The Pilot Wave Interpretation of Quantum Mechanics

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.

I will hold off on this claim until I fully understand what is sacrificed by giving up on MI, and whether this loophole is even actually open. Note that the Vervoort article was published in a very low impact factor journal and has absolutely no citations. While this by itself does not prove anything, I am wary to claim anything based on this article before the experts who work in this field say anything about Vervoort’s result. Perhaps there is something obvious that we are missing.

I can see how some people might think this way, but I don’t think this is fair. That the Schrodinger equation can be derived from the Hamilton-Jacobi equation is well known, and is literally a homework problem.

I don’t want to get too mathematical, but literally what one needs to do is just substitute psi=Exp[i S/hbar] into the Schrodinger equation and take hbar to zero to recover the Hamilton-Jacobi equation. (Sorry professors who use this problem as homework!)

What pilot-wave gives is an interpretation of what this psi and hbar is. In particular, that psi is an otologically real but unobservable wave. However, this interpretation is axiomatic and I don’t see how this is better than the orthodox interpretation that psi is the wavefunction.


That I did not know about. I’lll have to study up. Why does Fenyman say this then?

Why would he say that?

It is better just because it explains what the wave function “is”, right?

Given that Feynman also came up with some other ways to derive the Schrodinger equation, he did not meant that the Schrodinger equation is literally underivable. What he meant is that anything that can derive the Schrodinger equation can be derived by the Schrodinger equation. It is a chicken or egg problem. You have to take your axiom someplace.

Here is a much clearer example. Note that the Hamilton-Jacobi equation method is not the only way to derive the Schrodinger equation, I just mentioned it because that is the most pertinent for pilot-wave theories.

If you assume that the commutator of position and momentum to be ihbar, then you can derive the Schrodinger equation. However, if you start with the Schrodinger equation as axiom, you can derive that the commutator of position and momentum is ihbar. Indeed, historically the commutator being ihbar comes before the Schrodinger equation.

You have to pick your axiom somewhere. Similarly, the derivation of Schrodinger equation from pilot-wave mechanics (essentially just the Hamilton Jacobi derivation) can be run on reverse.

Orthodox quantum mechanics also explains what the wave function is: it’s a function that is related to the probability of having the system in a particular state after measurement. Is this really less impressive than “an unobservable, but ontologically real wave that we have no idea what the medium is”.


Makes a ton of sense. Thank you! I misunderstood Feynman, and what you are saying makes much more sense.


Yes is an important distinction. One is a phenomenological description and the other is a mechanistic description. The mechanistic model also give s framework for probing ways the “seams” might be exposed, as may happen in quantum computing with highly entangled states. The distinction seems very important to make.

The historical reason to a prior prefer the phenomenological description is positivism or scientism. A mechanistic framework might be a foundational for a testable theory too.

I’d also add the oil droplet experiments could be a phenomenal starting point for teaching and physics at the high school level, so it could be more intuitively understood rather than being so non intuitive as tone unintelligible. This would improve substantial on the Copenhagen bias of current textbooks.