Does the PBR theorem rule out the 'minimalist' Bohmian interpretation?

In summary: Human observers are quantum systems (the "Apparatus" in the paper).•We have free will (this is used in the proof of the theorem).So, if one assumes that there is no objective physical state λ for any quantum system, or if one assumes that all quantum states can be shared by some λ ′ , then the PBR theorem doesn't apply.In summary, the PBR theorem attempts to rule out the possibility of interpreting the quantum state as purely epistemic or statistical, leaving the option of it being ont
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I had trouble understanding this and had brought it up before but I thought I'd start a new thread on it, in case anyone has any further insights. In the original Leifer summary discussing the implications of PBR theorem on the various QM interpretations, Leifer argued that realists should become ψ-ontologists. He writes:
In quantum theory, we have a different notion of state-the wavefunction-and the question is: should we think of it as an ontic state (more like a phase space point), an epistemic state (more like a probability distribution), or something else entirely? Here are three possible answers to this question:

1. Wavefunctions are epistemic and there is some underlying ontic state. Quantum mechanics is the statistical theory of these ontic states in analogy with Liouville mechanics.
2. Wavefunctions are epistemic, but there is no deeper underlying reality.
3. Wavefunctions are ontic (there may also be additional ontic degrees of freedom, which is an important distinction but not relevant to the present discussion).

The theorem in the paper attempts to rule out option 1, which would mean that scientific realists should become psi-ontologists. I am pretty sure that no theorem on Earth could rule out option 2, so that is always a refuge for psi-epistemicists, at least if their psi-epistemic conviction is stronger than their realist one. Pretty much all of the well-developed interpretations that take a realist stance fall under option 3, so they are in the psi-ontic camp. This includes the Everett/many-worlds interpretation, de Broglie-Bohm theory, and spontaneous collapse models. Advocates of these approaches are likely to rejoice at the PBR result, as it apparently rules out their only realist competition, and they are unlikely to regard anti-realist approaches as viable.
Can the quantum state be interpreted statistically?
Can the quantum state be interpreted statistically? | Matt LeiferMatt Leifer

But this is what is confusing me. Harrigan and Spekken, whose definitions of ψ-ontic and ψ-epistemic are used in the PBR theorem briefly discuss the ontic nature of the different Bohmian interpretations and write:
Inspired by this pattern, Valentini has wondered whether the pilot-wave (and hence ontic) nature of the wave function in the deBroglie-Bohm approach might be unavoidable. On the other hand, it has been suggested by Wiseman that there exists an unconventional reading of the deBroglie-Bohm approach which is not ψ-ontic. A distinction is made between the quantum state of the universe and the conditional quantum state of a subsystem, defined in Ref. [79]. The latter is argued to be epistemic while the former is deemed to be nomic, that is, law-like, following the lines of Ref. [80] (in which case it is presumably a category mistake to try to characterize the universal wave function as ontic or epistemic). We shall not provide a detailed analysis of this claim here, but highlight it as an interesting possibility that is deserving of further scrutiny.
Einstein, incompleteness, and the epistemic view of quantum states
403 Forbidden

Supporting this non-ontic reading for the nature of the minimalist Bohmian interpretation, Belousek writes:
The first interpretive proposal I’ll call ‘minimalist’ (e.g., Durr et al. 1996). In this view, the only properties a Bohmian particle really possesses(in addition to its state-independent classical properties, mass and charge) are its actual position and velocity; all quantum properties or ‘observables’ represented by Hermitian operators, such as ‘spin,’ are regarded as merely fictions or as constructions that only catalogue possible position measurement outcomes and are thus eliminated from the theory’s ontology (because they add neither empirical content nor explanatory power to the theory). On this view one might further interpret the quantum state itself as having only an ‘instrumental’ significance for statistical predictions, as merely representing a convenient summary of the possible motions of a system, and thus as being an abstract mathematical entity in configuration space having no concrete existence in physical space (as do Durr et al .). On such an interpretation, there is simply no room for non-supervenience to arise in the first place, even when the quantum state is non-separable.
Non‐separability, non‐supervenience, and quantum ontology
Non-separability, Non-supervenience, and Quantum Ontology | Darrin Snyder Belousek - Academia.edu

Assuming that the PBR theorem is accurate, does this imply that the Durr et al. minimalist Bohmian interpretation is ruled out?
 
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  • #2
I have already explained that, but let me repeat.

No, PBR does not exclude Bohmian interpretation. Why? Because the word "ontic" in the PBR context has a different meaning than the same word in the Bohmian context as defined by Durr et al. If you accept the PBR definition of the word "ontic", then Bohmian wave function is fully ontic. If you accept Bohmian definition of the word "ontic", then PBR reasoning does not prove that wave function is ontic.

By the way, nearly half of all disagreements between people can eventually be reduced to a use of different definitions for some word.
 
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Demystifier said:
I have already explained that, but let me repeat.
No, PBR does not exclude Bohmian interpretation. Why? Because the word "ontic" in the PBR context has a different meaning than the same word in the Bohmian context as defined by Durr et al. If you accept the PBR definition of the word "ontic", then Bohmian wave function is fully ontic. If you accept Bohmian definition of the word "ontic", then PBR reasoning does not prove that wave function is ontic.
Thanks, I think I finally got. I was getting confused with the definition of "ontic". One of the assumptions of PBR is that there is an objective physical state λ for any quantum system. If one takes the minimalist (e.g. Durr et al.) Bohmian definition of "ontic", then this PBR assumption does not hold so PBR theorem does not apply.

Edit: I found this post on Physics Stack Exchange useful:

The Pusey-Barrett-Rudolph paper spells out some of its assumptions. (They do it most explicitly in the concluding paragraphs.) There may well be additional unmentioned assumptions (e.g. causality), but the ones they specifically mention are:

•There is an objective physical state λ for any quantum system

•There exists some λ ′ that can be shared between some pair of distinct quantum states ψ 1 and ψ 2 . That is, p(λ=λ ′ |ψ=ψ 1 ) and p(λ=λ ′ |ψ=ψ 2 ) are both non-zero. (This is what it means for an interpretation to be epistemic, according to Spekkens' definition.)

•The outcomes of measurements depend only on λ and the settings of the measurement apparatus (though there can be stochasticity as well)

•Spatially separated systems prepared independently have separate and independent λ 's.

It is from these that they derive a contradiction. Any theory that fails to make all of these same assumptions is unaffected by their result.
Bohmian loophole in PBR-like theorems
quantum interpretations - Bohmian loophole in PBR-like theorems - Physics Stack Exchange
 
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  • #4
perhaps rules out also ontic models, as has been stated by schlosshauer and fine, or is flawed in its core assumption.


https://www.physicsforums.com/showpost.php?p=4427595&postcount=121

audioloop said:
"leads to a very general nogo theorem that rules out not only the epistemic models
targeted by PBR but also ontic models"

"This blunts the PBR argument for the reality of the quantum state, even for the ontological hidden-variables models to which the argument applies."

"This is an important lesson about modeling quantum mechanics, but one that leaves open the question of "whether quantum states are real.



---------
ontic, epistemic... any model is ruled out...

Fuchs stands






.
 
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audioloop said:
perhaps rules out also ontic models, as has been stated by schlosshauer and fine, or is flawed in its core assumption.
I can't see how the PBR theorem rules out ψ-ontic models. I think that if one of the PBR core assumptions is questionable (e.g. separability), then in that case it would just mean that interpretation would be unaffected by the PBR theorem.
 
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yes i am puzzled too, read this one:
audioloop said:
"Our results suggest that rather than demonstrating the reality of the quantum state, the PBR theorem highlights quantum nonseparability in ontological hidden-variables models"

that disqualifies pbr, can sound logic to me, cos how you state objectivity, reality, in one just sentence (assumption) is risible at least.
 
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audioloop said:
that disqualifies pbr
I think this was Demystifier's original criticism of the PBR theorem to one of the authors of that paper. But I'm not sure if that's accurate because as I posted previously the authors argued that one of core and pertinent assumptions of PBR is preparation independence. I'm not sure what the difference is between this and separability assumption? This is summarized in these slides:
PBR theorem: Systems have an objective physical state + Preparation independence + QM → ψ-ontic
What is the quantum state?
http://www.cs.ox.ac.uk/qisw2012/slides/barrett.pdf

So it seems to me that one of the major assumption in PBR is preparation independence. Is that the same as a separability assumption? Well, if it is then would Bell's theorem also be prone to this criticism? Consider the summary of Bell's given in the link above:
Bell’s theorem: Systems have an objective physical state + Experimenter free will + QM → Non-locality
As Demystifier pointed out the difference between these 2 assumptions (e.g. experimenter free will vs preparation independence is likely to be minor:
It seems to me that the relevant aspects of those two assumptions are essentially the same. Namely, when in the Bell theorem we require that "experimenters have free will", all what we really need is that the choice made by one experimenter is INDEPENDENT on the choice made by another experimenter. These two experimenters choose the directions in which the spins will be measured, so we can say that they PREPARE the measuring devices. From this point of view, the difference between PBR and Bell lies in the fact that the former requires preparation independence of the two PARTICLES which will be measured, while the latter requires preparation independence of the MEASURING DEVICES for the two particles. Both require preparation independence, but for different objects - the measured system for PBR, or the measuring device for Bell. Now, if we assume that there is no fundamental difference between measured systems and measuring devices (e.g., that both are ultimately described by quantum mechanics), then these two kinds of preparation independence are actually the same.
I'm not sure how this fits in with the separability criticism of the PBR theorem provided by Schlosshauer and Fine but would it not also apply to Bell's (assuming the summary given by slides is accurate). In fact, there are some physicists who argue that Bell's theorem does not make any "realism" assumptions (e.g. systems have an objective physical state). So this is kinda confusing me.
 
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no preparation independence -> no objectivity / ?

all what we really need is that the choice made by one experimenter is INDEPENDENT on the choice made by another experimenter

that is no objectivity.
you can do the experiment, experimenter free, so ?

more important, independence to me, is independence of anything.

you can not subordinate objectivity..
 
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Related to Does the PBR theorem rule out the 'minimalist' Bohmian interpretation?

1. What is the PBR theorem?

The PBR theorem, also known as the Pusey-Barrett-Rudolph theorem, is a mathematical proof that shows that no hidden variable theory can reproduce the predictions of quantum mechanics. This means that there cannot be a theory that explains the seemingly random behavior of particles in quantum systems.

2. What is the minimalist Bohmian interpretation?

The minimalist Bohmian interpretation is a specific version of the Bohmian interpretation of quantum mechanics. It posits that particles have definite trajectories and the wave function is only a guide to these trajectories, rather than a physical entity. This interpretation attempts to provide a more intuitive understanding of quantum mechanics by maintaining a deterministic view of the universe.

3. How does the PBR theorem relate to the minimalist Bohmian interpretation?

The PBR theorem rules out the possibility of any hidden variable theory, including the minimalist Bohmian interpretation, reproducing the predictions of quantum mechanics. This means that the minimalist Bohmian interpretation is not a viable explanation for the behavior of particles in quantum systems.

4. Are there any other interpretations of quantum mechanics that are ruled out by the PBR theorem?

Yes, the PBR theorem also rules out other interpretations of quantum mechanics that incorporate hidden variables, such as the Many Worlds interpretation and the GRW theory. It essentially states that any theory that attempts to explain quantum phenomena through hidden variables is incompatible with the predictions of quantum mechanics.

5. Does the PBR theorem mean that the minimalist Bohmian interpretation is completely invalid?

No, the PBR theorem only rules out the minimalist Bohmian interpretation as a valid explanation for the behavior of particles in quantum systems. However, it does not necessarily mean that the interpretation is completely invalid. Some proponents of the minimalist Bohmian interpretation argue that it can still provide a useful framework for understanding the principles of quantum mechanics, even though it may not fully reproduce its predictions.

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