Can the PBR Theorem Prove the Reality of Quantum States?

[fanieh]

https://en.wikipedia.org/wiki/PBR_theorem

"The theorem was first published as an arXiv preprint with Pusey as the principal author,[1] a subsequent version published in Nature Physics,[2] that states the theorem that either the quantum state corresponds to a physically real object and is not merely a statistical tool, or else all quantum states, including non-entangled ones, can communicate by action at a distance."

This is very fantastic claim. Since many believe quantum state is just statistical tool. Does it mean all quantum states, including non-entangled ones, can communicate by action at a distance? This can be easily proved or disproved. Since it seemed it couldn't, then the claim at Wikipedia appears not to be correct. Hope someone can edit it to give the right context. Thank you.

 

[bhobba]

Its valid, but please read the entire paper - in particular note the assumptions (from the paper):
'One is that a system has a “real physical state” – not necessarily completely described by quantum theory, but objective and independent of the observer. This assumption only needs to hold for systems that are isolated, and not entangled with other systems. Nonetheless, this assumption, or some part of it, would be denied by instrumentalist approaches to quantum theory, wherein the quantum state is merely a calculational tool for making predictions concerning macroscopic measurement outcomes.'

That is the precise assumption many interpretations such as the ensemble reject or are silent on.

Thanks
Bill

 

[fanieh]

Its valid, but please read the entire paper - in particular note the assumptions (from the paper):
'One is that a system has a “real physical state” – not necessarily completely described by quantum theory, but objective and independent of the observer. This assumption only needs to hold for systems that are isolated, and not entangled with other systems. Nonetheless, this assumption, or some part of it, would be denied by instrumentalist approaches to quantum theory, wherein the quantum state is merely a calculational tool for making predictions concerning macroscopic measurement outcomes.'

That is the precise assumption many interpretations such as the ensemble reject or are silent on.

Thanks
Bill

I've been reading https://arxiv.org/pdf/1111.3328.pdf but I can't get the reason for the isolation.

Do you know why the assumption only needs to hold for systems that are isolated, and not entangled with other systems? What happens if the system is entangled with other systems. Why won't the PBR theorem no longer be valid?

 

[bhobba]

I've been reading https://arxiv.org/pdf/1111.3328.pdf but I can't get the reason for the isolation.

Do you know why the assumption only needs to hold for systems that are isolated, and not entangled with other systems? What happens if the system is entangled with other systems. Why won't the PBR theorem no longer be valid?

Its been a while since I have gone into that theorem - it caused a big stir when released I think 6 years ago now and I don't recall the details too well - except what I posted because people sometimes ask - how can you maintain its not real anymore.

So I will have to wimp out and let someone with more current knowledge answer that one.

Thanks
Bill

 

[kith]

The PBR theorem -under certain arguably weak assumptions- rules out that QM is a purely statistical theory about some underlying hidden variables which truly determine the physical state of a system.

In order to assess the significance of this, you should note that although some people vaguely hold such a view no currently popular interpretation is of this type. The Copenhagen interpretation denies that there are hidden variables and in the de-Broglie-Bohm theory (dBB), the wavefunction is not merely a statistical tool but influences the hidden variables.

The main influence of the PBR theorem on established interpretations is that it strengthens dBB against other conceivable hidden variable theories (HVTs). It proves that certain aspects of dBB are inevitable for HVTs and thus stands in the tradition of Bell's theorem (HVTs have to be non-local) and the Kochen-Specker theorem (HVTs have to be contextual).

For me, this leaves only one question about HVTs open: dBB is sometimes crticized for the fact that the wavefunction influences the hidden variables but not the other way round. I wonder if this is also inevitable for HVTs. (Maybe it is already known; I am no expert on these matters)

 

[kith]

Also check this blog post by Matt Leifer who discusses the PBR theorem by introducing the terminology of epistemic and ontic states which is often used in quantum foundations research.

 

[fanieh]

The PBR theorem -under certain arguably weak assumptions- rules out that QM is a purely statistical theory about some underlying hidden variables which truly determine the physical state of a system.

In order to assess the significance of this, you should note that although some people vaguely hold such a view no currently popular interpretation is of this type. The Copenhagen interpretation denies that there are hidden variables and in the de-Broglie-Bohm theory (dBB), the wavefunction is not merely a statistical tool but influences the hidden variables.

The main influence of the PBR theorem on established interpretations is that it strengthens dBB against other conceivable hidden variable theories (HVTs). It proves that certain aspects of dBB are inevitable for HVTs and thus stands in the tradition of Bell's theorem (HVTs have to be non-local) and the Kochen-Specker theorem (HVTs have to be contextual).

For me, this leaves only one question about HVTs open: dBB is sometimes crticized for the fact that the wavefunction influences the hidden variables but not the other way round. I wonder if this is also inevitable for HVTs. (Maybe it is already known; I am no expert on these matters)

Logic says the hidden variables (quantum potential or whatever) need to influence the wave function too.. what would it take to do this.. Demystifier? other Bohmians?

 

[DrChinese]

Logic says the hidden variables (quantum potential or whatever) need to influence the wave function too.. what would it take to do this.. Demystifier? other Bohmians?

Here is something Demystifier prepared a while back, pretty nice overview of PBR:

https://www.physicsforums.com/attachments/pbr-pdf.72453/

 

[vanhees71]

What I still not get about this proof (as summarized nicely in @Demystifier 's slides as well as in the PBR paper) is that they somehow seem to prove the ontic nature of quantum states under the assumption that there's some hidden variable $\lambda$ that determines the QT probabilities, making these "ontic". Don't they just put what they claim to prove into this assumption? In standard minimally interpreted QT there's nothing like $\lambda$, and then isn't there again a loophole to the theorem in the sense that an epistemic interpretation of quantum state doesn't lead to a contradiction?

In my opinion minimally interpreted QT strongly suggests an epistemic interpretation of the quantum state, but as I tried to explain earlier in this thread, this doesn't imply non-objectivity either.

 

[Demystifier]

What I still not get about this proof (as summarized nicely in @Demystifier 's slides as well as in the PBR paper) is that they somehow seem to prove the ontic nature of quantum states under the assumption that there's some hidden variable $\lambda$ that determines the QT probabilities, making these "ontic". Don't they just put what they claim to prove into this assumption?

Not exactly. They assume that there is some $\lambda$, but a priori it is not obvious that $\lambda$ can determine $\psi$. As I explained at page 15, the result is actually very surprising.

In standard minimally interpreted QT there's nothing like $\lambda$, and then isn't there again a loophole to the theorem in the sense that an epistemic interpretation of quantum state doesn't lead to a contradiction?

In my opinion minimally interpreted QT strongly suggests an epistemic interpretation of the quantum state, but as I tried to explain earlier in this thread, this doesn't imply non-objectivity either.

You are right, this interpretation is not ruled out by the PBR theorem. What is ruled out are some Einstein-like attempts to find a hidden-variable theory in which $\psi$ is eliminated completely. Roughly speaking, the PBR theorem tells: don't even try, you cannot find such a theory.

 

[Demystifier]

Logic says the hidden variables (quantum potential or whatever) need to influence the wave function too.. what would it take to do this.. Demystifier? other Bohmians?

Well, Bohmian hidden variables (that is, particle positions) do not inflence the wave function. And this is fully analogous to classical HJ theory where particle trajectories do not influence the S-function. So your logic is faulty.

 

[fanieh]

Well, Bohmian hidden variables (that is, particle positions) do not inflence the wave function. And this is fully analogous to classical HJ theory where particle trajectories do not influence the S-function. So your logic is faulty.

In message #5, Kith last sentence was "For me, this leaves only one question about HVTs open: dBB is sometimes crticized for the fact that the wavefunction influences the hidden variables but not the other way round. I wonder if this is also inevitable for HVTs. (Maybe it is already known; I am no expert on these matters)"

If it was criticized.. this means some want the hidden variables to affect the wave function.. but in classical HJ theory, particle trajectories do not influence the S-function. So to avoid dBB being criticized, what should be the ontology such that the wave function can be influenced.. or if it can't be fixed within dBB.. can you please give example of another interpretation where the wave function can be influenced by a hidden variable such that the PBR theorem can apply? But then Kith mentioned "no currently popular interpretation is of this type".. so how do you cook up an interpretation which can support PBR theorem per Kith context? Many thanks.

 

[Demystifier]

In message #5, Kith last sentence was "For me, this leaves only one question about HVTs open: dBB is sometimes crticized for the fact that the wavefunction influences the hidden variables but not the other way round. I wonder if this is also inevitable for HVTs. (Maybe it is already known; I am no expert on these matters)"

If it was criticized.. this means some want the hidden variables to affect the wave function.. but in classical HJ theory, particle trajectories do not influence the S-function. So to avoid dBB being criticized, what should be the ontology such that the wave function can be influenced.. or if it can't be fixed within dBB.. can you please give example of another interpretation where the wave function can be influenced by a hidden variable such that the PBR theorem can apply? But then Kith mentioned "no currently popular interpretation is of this type".. so how do you cook up an interpretation which can support PBR theorem per Kith context? Many thanks.

Yes, some people criticize the fact that dBB trajectories do not influence the wave function. All I can do about it to accuse them for hypocrisy, for why then they don't criticize the fact that classical trajectories do not influence the HJ S-function?

 

[vanhees71]

Ok, then again a stupid question. What are dBB trajectories good for? AFAIK they are not (!) observable according to dBB.

 

[martinbn]

Yes, some people criticize the fact that dBB trajectories do not influence the wave function. All I can do about it to accuse them for hypocrisy, for why then they don't criticize the fact that classical trajectories do not influence the HJ S-function?

But in the classical case they don't say that S-function influences the trajectories. And in dBB they say that.

 

[Demystifier]

But in the classical case they don't say that S-function influences the trajectories.

Of course they do (even if by using different words). Take a look at an analytical mechanics book again.

 

[Demystifier]

Ok, then again a stupid question. What are dBB trajectories good for? AFAIK they are not (!) observable according to dBB.

That's the wrong question. The correct one is: Who are dBB trajectories good for? The answer is: They are good for (some of) those who think that there is a measurement problem in standard QM. Which, of course, excludes you.

This is analogous to atoms in 19th century, which were not observable at that time, but were still good for Boltzmann.

 

[martinbn]

Of course they do (even if by using different words). Take a look at an analytical mechanics book again.

To me the wording is important. What words do they use and why don't the Bohmists use similar phrasing instead of influence? The thing is that for me the wave influences the trajectory sounds like the electric field influences the trajectory of a charged particle, which involves interaction between the particle and the field. And I have seen the pilot wave being compared to the electromagnetic field. If there is an interaction, the particle will influence the field as well, at least in principle.

 

[Demystifier]

To me the wording is important. What words do they use and why don't the Bohmists use similar phrasing instead of influence?

Actually, Bohmians rarely say "influence", except as a response to someone else who used the same word. Personally, I usually say "determine", in both the HJ theory and Bohmin mechanics.

 

[martinbn]

Actually, Bohmians rarely say "influence", except as a response to someone else who used the same word. Personally, I usually say "determine", in both the HJ theory and Bohmin mechanics.

Which is perfectly clear and unambiguous.

 

[Demystifier]

And I have seen the pilot wave being compared to the electromagnetic field. If there is an interaction, the particle will influence the field as well, at least in principle.

Yes, some people use this analogy. I guess it's addressed to mathematically less sophisticated readers who are familiar with electromagnetic theory but not with HJ theory. For more sophisticated readers, the HJ analogy is much better.

 

[martinbn]

Hm, now you'll make me read something about dBB. I was perfectly happy hating it and being ignorant about it. Damn you!

 

[fanieh]

Actually, Bohmians rarely say "influence", except as a response to someone else who used the same word. Personally, I usually say "determine", in both the HJ theory and Bohmian mechanics.

I'm studying the events leading to Solvay 1927 and the years after it and reading this paper... https://arxiv.org/abs/quant-ph/0609184

De Broglie has been using the Hamilton-Jacobi equation as early as 1927 in his Pilot Wave theory. Let's say we totally ignore Bohm's quantum potential concepts. Can the Pilot Wave be independent or stand on its own without Bohm's 1950s Bohmian Mechanics?? Some authors seemed to say de Broglie pilot wave is more elegant. As a Bohmian, can't (or won't) you become a pure de Broglian? Why not?

page 267:
"Pilot-wave theory is sometimes seen as a return to classical physics (welcomed by some, criticized by othes). But in fact, de Broglie’s velocity-based dynamics is a new form of dynamics that is simply quite distinct from classical theory; therefore, it is to be expected that the behavior of the trajectories will not conform to classical expectations. As we saw in detail in chapter 2, de Broglie did indeed originally regard his theory as a radical departure from the principles of classical dynamics. It was Bohm’s later revival of de Broglie’s theory, in an unnatural pseudo-Newtonian form, that led to the widespread and mistaken perception that de Broglie-Bohm theory constituted a return to classical physics. In more recent years, de Broglie’s original pilot-wave dynamics has again become recognized as a new form of dynamics in its own right (Durr, Goldstein and Zanghi 1992, Valentini 1992)."

page 85:
"In retrospect, de Broglian dynamics seems as radical as – and indeed somewhat reminiscent of – Einstein’s theory of gravity. According to Einstein, there is no gravitational force, and a freely falling body follows the straightest path in a curved spacetime. According to de Broglie, a massive body undergoing diffraction and following a curvilienear path is not acted upon by a Newtonian force: it is following the ray of a guiding wave. De Broglie’s abandonment of Newton’s first law of motion in 1923, and the adoption of the a dynamics based on velocity rather than acceleration, amounts to a far-reaching departure from classical mechanics and (arguably) from classical kinematics too – with implications for the structure of spacetime that have perhaps not been understood (Valentini 1997. Certainly, the extent to which de Broglie’s dynamics departs from classical ideas were unfortunately obscured by Bohm’s presentation of it, in 1952, in terms of acceleration and a pseudo-Newtonian quantum potential, a formulation that today seems artificial and inelegant compared with de Broglie’s (much as the rewriting of general relativity as field theory on flat spacetime seems unnatural and hardly illuminating). The fundamentally second-order nature of classical physics is today embodied in the formalism of Hamiltonian dynamics in phase space. In contrast, de Broglie’s first-order approach to the theory of motion seems more naturally cast in terms of a dynamics in configuration space."

By the way. In Broglie's Pilot Wave, there is no Quantum potential invented by Bohm, what is the counterpart of "quantum potential" in de Broglie's Pilot wave approach?

I'm interested in reading combination of Aether-like physics with either de Broglie's Pilot Wave or Bohmian's quantum potential to get more degrees of freedom to explain our world more completely because our current theory seems to be so tunnel vision as if (I sometimes wonder) they were designed that way to hide certain things..

 

[Demystifier]

@fanieh the formulation without the quantum potential is much more elegant, especially when one wants to introduce spin. In the de Broglie formulation, the role of wave function is took by the wave function itself. However, the thing that de Broglie missed is the proof that this theory leads to same measurable predictions as standard QM. It was Bohm who first proved it, which is why the work of Bohm is much more important than the work of de Broglie.

 

[fanieh]

@fanieh the formulation without the quantum potential is much more elegant, especially when one wants to introduce spin. In the de Broglie formulation, the role of wave function is took by the wave function itself. However, the thing that de Broglie missed is the proof that this theory leads to same measurable predictions as standard QM. It was Bohm who first proved it, which is why the work of Bohm is much more important than the work of de Broglie.

So can one proceed by noting de Broglie formulation have same measurable predictions as standard QM and yet bypassing Bohm's quantum potential since the one without is more elegant? Why do all current BM use idea of quantum potential?

In the other thread. You hinted it was possible the fundamental particles (in contrast to the phonon quasiparticles) are the aether themselves (or other terms to describe it). So would it be better to use de Broglie (without quantum potential) in it or Bohm's quantum potential version or even Bohm third and final version that involves the implicate order (which seems to be similar to the AdS/CFt stuff)?

 

[Demystifier]

So can one proceed by noting de Broglie formulation have same measurable predictions as standard QM and yet bypassing Bohm's quantum potential since the one without is more elegant?

Yes.

Why do all current BM use idea of quantum potential?

They do not. Quantum potential is perhaps often discussed in popular science literature, but in serious research it is not used so much.

In the other thread. You hinted it was possible the fundamental particles (in contrast to the phonon quasiparticles) are the aether themselves (or other terms to describe it). So would it be better to use de Broglie (without quantum potential) in it or Bohm's quantum potential version or even Bohm third and final version that involves the implicate order (which seems to be similar to the AdS/CFt stuff)?

The de Broglie approach would be the best.

 

[fanieh]

Yes.They do not. Quantum potential is perhaps often discussed in popular science literature, but in serious research it is not used so much.The de Broglie approach would be the best.

Thanks for the thought. Before this week I thought de Broglie Pilot Wave were attempt at particle/wave duality which was ancient stuff that modern physicists do away by Born probability square interpretation. So it's not so at all. I think many sources only mentioned de Broglie 1923 idea and not the one in 1927 after the Born interpretation...

 

[stevendaryl]

Well, Bohmian hidden variables (that is, particle positions) do not inflence the wave function. And this is fully analogous to classical HJ theory where particle trajectories do not influence the S-function. So your logic is faulty.

Well, I guess it depends on how you think of classical dynamics. One way, which I guess is the "ontological" approach is to declare that classical dynamics has certain "degrees of freedom":

1. The positions and momenta of particles.
2. The values and derivatives of fields.

The goal of classical dynamics is to describe the evolution of these degrees of freedom. If you manage to come up with a Lagrangian (some local expression involving the degrees of freedom), then the Lagrange-Euler equations automatically give you the dynamics. And the amazing thing about the Lagrangian approach is that you automatically get a generalization of Newton's third law: If the equations of motion for one degree of freedom involves a second, then the equations of motion for the second degree of freedom automatically must involve the first. So you don't have anything that is godlike in the sense of influencing but not being influenced by. That to me is a very profound consequence of lagrangian dynamics.

If you turn your attention, instead, to the Hamiltonian-Jacobi principle function S, that is indeed something that acts on everything, but is not acted upon. It's the godlike function.

Now, what you are saying is that the wave function for Bohmian mechanics is analogous to S. It acts on particles, but is not acted upon by them. But what then is the analog of the classical degrees of freedom? Or maybe there just isn't any analog?

 

[Demystifier]

If you turn your attention, instead, to the Hamiltonian-Jacobi principle function S, that is indeed something that acts on everything, but is not acted upon. It's the godlike function.

Now, what you are saying is that the wave function for Bohmian mechanics is analogous to S. It acts on particles, but is not acted upon by them. But what then is the analog of the classical degrees of freedom? Or maybe there just isn't any analog?

In that sense, BM does not have a true analogue of classical degrees of freedom.

 

[martinbn]

In that sense, BM does not have a true analogue of classical degrees of freedom.

In the other thread you also said 'yes' to the question 'So nothing more than an equation that gives the result...' Then my question is what is the point of BM?

 

[Demystifier]

In the other thread you also said 'yes' to the question 'So nothing more than an equation that gives the result...' Then my question is what is the point of BM?

Ontology.

https://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/files/duerr_ontology.pdf

And by the way, the point of PBR theorem is also ontology, as is the point of most non-minimal interpretations of QM.

 

[martinbn]

What is the ontology? When I asked you, you said that the wave function is not like the electric field, I took it to mean that there is no ontology for the wave function?

 

[Demystifier]

What is the ontology? When I asked you, you said that the wave function is not like the electric field, I took it to mean that there is no ontology for the wave function?

According to BM, the only primitive ontology is particle positions. In that sense, it is just like classical mechanics. All other mathematical objects (Hamiltonians, HJ S-functions, wave functions) are only auxiliary nomological objects. Classical and Bohmian mechanics have different nomologies, but the same ontologies.

Talking about physical laws without talking about ontology is like talking about legal laws without talking about humans. A professional can do it to make the laws more efficient, but then one can miss what the laws are really about.

 

[stevendaryl]

Ontology.

https://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/files/duerr_ontology.pdf

And by the way, the point of PBR theorem is also ontology, as is the point of most non-minimal interpretations of QM.

Okay, but this sort of gets to what I don't like about Bohmian mechanics. It restores ontology, in the sense of now we can think of particles having definite positions moving along definite trajectories. But as we have been discussing, those particles don't actually have any effect on anything. To me, a large part of wanting an ontology is to understand what's going on in terms of cause and effect--explaining appearances in terms of an underlying reality. But if the reality has no causal power...

I guess an analogy might be something like watching a planetarium show. Looking up, you see stars and planets doing interesting things. Those celestial objects are real, in the sense that they are actually spots of light on a ceiling. But the dynamics of them can't be understood by studying the objects themselves, because they are just projections. All the "physics" is in the projector. In Bohmian mechanics, the particles might be real, but all the physics is in the wave function (or pilot wave, or whatever it's called).

 

[vanhees71]

All that's really interesting is, whether the trajectories in configuration space claimed to be "ontic" in BM are observable. For me it's a contradiction to say something is "ontic" and at the same time claiming it's unobservable. The only true "ontology" of any physical theory is whether it describes quantitatively and at least to the precision available in experiment what's observable. The mathematical "world" is epistemic, and just a construct of the human mind (I'm very anti-Platonic in this sense, although of course Platon's obsession with symmetries sounds very modern to physicists) and for some reason very suitable to describe observations in nature.