# Does the de Broglie-Bohm pilot wave theory make predictions?

• I
I find the de Broglie-Bohm pilot wave theory interesting but what I still feel missing in the descriptions I could find so far is that it reformulates what we already know but nobody speaks of new testable predictions that could eventually distinguish it from other interpretations (such as a new phenomenon, new particles, etc.. that classical QT does not predict or that it sheds light on anomalies, etc). Are there any?

PeterDonis
Mentor
nobody speaks of new testable predictions that could eventually distinguish it from other interpretations

That's because there aren't any. All interpretations of QM make the same predictions; that's why they're called interpretations instead of different theories.

DrChinese
atyy
In principle, interpretational approaches like Bohmian mechanics and physical collapse theories could make predictions of new physics. The current shortcoming of these approaches is that we do not know if they explain all of current physics. These possibilities of new physics are discussed by

https://arxiv.org/abs/1407.8262
Primordial quantum nonequilibrium and large-scale cosmic anomalies
Samuel Colin, Antony Valentini

https://arxiv.org/abs/1611.09776
Improved noninterferometric test of collapse models using ultracold cantilevers
A. Vinante, R. Mezzena, P. Falferi, M. Carlesso, A. Bassi

https://arxiv.org/abs/1410.0270
Testing the limits of quantum mechanical superpositions
Markus Arndt, Klaus Hornberger

PeterDonis
Mentor
In principle, interpretational approaches like Bohmian mechanics and physical collapse theories could make predictions of new physics.

Yes, and if they do, they are no longer interpretations of standard QM; they are new theories, which have standard QM as an approximation in some appropriate limit.

HAYAO
atyy
Yes, and if they do, they are no longer interpretations of standard QM; they are new theories, which have standard QM as an approximation in some appropriate limit.

Not everyone uses "interpretation" in this way, although it is certainly a valid sway to define your terms. The more general idea of an interpretation is a solution of the measurement problem of Copenhagen. In that sense, Copenhagen is the only "interpretation" that is not an interpretation.

PeterDonis
Mentor
Not everyone uses "interpretation" in this way

That's true; however, when push comes to shove, nothing that is commonly referred to as an interpretation of QM makes any testable predictions that aren't made by all the other interpretations. Things that do--for example, the GRW stochastic collapse model--aren't called interpretations in the literature; they are called theories or models. For example, none of the papers you linked to (all of which are very good references) describe themselves as testing QM interpretations; they are testing models that make potentially testable predictions that are not made by standard QM, in order to see to what extent the basic postulates of standard QM remain valid in domains outside those in which they have already been tested.

The de Broglie-Bohm "predicts" classical mechanics. More precisely, it explains in a simple way the quasi-classical evolution of the macroscopic world, which is not the case for ortodox quantum mechanics.

Demystifier
Bohmian mechanics will predict something different *if* you allow the possibility that the particle distribution at some time does *not* conform to the Born rule. The reason this is hypothesized is that there is a theorem that suggests that if you start with a non-Born distribution, then over time it will gradually evolve, in a manner akin to thermalization in thermodynamics, to a Born rule distribution asymptotically, and it will do so with probability 1. And thus if you allow for this, it makes the Born rule able to be a derivable theorem, as opposed to a postulate that has to be assumed from the beginning, and thus makes the theory slightly simpler. Such a deviation from Born behavior could be imagined to have been at the Big Bang, and this has been suggested would lead to possible observable consequences in cosmological studies for the structure of the early Universe and thus of remote areas such as the CMB radiation. However, failure to observe this would not falsify Bohmian mechanics, rather merely those versions that posit non-Born behavior at the Big Bang. We could still assume the Born rule as a postulate that has held from the beginning, and then there is no refutation.

How does this jive with the issue of interpretation versus theory? Simple. The Born rule is part of standard quantum mechanics. If you remove the rule to derive it later as a theorem where you start the hidden parameter with a non-Born distribution, then you are no longer simply interpreting QM, you are creating a new theory, as you have modified the original theory by removing a component as a basic element and instead substituted in that role a different element (the hidden positions) from which you are going to derive it. If, however, you do not do this, then you do indeed have an interpretation: no prediction it makes is different from that made by standard QM. You have added a new element, but you have not modified any of the rest, and the new element admits of no contradiction, and simply serves to fill a philosophical gap.

The only reason this modification is considered is that it looks attractive since the theorem of approach to Born behavior in the limit is mathematically proven, and thus it is tempting to go there as fewer assumed principles in a theory is a nice thing to have, but it is not at all necessary.

That said, if we DID observe the variations predicted by the non-Born distribution hypothesis, then we would know that Bohmian mechanics is the "correct" way to understand QM, and moreover, standard QM is falsified as a strict theory.

If anything, the real difficulty with Bohmian mechanics is that it really only works naturally for nonrelativistic particle QM (and so also, the appearance of faster than light speeds in it should not be taken as a strike against, it IS formulated on a Galilean space-time, not a Lorentzian one, where that infinite speed is allowed, just as in Newtonian mechanics!). It doesn't straightforwardly generalize itself to the case of relativistic quantum field theories which we know are the more broadly-applicable ones, and moreover it does not provide a general framework for interpreting an arbitrary quantum theory. However, this is actually not something that should be taken as a surprise: It is often forgotten, but Bohm actually technically did not intend for this interpretation to be a final one. He simply gave it as an example to show that you *could* make a theory in which a classical-like, deterministic reality could exist between measurements, and have it reproduce all the observable predictions of standard QM, contrary to some detractors at the time (and some which still exist now), and in that, he was absolutely correct. Thus its non-generalizability should not be a surprise because it was not created for that purpose to begin with. It was a proof of concept, so to speak.

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Demystifier
Gold Member
That said, if we DID observe the variations predicted by the non-Born distribution hypothesis, then we would know that Bohmian mechanics is the "correct" way to understand QM, and moreover, standard QM is falsified as a strict theory.
Even though I am a strong supporter of Bohmian mechanics, I disagree with this statement. Bohmian mechanics allows deviations from the Born rule, but it doesn't make clear predictions of what exactly those deviations are. The specific computations by Valentini are not unambiguous predictions, but just ad hoc examples of what those deviations might look like.

Demystifier
Gold Member
Are there any?
The approach I advocate in https://arxiv.org/abs/1703.08341 makes a generic prediction that, at some lower distances, fundamental physics should be described by non-relativistic QM, and not by relativistic QFT. In particular, it predicts violation of Lorentz invariance. However, those predictions are not very specific in a quantitative sense, so experimental verification of Lorentz violation would at best be a hint, certainly not a proof, that Bohmian mechanics might be right.

martinbn
The approach I advocate in https://arxiv.org/abs/1703.08341 makes a generic prediction that, at some lower distances, fundamental physics should be described by non-relativistic QM, and not by relativistic QFT. In particular, it predicts violation of Lorentz invariance. However, those predictions are not very specific in a quantitative sense, so experimental verification of Lorentz violation would at best be a hint, certainly not a proof, that Bohmian mechanics might be right.
What about the other way around? No violation of Lorentz invariance so far is a hint that Bohmian mechanics might be wrong.

Demystifier
Gold Member
What about the other way around? No violation of Lorentz invariance so far is a hint that Bohmian mechanics might be wrong.
Yes, it's a hint that the Bohmian approach in the paper above might be wrong. It's always easier to defend standard current theories than the alternative ones.

atyy
What about the other way around? No violation of Lorentz invariance so far is a hint that Bohmian mechanics might be wrong.

There is no known rigorous construction of interacting special relativistic quantum theory in 3+1 dimensions.

Demystifier
martinbn