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.
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.
Haha, that is a great way to describe the conceptual difficulty of QM. It took me a long time to begin to understand these things. I think general relativity is much easier!
Here is a short review article listing some of the options. (There’s a longer, more detailed one by the same author, also available on arxiv.)
But as an example, it is possible to construct a deterministic pilot-wave theory for a bosonic field, where the values of the field at every point in space form the ontology of the actual world, and the evolution of the field values is given by the wavefunctional on the infinite-dimensional configuration space (the space of all possible configurations of the field values). The analogy from non-relativistic pilot-wave theory is: N particle positions in 3-space → field values at every point in 3-space; wavefunction on 3N-dimensional configuration space → wavefunctional on infinite-dimensional space of field configurations.
Thank you for these articles. I went and skimmed the Struyve article and some of his other papers. From the list presented, the only pilot-wave model that really resonate with me is his “minimalist approach”, in which there are no beables except bosonic ones. Notably, none of his particle ontologies are deterministic.
While I can see that this “minimalist approach” might be correct, I still have some reservations with it. I skimmed his other papers describing this approach, and while it seems to be able to reproduce the observation of QED, I have the following issues:
Presumably, proponents of this interpretation believes that a similar construction can be made with gravity, but this is not proven.
It seems extremely ad-hoc to have a psi_f(A_T, t) that just so happen to give the “impression” that there is fermionic matter when ontologically there is none. This seems to me like an ad-hoc mechanism that is proposed exactly to cover up a “fermion-shaped hole” in the theory. I believe that Struyve himself agrees with me: “Starting from the minimalist model, there actually is a simple way to introduce field configurations for the fermions, by constructing them out of the bosonic field configurations and the wave 10 function. However, this approach has a rather arbitrary and artificial flavour to it.”
He did mention that there are ways to incorporate fermionic beables to this picture, but I did not have the time to read it in detail yet.
The “Dirac Sea” model that he develops is deterministic, though in my opinion the best that one can hope for this model is that it will look more like a field-ontology theory than a particle-ontology theory in the continuum limit (and after figuring out some way to subtract the infinite energy of the Dirac sea).
Interestingly, it seems like a continuum limit of this theory would have to have a wavefunction which takes values in an infinite-dimensional vector space (in addition to being defined on an infinite-dimensional configuration space), something which I think may also be true of both the “Grassmann variables” approach that Valentini explores, and a formulation of the model in terms of angular variables that Holland proposes, as far as I can understand them.
You can write down a pilot-wave theory for canonical quantum gravity, and it actually makes way more sense than the standard interpretation (conceptual issues like the “problem of time” completely disappear). It doesn’t make the theory renormalizable, but its a start.
I agree with you on that (though note that the A_T as the relevant variable is chosen to fix the gauge freedom), so I don’t consider the “minimalist approach” to be successful. I think a satisfactory pilot-wave QFT has to include fermions in the primitive ontology somehow. But, simply as a matter of historical contingency, pilot-wave theory has not received much attention, so the development of these ideas is still in its early stages.
From the Struyve article, this approach seems to only be deterministic for when the fermion number is conserved, which is not true both at high energies and from BSM mechanisms in the cosmological reheating epoch.
I need to read more about this, it seems dubious to me that a theory with preferred time-space splitting can handle non-globally hyperbolic spacetimes. Indeed, this assumption is used in the paragraph under equation (10) in that paper. However, I am from the gravity side, which makes me worry too much about stuff like this. I will give that the status of non-globally hyperbolic manifolds is still contentious even for orthodox QFT - though I would think that it would be much more problematic for pilot-wave theory.
By the way, it makes perfect sense that the theory is non-renormalizeable. If it is, most physicists would have heard of it .
Time scales for dynamical relaxation to the Born rule
BY M. D. TOWLER, N. J. RUSSELL and ANTONY VALENTINI
The numerical simulations performed in this work demonstrate clearly and unequivocally the tendency for Born rule distributions to arise spontaneously as a consequence of ordinary pilot-wave dynamics, even for a system as simple as the electron in a two-dimensional potential well. Contrary to popular belief, therefore, the Born rule does not have to be introduced as a postulate of non-relativistic quantum mechanics. What is the price paid for this? We must suppose merely that particles have well-defined positions (and hence trajectories) continuously rather than only when a position measurement is performed. The main technical result of this work is the emergence of the relationship t ∝ M−1 showing the dependence of the relaxation time on the number of modes in a superposition.
Physically speaking our results suggest very short relaxation times with a range of values observed for t between approximately 1 and 1000. Using natural units c = h¯ = 1 and an electron with mass m = me = 1 this corresponds to relaxation times of the order of 10−21–10−18 s. This is consistent with our current understanding of quantum mechanics and modern experimental investigations in which no deviation from quantum equilibrium is observed.
I suspect that a pilot-wave physicists’ answer to that may just be that non-globally-hyperbolic spacetimes are unphysical solutions of GR. (As far as I know, our observations of the universe are consistent with a globally hyperbolic spacetime - is that correct?) If the conceptual problems of bringing GR and quantum physics can be resolved by pilot-wave theory, then it is worth exploring in that direction, even if it means ruling out some intriguing possibilities from classical GR.
The question of whether non-globally-hyperbolic spacetimes are possible also gets into the philosophy of time - A-theory vs. B-theory and so on - and the question of what Bell’s theorem means for the compatibility of QM and relativity. But that is perhaps a question for a different thread.
So, these phenomena are related to the way that the pilot-wave theory explains/derives the Born probability rule. (Here’s a recent article on that topic, which provides a synthesis of two previously somewhat-competing explanations.) The upshot of the explanation is that in a typical universe governed by Bohmian mechanics, it is extremely probable that any ensemble of systems prepared in a corresponding way (e.g. a collection of electrons describable by the same wavefunction, sent one-at-a-time through a pair of slits) will obey Born rule statistics. (And this explanation would carry over to any other pilot-wave theories that preserve certain core features of Bohmian mechanics.)
But, according the the theory, there is the remote possibility that we could find some ensemble of systems that happens not to obey Born rule statistics. We never have, so none of these phenomena have been tested and this is all hypothetical. But if we did find such an ensemble, and if it had certain properties, a number of new phenomena would be available to us: including undetectable eavesdropping on quantum cryptography key distribution, extremely powerful quantum computation, and faster-than-light signalling (with a preferred foliation, so no time-travel paradoxes).
We’ll probably never get to access these new phenomena, but if we did, it would be pretty decisive evidence in favour of pilot-wave theory (not to mention, providing a fantastic example of fine-tuning in physics).
No, current astronomical observations cannot really tell whether the universe is globally hyperbolic or not. Recent calculations show that certain types of black holes that could cause the failure of global hyperbolicity might be benign after all, but these do not exclude the possibility of global hyperbolicity being violated in other contexts.
Further, it was argued that under very reasonable assumptions, malignant singularities would still plague quantum gravity theories.
Also, note that global hyperbolicity is the topmost rung in the causal ladder. As the approach delineated in (gr-qc:1801.03353) requires global hyperbolicity, it will fail in every single rung of the ladder under it.
In other words, we don’t have significant evidence that the universe is not globally hyperbolic, in other words, the evidence is consistent with a globally hyperbolic spacetime; we can consider models that require such spacetimes without contradicting the evidence.
Absolutely! However, this means that pilot-wave proponents cannot claim that non-globally hyperbolic spacetimes are unphysical from observational evidence. This is not a tall order; most physicists who are non-relativists are not bothered by non-globally hyperbolic spacetimes, and consider them unrealistic due to philosophical reasons (of course relativists such as myself are not happy with this argument).
Note also that as I mentioned, under reasonable assumptions we still expect singularities to form in quantum gravity. The belief that the universe is globally hyperbolic is the belief that these singularities are null or are inextendible! This is a large claim to make.
Thank you for this paper, I’ve read it last night (okay, I’ve was only able to spend ~1 hour on it, so I rushed through some parts and probably misunderstood some arguments ). Besides the afromentioned global-hyperbolicity concerns, here are my comments.
First of, this paper does not address my original concern
which is that the construction of a minimalist theory with only boson beables that gave the impression of the existence of fermions through an extremely ad-hoc psi_f(A_T, t) have to be consistent with those ontologically-not-there fermions being “impressed” also upon the gravitational field. I believe my objection still stands.
Second, there are large chunks of texts devoted on singularities. However, the authors’ definition of singularities is very basic, and not the definition of singularities a relativist would use.
The authors state multiple times that there is a “real metric” thus the definition of singularities in their theory is the same as the definition of singularities in GR. However, what is ontologically real in their theory is not a “real metric” but a real spatial metric and a preferred lapse function. This made more sophisticated definitions of singularities favored by relativists difficult (or perhaps even impossible) to use. While their definition of singularities suffices for the cosmological models that they considered in the paper, it won’t suffice for more complex models. As with previous concerns, my background is from the gravity/relativity side, so I care too much about stuff like this. I would give that these issues might not be too troubling for most physicists.
I’m really not sure what that is supposed to mean, except that it sounds like many of the common misconstruals of pilot-wave theory that get often bandied about. May I recommend checking out some of the resources I shared in my first post in this thread for an introduction to the pilot-wave theory?
I know. I agree with that concern, and I think a successful pilot-wave theory must include fermions as part of the primitive ontology. But not much work has been put into this yet, and I think there is still quite a lot of room for the possibility that a successful model can be found.
The main lesson of pilot-wave theory, is, in my opinion, that some of the radical metaphysical claims that people make on the basis of quantum theory (such as “reality is made by observation”, “particles don’t have definite properties when unobserved”, or Bohr’s anti-realist “physics isn’t concerned about what nature is, just what we can say about nature” etc) simply haven’t been proven. Pilot-wave theory could be true; there could be a clear, coherent, precise, observer-independent microscopic description of reality after all.
From following the last half of this exchange, I am thoroughly disabused of any illusion I had that I know the first thing about physics. @dga471, how much of this are you following?
I haven’t had time to read the latest round of posts more carefully. Though I recognize most of the terms from grad school classes a few years ago, I don’t remember their precise meanings any more, since I don’t use them at all in my day-to-day experimental work. Also as some of the discussion touches general relativity, which I only took one class in (and barely passed it ). I do believe that I could look up most of these terms and get a clearer idea of what they’re talking about if I’m so inclined.
Also, experimentalist concerns tend to be different from theorists. Ernest Rutherford, the ultimate experimentalist, was (in)famous for saying, “theorists play games with their symbols while we discover truths about the universe.”
Because you replied to my objection with the Pinto-Neto & Struyve paper I thought you meant it as a response to said objection. I apologize for my misunderstanding your intent. Thank you for showing me that paper, it was an interesting read.
I can agree with this. I have misgivings due to its reliance of a preferred foliation, but that is not sufficient reason to outright reject pilot-wave theories.
I will be happy to explain any terms or concepts that is unclear or confusing .
The essence of the Pilot Wave model is how a wave and a particle can be packaged together.
If you want to foster discussion about said model, then implying people are fools for taking an interest in the “packaging” is not a good way to do it.
George, I don’t believe there was any implication at all in that regard.
It seems as though @structureoftruth 's response was to your appeal to the readers to comment, not to your question. He didn’t know what you were saying, thought that you weren’t clear on the topic, and then referred you to some basic information that was posted earlier in the thread. I think that you forgot about your own initial first comment, and assumed that the response was to your second.
@gbrooks9, I was not in any way implying that you are a fool. I was simply expressing that i) I really don’t have any idea what a “dimensional pocket” is, and ii) “particle embedded in a wave” really is a slight misrepresentation of what pilot wave theory is, because the particles and the wave exist in different spaces.
“Not fully conversant in the nuances of pilot wave theory” is a far cry from “foolish”!
.
). Besides the afromentioned global-hyperbolicity concerns, here are my comments.
). I do believe that I could look up most of these terms and get a clearer idea of what they’re talking about if I’m so inclined.