The Pilot Wave Interpretation of Quantum Mechanics

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”.

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

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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.

I understand where you are coming from, and I agree with you in principle. My problem is: how mechanistic really is a description that depends on a non-observable medium whose properties we can choose arbitrarily? In practice the pilot-wave description seems very phenomenological to me.

It may not be unobservable. There are versions of pilot wave theory that could appear in experiments. The key point I’d make is that this has been under-contemplated. We’d have to do much more careful thinking to conclude it is ultimately non-observable.

If the pilot waves are observable directly (beyond just the forces they impart on the particles) then it changes the character of the theory completely. Such an observation would be an enormous news in the physics world, as it would take this theory from the realm of QM interpretation to QM extension, i.e. this would be a theory that can predict observables that QM cannot. If that is the case I would agree that it stands on firmer ground than orthodox QM.

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I don’t think it would be “directly” observable. Almost nothing in physics now days is “directly” observable, what ever that means.

However, if perhaps QM describes the equilibrium state of some sort of “mechanical” evolution of a system outside of view, it might take time to reach equilibrium. As entanglement is more complex, over wider distances, and probed more rapidly, it is possible that deviations from standard QM might be observed. That is the “test” I see on the horizon with quantum computers. In fact the whole endeavor of quantum computing depends on the yet untested assumption that quantum entanglement will work with out modification up to hundreds of atoms, or even more. At the moment, this is an untested assumption, which may or may not prove to be the case.

Quantum computing and communication, therefore, might be one place, for example, where some pilot wave frameworks might begin to produce different predictions, especially if it is a sub-luminal wave that takes exponential passes to resolve entanglement, perhaps does not ever find equilibrium in some cases, or perhaps has more than one possible equilibrium in some cases.

I’ve run this by some physicists and they don’t think I’m crazy. If you guys take it up and write something on it, let me know. I’d love to get a middle authorship on something like that, though I don’t have physics chops to fully develop it.

Okay, unless you are using a different definition of direct observation as physicists do, this is not true. Direct detections in physics just means that the thing you are observing only interacts with your detectors when you are “doing the detecting”. This is why we claimed that we have direct detection of gravitational waves even though the indirect detection had won a Nobel prize decades ago.

If the speed in the medium is finite, and thus entanglement are not instantaneous, then this would be a point towards pilot-wave. Again, this would change the character of the pilot-wave vs Copenhagen debate, in the sense that they are no longer equivalent and one would be the extension of the other.

As it stands however, Copenhagen and pilot-wave to me seems to be equally phenomenological.

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True. I’m just curious if this will remain the situation in the long term future.

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This is somewhat unrelated and wacky, but this reminds me of the mysterious and controversial EM drive phenomenon, which violates conservation of momentum, so unsurprisingly most scientists regard it as bunk, but regardless a few groups, including one at NASA JPL, have obtained unexpected experimental results. In the experimental paper by the NASA group, pilot wave theory was mentioned as a possible explanation. I remember being puzzled because I thought that pilot-wave doesn’t predict anything different compared to the mainstream interpretation. But, the NASA scientists made a rough model where pilot waves could interact with the thruster to allow it to exchange energy/momentum with the background field (possibly the same kind that the Vervoort paper is talking about).

Of course, the whole thing is wacky and probably wrong (and the model has no other evidence for it besides the EM drive itself), so take it with a HUGE grain of salt, but this is one actual instance where PWT vs. Copenhagen was claimed to be more than phenomenological.

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I’m not convinced by this EM drive at all. Appealing to pilot waves here seems to be grasping at straws.

Coming back to the less controversial world of agreed upon physics, there are probably several classes of pilot wave theories. Some might never produce a different prediction than current theory. Some might in experiments for which we already have a ton of data, and are therefore ruled out. Some might produce different predictions in experiments we have not yet done. It is that third class that could be most interesting.

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Once again, what heightens my interest in this is the advance of quantum computing. That will enable whole new classes of experiments at whole new scales. We might see new physics here.

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Well, if we’re talking about entangling many atoms, even apart from quantum computing, there are already groups which have observed entanglement from millions of them (example).

That being said, a justification I’ve heard being mentioned for doing these Bell test experiments closing loopholes such as freedom of choice is that if the inequality is not violated, the security of future quantum communication channels might be compromised.

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@swamidass and @dga471, I read up on the relativistic field theory generalization of the pilot-wave mechanics (analogous to Orthodox QM -> Orthodox QFT), and it turns out that the pilot-wave interpretation is no longer deterministic in this wider picture. Interestingly, it seems that people who are in favor of the pilot-wave interpretation are not perturbed by this despite the fact that it destroys what I think is the main draw towards the pilot wave interpretation.

What follows is my summary. To non-physicists reading this post: unfortunately it’s hard to talk about this subject without a little bit of jargon, so forgive my somewhat liberal use of them. I did not use any jargon that is silly enough to not have their own wikipedia page, so you can consult wiki for the meaning of specific terms.

The gist of the issue is that the pilot-wave interpretation puts a special emphasis on the position basis. In my previous post, I call this a choice of a preferred frame/foliation of spacetime. Now, in QFT the position basis is not well defined. This just comes from the fact that states in QFT have a variable number of particles, so it does not make sense to have a state where there exists # number of particles at (x1, x2, x3, …). Because of this, there is a huge disconnect between the pilot-wave’s special emphasis of the particle position and the non-existence of the position basis in QFT.

The way this is remedied is by setting up a large, time-dependent configuration space of possible positions for a variable number of particles, which I will call Q.

Think of the configuration space of one particle as a box where position in the box labels the position of a particle; call this C1. Suppose there are two particles, this is a higher dimensional box (3 spatial dimension * 2 particles = 6 dimensional box), and the position in this higher dimensional box corresponds to the positions of the two particles; call this C2. Since particles in a QFT can be created and destroyed, the configuration space Q must include both C1 and C2. Indeed, Q must include not only C1 and C2 but everything up to CInfinity. So, Q is a disjoint union of all the n-particle configuration spaces.

If you think this is a super clunky configuration space, you would be correct. When the path of the system is within a single Cx, the path is given by the pilot-wave equation deterministically. However, the jumps between Cx and Cy (remember these are disjoint sets within Q) is completely stochastic in both when the jump happens and where the jump leads to in the next hyperbox.

The main point is that once relativity and thus field-theory is taken into account, the pilot-wave interpretation is not deterministic. Since in the real world relativity is true, I think a more punchy statement can be said: In the real world, the pilot-wave interpretation is not deterministic.

Edit: grammar

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@PdotdQ @dga471 I hope you don’t mind if I intrude upon this thread… I am not formally educated in quantum physics, but I have done a fair bit of reading about pilot-wave theory and other interpretations of QM, and I think there are a couple misconceptions that I could help clear up.

First, the droplet experiments that are mentioned at the beginning of this thread are only roughly analogous to the pilot wave theory, as far as I understand them. Better to learn about the theory from the people who study it. Here and here are some good introductions to its main incarnation, often called Bohmian Mechanics (though at least one proponent of pilot wave theory, Antony Valentini, considers that a misnomer). This is a non-relativistic theory that makes the same predictions as standard non-relativistic QM, but that explains quantum phenomena entirely as the motion of particles that have definite positions at all times, so that there is no need for measurement axioms or a divide between the microscopic and macroscopic worlds.

Second, @PdotdQ, you mention a relativistic generalization of pilot-wave theory that is indeterministic, but it should be noted that this is not the only relativistic generalization of the theory that has been explored. There are others. (There is, I think, a review article by Ward Struyve that surveys some of them.) Some of them retain the determinism of the non-relativistic theory.

However, you’re right that proponents of pilot-wave theory are not really perturbed by the possibility of ontological indeterminism. The main draw of pilot-wave theory for most of its supporters is that it explains quantum phenomena with a clear ontology of physical entities located in physical space - as opposed to a wavefunction in abstract configuration space, which has an unclear relationship with the world we observe under the conventional interpretation. Whether those entities are particles or fields, and whether they behave deterministically or indeterministically, is secondary.

Third, the privileged position of the position basis in non-relativistic pilot-wave theory is related to the way that the theory describes the physical world (as a collection of particles moving in space), and isn’t specifically related to the preferred frame/preferred foliation of spacetime required by the theory. A pilot-wave QFT could use something like the configuration space described by @PdotdQ (Fock space), to describe the world as a variable number of particles moving in space and being created and annihilated. Another pilot-wave QFT could describe the world as a collection of fields that pervade all of space (with actual, numerical values for the fields, related but not identical to the operator-valued fields of standard QFT). So pilot-wave theory isn’t as bound to the position basis as it seems.

(The preferred foliation of spacetime, on the other hand, comes from the way that the pilot-wave theory implements the non-locality required by Bell’s theorem.)

Hope that helps.

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Very bold step @structureoftruth. Though it seems I agree with all your cautions. Well done.

@structureoftruth are there any pilot wave theory candidates in this class?

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There are. As far as I have seen most pilot-wave theories are constructed so that, in principle, they match the predictions of standard quantum theory exactly. (The real goal of pilot-wave theories is to have a conceptually clear and precise explanation of what is physically going on, without the vagueness inherent in the concept of “measurement” in the standard formulation, and without the difficulty of explaining how the reality we observe is supposed to emerge from the wavefunction in the many-worlds interpretation.)

However, some ways of formulating pilot-wave theory leave open the possibility (although it is predicted to be highly unlikely) that we could find violations of the Born rule in nature, and that this would open up a new class of phenomena. Antony Valentini has done some work in this area.

I could also mention that some physicists who work on pilot-wave theory are also exploring what are called “objective collapse theories,” which share the same goal of finding a clear and precise description of physical reality and resolving the measurement problem, though they do it in a different way. These do make different predictions than standard QM, and some progress has been made on narrowing down the parameter space available to these theories based on experimental evidence. Unlike the non-relativistic pilot-wave theories, objective collapse theories contain irreducible indeterminism.

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Thank you @structureoftruth for clarifying the pilot-wave interpretation. As I mentioned in a previous post, I am a classical physicist who is allergic to hbars, so this whole quantum stuff really befuddles me.

Would you mind giving us an example for this?

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