Pilot wave persistence after measurement in Bohmian entanglement

[PeterDonis]

what mathematical object they mean when they say "the wave function" (or the pilot wave).

The wave function that describes the quantum system being modeled. That would be particles A and B (and C and D in the entanglement swapping cases @DrChinese has brought up).

Are we talking about the universal wave function (including measurement apparatuses)

Not in this thread as I understand it, no. I don't know if there's even a version of BM that tries to model measurement apparatuses and observers using a wave function.

the wave function of particle A and B or just A or just B (at some point in time where the joint A B wave function is approximately a product state)

In the simplest case we've been discussing, it would be the wave function of the A-B entangled system before A is measured, and the wave function of B, adjusted by the effective collapse when A is measured, after A is measured.

the relative wave function of A relative to B

I don't know what this means.

 

[Demystifier]

I'm not sure I agree. The velocity change is due to the effective collapse of the wave function because of the measurement of A, which changes the effective quantum potential in B's Hamiltonian. That is a change in the properties of the wave function.

Yes, but the effective collapse refers to the effective wave function, not to the fundamental wave function.

For various notions of "wave function" in BM, see e.g. my lecture
http://thphys.irb.hr/wiki/main/images/e/e6/QFound4.pdf
pages 23-24.

 

[Matterwave]

Not in this thread as I understand it, no. I don't know if there's even a version of BM that tries to model measurement apparatuses and observers using a wave function.

Yes, but the effective collapse refers to the effective wave function, not to the fundamental wave function.

It did seem to me like "which wave function"? Was the disagreement in post #89.

I don't know what this means.

Apologies, I've been reading Everett's dissertation lately and that terminology is used by him. I meant the relative state in his sense. For particle A: $|\psi^{b_i}_{rel}\rangle=\text{Norm}(\langle b_i|\Psi\rangle)$

 

[PeterDonis]

the effective collapse refers to the effective wave function, not to the fundamental wave function

Yes, that's true, but the effective wave function, as your slides note, is what determines future trajectories, so that's the one that's relevant to this discussion.

 

[PeterDonis]

I've been reading Everett's dissertation lately and that terminology is used by him. I meant the relative state in his sense

I don't think that plays any role in BM.

 

[Sambuco]

b) Particles A and B can be entangled retroactively, after they cease to exist. See for example: Experimental delayed-choice entanglement swapping "This can also be viewed as 'quantum steering into the past'".
c) Particles A and B can be entangled when A is measured (destroyed) before B is even created. See: Entanglement Between Photons that have Never Coexisted "The observed quantum correlations manifest the non-locality of quantum mechanics in spacetime."

So:

b) BM is inconsistent with this. If A and B are no longer in existence, the Bohmian concept of a shared configuration space for entanglement makes no sense. There is no delayed action in Bohmian Mechanics.
c) BM is inconsistent with this. Similar to b), if A is no longer in existence, the Bohmian concept of a shared configuration space with B for entanglement makes no sense. Bohmian action is instantaneous, no time delay.

All those entanglement-swapping experiments can be satisfactorily described by Bohmian mechanics, but it's important to note that its interpretation is completely different from the one given in the papers you cited. For an information-based interpretation like Zeillinger's, where the wave function is just a "catalog of our knowledge," there is nothing wrong with saying that Alice and Bob's particles are entangled from Victor's (who chooses between BSM/SSM) perspective, as the wave function he constructs from his own experimental results proves it. However, in a $\psi$-ontic interpretation, such as Bohmian mechanics, the wave function from Victor's perspective is not "real", because there is a single "real" wavefunction that (only) evolves forward in time, so the correlation between Alice and Bob's particles is interpreted as being induced by post-selection based on Victor's results. This is discussed in Cohen's paper, which we've mentioned in another thread. He called it a "counterfactual entanglement".

Lucas.

 

[PeterDonis]

in a $\psi$-ontic interpretation, such as Bohmian mechanics

While BM is indeed referred to in the literature as $\psi$-ontic, it's very different from other such interpretations, because, as has been noted several times in this thread, $\psi$ plays a completely different role in BM relative to the quantum system. In other $\psi$-ontic interpretations, $\psi$ is the state of the system--though not a "complete" state in the sense that it does not allow you to predict with certainty the results of all possible measurements on the system. In BM, $\psi$ (as the quantum potential) is part of what determines the system's equation of motion; the system itself is described by unobservable particle positions.

 

[Sambuco]

While BM is indeed referred to in the literature as ψ-ontic, it's very different from other such interpretations, because, as has been noted several times in this thread, ψ plays a completely different role in BM relative to the quantum system. In other ψ-ontic interpretations, ψ is the state of the system--though not a "complete" state in the sense that it does not allow you to predict with certainty the results of all possible measurements on the system.

Yes, I completely agree with what you're saying. In fact, I put that BM is a $\psi$-ontic interpretation because that's the usual way and to avoid confusion, but personally, I consider it a $\psi$-nomological interpretation.

In BM, ψ (as the quantum potential) is part of what determines the system's equation of motion; the system itself is described by unobservable particle positions.

I would like to clarify that the mention of the "quantum potential" is closely related to Bohm's original work, which presented a modified version of Newton's second law that included such a potential. In a modern approach, such as the Dürr-Goldstein-Zanghì one, the fundamental guide equation is first-order, relegating the quantum potential to a secondary (non-fundamental) role.

Lucas.

 

[DrChinese]

No, BM does not say that.

BM says that the wave function changes instantaneously and nonlocally because of the "effective collapse" when A is measured. But as I have said multiple times now, the wave function is not the particle. This change in the wave function is not a change in B. It's a change in the equation of motion that determines B's motion. In other words, what changes instantaneously and nonlocally when A is measured is the thing that we use in BM to determine B's future trajectory. But B's current position when A is measured does not change at all. There is no random jump or any other such process.

Norsen absolutely says B changes: "If particle 1 goes up, the collapse suffered by the CWF of particle 2 (on the left) causes it to go down (solid trajectories) regardless of its initial z-coordinate."

You can attempt to distinguish between B's "future trajectory" (I might call that momentum) versus B's "current position", whatever relevance you think that makes. But the fact is that B thereafter has an observable spin component that changed. Not only has it changed, it won't change again prior to Bob seeing it.

I am not confused by Norsen's unambiguous description. A physical change occurs to B as a result of something occurring to A, and presumably that occurs on the configuration space being shared in some manner by A and B while they are spin entangled.

 

[PeterDonis]

n a modern approach, such as the Dürr-Goldstein-Zanghì one

Can you give a link?

 

[DrChinese]

This nonlocal change refers to the velocity of the Bohmian particles, not to the properties of the wave function (aka pilot wave). So is there a nonlocal change of the spin? It depends on what do you mean by "spin". If you mean a property of the wave function, then there is no such nonlocal influence. But if you mean a macroscopic position of the spot on Stern-Gerlach apparatus (that experimentalist interprets as a measurement outcome associated with measurement of spin), then there is a nonlocal influence on "spin" defined as the positition of the spot.

@Demystifier: Your attempts to deny the obvious by language twists surprises me. You're a Bohmian, and yet you find it difficult to agree with the meaning and intent of Norsen's language: "If particle 1 goes up, the collapse suffered by the CWF of particle 2 (on the left) causes it to go down (solid trajectories) regardless of its initial z-coordinate." Cause, effect.

A measurement on A causes an experimentally verified nonlocal physical change to the Bohmian observable on B. How hard is it to say that without hiding behind some perceived semantic difference between spin as a "property of the wave function" and "macroscopic position ... associated with measurement of spin". Spin, even if you don't believe it exists as a distinct orthodox quantum property taught in textbooks, is still the exact same observable scientists study and get Nobel prizes for.

 

[PeterDonis]

Norsen absolutely says B changes

He says that B's future trajectory after A's measurement is affected. He does not say that B's current position at the time of A's measurement changes.

You can attempt to distinguish between B's "future trajectory" (I might call that momentum) versus B's "current position", whatever relevance you think that makes.

It makes a huge difference. See below.

the fact is that B thereafter has an observable spin component that changed.

No. That is not the fact. (I use the same emphasis you did.) The fact is that the wave function that appears in B's Hamiltonian changed. And that is all that changed.

B's "observable spin component" doesn't even exist in BM until B's spin is measured. Once more I have to emphasize that the wave function is not the particle. So the wave function changing does not mean the particle changed. The fact that the wave function includes a Z spin component that now has only one possible branch does not mean "the spin of B" has been set to a particular value. All it means is that the wave function has changed.

To you these perhaps seem like arbitrary hairsplitting distinctions, but they're not, because your repeated failure to make them is keeping you from actually understanding how BM models the scenario under discussion. And thus you keep making the same wrong statements despite repeated corrections. And thus this thread keeps going around in circles.

I am not confused by Norsen's unambiguous description.

Yes, you are, because you immediately make the same wrong statement again:

A physical change occurs to B

No. A change to the wave function is NOT a physical change to B. The wave function is not the particle.

Your attempts to deny the obvious by language twists surprises me.

You are in no position to make this kind of criticism given your own repeated misunderstandings, as noted above. I strongly suggest that you stop posting further in this thread until you have read and re-read my post above, and the previous ones that said the same thing, and let what they are actually telling you sink in.

A measurement on A causes an experimentally verified nonlocal physical change to the Bohmian observable on B.

Wrong. See above. Please do not continue making these wrong claims.

 

[DrChinese]

All those entanglement-swapping experiments can be satisfactorily described by Bohmian mechanics, ...

Lucas.

And I say it can't. Now, I've quoted actual experiments that describe the orthodox quantum theory and its well-accepted and confirmed experimental implementation. Show me any Bohmian step by step explanation of the mechanics - in precise time order as required by Bohmian theory. These experiments clearly defy Bohmian cause and effect concepts, which specifically require instantaneous action at a distance in a forward time direction only.

Must not be a reference that says "the details are trivial to be worked out be the reader".

 

[PeterDonis]

And I say it can't.

And you say this despite not understanding what BM actually says. That's enough. I am closing this thread for moderation, so that other moderators can decide whether it has run its course and what, if any, action might be required.

 

[PeterDonis]

I am saying there is no counterfactual information in existence. (It would run afoul of Bell if it did, IMHO.)

As a note for future readers of the thread: BM violates Bell's locality assumption, so it does not have to violate counterfactual definiteness in order to violate the Bell inequalities.

 

[PeterDonis]

A new thread has been started by @Demystifier on the topic of how BM accounts for entanglement swapping experiments. The new thread is here:

Undergrad Thread 'Entanglement swapping and Bohmian mechanics'

Sunday, 5:03 AM

Since the recent thread on Bohmian mechanics (BM) is now closed, I open a new thread in which I want to explain something that bothers @DrChinese for a long time. How can BM explain the entanglement swapping? But I want to make this explanation simple and intuitive, rather than technical. I want to explain what, in my opinion, is the main conceptual misunderstanding behind DrChinese's impression that BM can't explain entanglement swapping. For that purpose I will start with something completely fictional, not directly related to actual science, because this fiction, I believe, will...

• Demystifier
• Replies: 116
• Forum: Quantum Interpretations and Foundations

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This thread will remain closed.