local variables that could be at work.

For example Non-Locality could be accomplished by worm holes that exist at the atomic level.

Well this is neat. I’m showing you something new!

Also, it is oil droplets, not water droplets. This matters, it seems. It does seem to tell us something about QM. A classical system clearly is a local system, yet its waves are non-local, and these 2D waves reproduce several of the weird dynamics of QM. That is striking and surprising. If that holds up and can be extended, it gives a realist interpretation of QM.

If you go back and look at the history of QM, the resistance to pilot wave theory was driving by logical positivism and some other philosophical pre-commitments. Those pre-commitments are now relaxed. Moreover, there are some new tests of QM that might be relevant to this on the horizon too.

That is the interesting part. I’m curious what you think on a closer read. Also read the links in the OP on the oil droplets. It is important background.


@dga471 and @PdotdQ this is another paper worth reading:

No-Go Theorems Face Background-based Theories for Quantum Mechanics
Louis Vervoort

Recent experiments have shown that certain fluid-mechanical systems, namely oil droplets bouncing on oil films, can mimic a wide range of quantum phenomena, including double-slit interference, quantization of angular momentum and Zeeman splitting. Here I investigate what can be learned from these systems concerning no-go theorems as those of Bell and Kochen-Specker. In particular, a model for the Bell experiment is proposed that includes variables describing a ‘background’ field or medium. This field mimics the surface wave that accompanies the droplets in the fluid-mechanical experiments. It appears that quite generally such a model can violate the Bell inequality and reproduce the quantum statistics, even if it is based on local dynamics only. The reason is that measurement independence is not valid in such models. This opens the door for local ‘background-based’ theories, describing the interaction of particles and analyzers with a background field, to complete quantum mechanics. Experiments to test these ideas are also proposed.

You’ll probably still give a better answer than someone who is allergic to h-bars like I am.

I have read the paper halfway. First off, I must admit that I never considered that the hidden variable could be from the background instead of the particles. This is a key assumption that allows an extra loophole (measurement independence) to crept into the paper’s pilot-wave interpretation.

I followed the math and I think it’s all kosher (at least until halfway through the paper). However, besides the formal definition of measurement independence (equation 2.1c), I don’t really have a feel of what measurement independence actually entails, and what are the consequences for theories that violates it.

@dga471, does this mean that violation of measurement independence is a smaller, more local version of superdeterminism?


That is the crazy thing about this proposal. It has been hiding in plain sight. It could resolve many (though probably not all) of the weirdness of QM. In particular, it explains why Schrödinger’s equation. Remember what Fenyman said about this?

Where did we get that [Schrödinger’s equation] from? It’s not possible to derive it from anything you know. It came out of the mind of Schrödinger.

The Feynman Lectures on Physics

That equation is nearly dues ex machina, right? It works, but we are not precisely sure why it works. Pilot waves would give explanation for why it works, or how to derive it.