Entanglement swapping and Bohmian mechanics

[martinbn]

Sure, it could be. I'm certainly willing to acknowledge anything I portray incorrectly. However, I have a habit of providing exact relevant quotes with my own words following that. I recognize it takes time to find quotes from authorities and don't expect most posters to invest that time. But apparently, my quotes are not in question so much; I mostly see them being ignored.

Why do you do that? Why don't you present your logical arguments that support your position? Quotes from authority are never convinsing, and taken out of context can be even irrelevent.

 

[martinbn]

Now I read this to mean: All particles have definite positions. Further, there is a relationship between the positions of all particles in the universe; and there's action/influence upon each individual particle due to what he calls the "pilot wave".

I think this is correct in BM, all particles have well defined positions at all time, and their motions is influenced by the pilot wave. But why do you write "what he callse the pilot wave"?! Everyone calls it the pilot wave.

He does not mention the word "entanglement" to describe that relationship.

Because entanglement is a specific instance of that. It depends on the actual wave functions. More specifically on whether it is factorisable or not. I know that we had a heated argument about that, but this is the standart definition of entanglement.

I can't quote that, because Norsen doesn't say it. So I will read between the lines myself, and state: The pilot wave is not entanglement, it's the "pilot wave" or "guiding equation" (Goldstein).

This is confused. The pilot wave cannot be enetanglment. The mathematical form of the pilot wave tells you whether there is intanglment.

 

[martinbn]

Now I read this to mean: After Particle 1's spin is measured, Particle 2's spin on the same basis is fixed (and will not change, regardless of dynamic changes elsewhere in the universe). This is of course what happens in actual entanglement experiments.

I think this is the first thing you need the clear up, because in BM there is no such thing as the spin of the particle! Particles do not have spin. Spin is not a property of the particle alone.

 

[DrChinese]

1. @DrChinese here is one quote for you by Goldstein et al in https://arxiv.org/abs/quant-ph/0308039 (page 18):
"In order to avoid inconsistency we must regard Bohmian mechanics as describing the entire universe, i.e., our system should consist of all particles in the universe: The behavior of parts of the universe, of subsystems of interest, must arise from the behavior of the whole, evolving according to Bohmian mechanics."

2. From this quote it may still not be obvious to you that it is related to entanglement, but Norsen is even more explicit in his book (T. Norsen, Foundations of Quantum Mechanics, page 200):
"The pilot-wave theory is manifestly non-local in the following sense: the velocity of each particle, at a given instant, depends on the instantaneous positions of all other
particles (at least when there is entanglement)."

1. Yes, I said I accepted that as being an essential premise of BM. And I highlighted that actually by quote, it's the same essential point of his (2) in Norsen's first paragraph of his 2013 paper.

2. Yes, the pilot wave is said to be a function of all the particles in the universe as a whole. But your quote from him says absolutely nothing about bits in a computer somewhere being entangled with anything. No particular effect to that guiding equation velocity attached to bits anywhere. In fact, I could print the result on a piece of paper and look at it while Photon B (traveling at a constant c) travels to its final detector. I really don't think that piece of paper is going to change, and neither do you. So claiming there is "entanglement" there is meaningless. Those bits play no relevant part in the spin of a distant particle, even if they are members of the "entire universe".

And what role does the "entire universe" play in our entangled example anyway? Let's look again at that quote you provided. I'm not sure he intended it to supercede his more detail explanation which I previously quoted. But the book is more recent, so what does he mean?

In the same paragraph as your partial quote, Norsen says it is one particle that affects the other in an entangled situation. No mention of any other particles (or the rest of the universe) anywhere else, see his (7.54). And... no mention of computer bits. Did I express Norsen's words fairly just now? The end of the same paragraph, from his book: "The point is that the right hand side depends on X1(t), the position of the other particle – even though this could be a million miles away. How particle 1 moves will depend, according to the theory, on what’s happening with particle 2, and the dependence is immediate (with nothing like a speed-of-light time delay) and independent of the distance between the particles." The following paragraphs are much the same as his explanation I have previously quoted from his paper. So I don't think his views have changed.

---

So basically: I continue to stand by what I've said. (That shouldn't be a shock )

And what is my point anyway, why do I even care? I want to understand if the particle midflight in our example (recall it's photon B, after photon A was measured on the +/- basis) stays in the same definite spin state all the way through it's ultimate final measurement. That could be a measurement on the +/- basis, in which case the outcome is predictable and certain. Or, it could be a participant in a Bell State measurement with photon C, if B & C are made to overlap physically.

As best I can discover, from quotes I provided by Goldstein, Norsen, Oriols et al, the answer is:

Yes, a polarization entangled "Bohmian" photon B will remain in a fixed definite polarization state up to and including its later measurement on the same basis (after a previous measurement on its partner photon A). Certainly, there is no influence from the future measurement apparatus itself (other than its orientation at detection), which is never even mentioned in any of the referenced discussions.

If that conclusion is unacceptable to anyone, please chime in with your alternative ideas.

 

[DrChinese]

Why don't you present your logical arguments that support your position? Quotes from authority are never convinsing, and taken out of context can be even irrelevent.

First, I'm not a Bohmian and I am not qualified. Which is why I am asking. I'm trying to synthesize the views of a variety of writers, and there aren't as many in the Bohmian regime as in oQM.

Second, quotes from authority ARE to be respected on PhysicsForums. As you well know, we discuss generally accepted physics. Even here in Interpretations/Foundations, wildcat speculation is not appropriate. So yes, I quote others looking to get confirmation or rejection of their ideas per published works.

 

[DrChinese]

I think this is correct in BM, all particles have well defined positions at all time, and their motions is influenced by the pilot wave. But why do you write "what he calls the pilot wave"?! Everyone calls it the pilot wave.

Goldstein frequently uses "Guiding Equation". I've seen it mentioned in other terms too.

I think this is the first thing you need the clear up, because in BM there is no such thing as the spin of the particle! Particles do not have spin. Spin is not a property of the particle alone.

I realize that. Yet, spin is an observable. For BM to be a candidate theory/interpretation, it must reproduce the prediction of QM vis a vis spin and polarization. So however the Bohmian gets from particle position/velocity/pilot wave to spin, that probably works for me as a "black box" unless the spin rules are to change.

 

[DrChinese]

Are you saying that pilot wave cannot describe entanglement?

Being a term in a formula/function containing a very large number of terms does not make things (individual components) entangled. Whenever lay people say "everything is entangled" I tell them no, they are not. Ditto with the Pilot Wave. As mentioned previously: every atom in the Milky Way influences the movement of my body via gravitation. But that doesn't make us entangled.

As to whether the pilot wave can describe entanglement, I think you are in a better position to assess that. My working assumption in understanding BM is that it can and does up to some point.

However, it is shocking (to me) that there are virtually no papers* that attempt to describe advanced entanglement concepts in Bohmian terms. And of course I mean to exclude explicitly all pro-BM arguments to the effect that "BM reproduces all of the predictions of QM"; implying further explanation is not necessary. If Bohmian Mechanics hopes to represent itself as a theory (and not an interpretation), that argument falls flat - obviously. Asking questions about how Bohmian Mechanics treats entanglement swapping is fair game. But we haven't gotten there quite yet. I am hoping to!!

*Norsen does at least talk a bit about EPR/Bell tests from the Bohmian view. But even his book - which is only intended for an undergraduate audience - does not mention swapping or delayed choice. Entanglement, while mentioned, is barely discussed. That's not a criticism, just a statement.

 

[Matterwave]

I realize that. Yet, spin is an observable. For BM to be a candidate theory/interpretation, it must reproduce the prediction of QM vis a vis spin and polarization. So however the Bohmian gets from particle position/velocity/pilot wave to spin, that probably works for me as a "black box" unless the spin rules are to change.

I will say though, as a mostly passive observer, I feel you do often use language that is going to get push-back from the BM view, especially each time you insist on calling the spin/polarization a property of the particle itself.

There are some rather strong quotes from Norsen, Durr, Goldstein, Zhanghi, pushing back against the view that in BM something like spin is a pre-existing property of the particle itself. For example:

Norsen (https://arxiv.org/pdf/1305.1280):

The idea that there should be something contrived or intolerable about contextuality undoubtedly arises from the idea that, if a property really exists, measurement of it should – by definition – simply reveal its value. It would be hard, actually, to disagree with this sentiment. The key question, though, is precisely whether any such property exists. As has been discussed in illuminating detail in Ref. [25], the real lesson to be taken away from examining the pilot-wave perspective on spin is that so-called “contextual properties” (like the individual spin components in the pilot-wave theory) are not properties at all. [26] They simply do not exist and there is nothing mysterious about this at all, just as there is nothing mysterious in the fact that the eventual flavor of a loaf of bread (which depends not just on the ingredients but also on how it is later baked!) is not a pre-existing property of the raw dough

Norsen goes on to quote Durr, Goldstein, Zhanghi:

“Note that one can completely understand what’s going on in [a] Stern-Gerlach experiment without invoking any putative property of the electron such as its actual z-component of spin that is supposed to be revealed in the experiment. For a general initial wave function there is no such property. What is more, the transparency of the [pilot-wave] analysis of this experiment makes it clear that there is nothing the least bit remarkable (or for that matter ‘nonclassical’) about the nonexistence of this property.” [27]

 

[Matterwave]

I mention this because even if it might not be *your* point whether the spin/polarization exists as a property of the particle in BM or not (or you don't care), such use of language will invariably make it more difficult to discuss your points in general because people will naturally want to correct you. Using language that is precise about the viewpoint it is addressing is important to having a productive conversation.

 

[iste]

Yes, a polarization entangled "Bohmian" photon B will remain in a fixed definite polarization state up to and including its later measurement on the same basis (after a previous measurement on its partner photon A). Certainly, there is no influence from the future measurement apparatus itself (other than its orientation at detection), which is never even mentioned in any of the referenced discussions

I have lost track of the thread arguments, so can I ask what is the sigbificance and consequence of this statement again for entanglement swapping regarding Bohmian mechanics (and orthodox)?

 

[Demystifier]

I really don't think that piece of paper is going to change, and neither do you. So claiming there is "entanglement" there is meaningless.

I've already explained to you, but you ignored it, that the lack of change does not imply the lack of entanglement. If you look at the definition of entanglement, in any book or paper you like, there is no mention of "change" in the definition. It is your own misconception that entanglement must be associated with a change.

But I have a question for you. Are you familiar with the Schrodinger cat thought experiment? Do you agree that, in that experiment, the state of the cat (dead or alive) is entangled with the state of the atom (decayed or not)? Or to be more precise, do you agree that in this experiment the state is of the form
$$|{\rm cat \;\; dead}\rangle |{\rm atom \;\; decayed}\rangle + |{\rm cat \;\; alive}\rangle |{\rm atom \;\; not \;\; decayed}\rangle ?$$
And do you agree that this state, as written above, is an entangled state?

When you answer these questions (which is really one question put in different forms), it will be much more clear how you understand the notion of entanglement, and how your understanding differs from the understanding of others.

And until you answer it, my working hypothesis will be this: You don't understand what is entanglement, not even in the context of standard QM.

And needless to say, you cannot understand entanglement swapping before you understand entanglement.

 

[DrChinese]

I mention this because even if it might not be *your* point whether the spin/polarization exists as a property of the particle in BM or not (or you don't care), such use of language will invariably make it more difficult to discuss your points in general because people will naturally want to correct you. Using language that is precise about the viewpoint it is addressing is important to having a productive conversation.

Well certainly the language of entanglement used by top physicists should be currency in our discussions. Not sure why I would defend that. It’s what I use, I stand by it 100%.

I am discussing experiments that have been performed following generally accepted physics of quantum spin theory. If anyone wants to deny those results or that theory, I’m not really sure why they would say so here.

So me being the odd person out? Seriously? Spin and polarization are real. No Bohmian can deny these as observables at a bare minimum. Or maybe some do? Who?

The results of experiments are the results. A |V> polarized photon comes out of only one port of a PBS… always. You’re going to deny that minor detail because spin doesn’t exist? A Bohmian should explain it - as Norsen attempts - not deny it or hide under a veil of semantics. Acknowledge documented experiments and that is our common ground.

 

[DrChinese]

I've already explained to you, but you ignored it, that the lack of change does not imply the lack of entanglement.

Umm, it does actually. At least under Bohmian concepts. Norsen specifically lays that out in his paper describing an entangled spin pair. One entangled particle’s outcome completely dictates the other’s, nothing else does which is not entangled.

---

Note: I will gladly discuss an actual experiment with you, but discussions of hypothetical cats are outside my field. Do you not see that making up false dichotomies is not actually moving anything forward? I am sure many people understand entanglement better than I, but you certainly are not one of them. I have asked straightforward questions about basics of spin experiments from top teams, and you avoid a direct Bohmian answer. Of course you are not obligated to, but that is no reason to cast aspersions towards me.

Photon B is midflight with a certain measurement outcome, say |+>. Does it/can it change polarization midflight prior to measurement, or is it static in the Bohmian view as Norsen says/implies? That photon might participate in a future swap with photon C (say on the H/V basis), or it might be measured on the same original basis as photon A. That’s our thread.

Again, neither you nor anyone else is obligated to answer. But not answering and instead questioning my understanding level is not actually an answer. And if you don’t know, that’s ok too. No big deal. I’m asking a question, looking for an answer that someone can connect to some recognizable experiments by top teams.

 

[DrChinese]

I have lost track of the thread arguments, so can I ask what is the sigbificance and consequence of this statement again for entanglement swapping regarding Bohmian mechanics (and orthodox)?

Great comment! Here’s my question, followed by the consequence of the answer:

Photon B is midflight with a certain measurement outcome, say |+>. Does it/can it change polarization midflight prior to measurement, or is it static in the Bohmian view as Norsen says/implies? That photon might participate in a future swap with photon C (say on the H/V basis), or it might be measured on the same original basis as photon A (+/-).

Once the above is answered: Now IF Photon B is in the actual state |+>, THEN would it be also able to participate in a swap with Photon C? This is a murky area, but it is not particularly more clear in orthodox QM either. But Bohmian theory is strictly forward in time only (FITO). So maybe there is a distinction. I don’t know, it’s why I’m asking.

-DrC

 

[Matterwave]

Well certainly the language of entanglement used by top physicists should be currency in our discussions. Not sure why I would defend that. It’s what I use, I stand by it 100%.

Many (most) "top physicists" use the language of standard QM, a lot of which is what Bohmians complain against.

But I can not force you to use some particular language. You can view my post as an attempt to move the conversation forward, but if you think it's not helpful, you can certainly ignore it. :)

If anyone wants to deny those results

I don't believe my post implied this.

 

[DrChinese]

There are some rather strong quotes from Norsen, Durr, Goldstein, Zhanghi, pushing back against the view that in BM something like spin is a pre-existing property of the particle itself. For example…

I am not asserting BM is wrong in its views on spin. On the contrary: I am assuming there IS a Bohmian explanation for all referenced spin experiments.

No authors you mention really touch on modern experiments though. They are mostly about 30+ years behind. And I’m not talking about claims, which are a dime a dozen. I’m asking for a good reference I can get my teeth into. And again, the lack of good references is not itself a criticism on my part. I’ve looked, can’t find any, and would love to add something worthwhile to my links.

Got anything good you can share?

 

[DrChinese]

Many (most) "top physicists" use the language of standard QM, a lot of which is what Bohmians complain against.

But I can not force you to use some particular language…

Understood.

I readily accept the basic Bohmian premises for discussion purposes, and am happy to adapt my terminology as best as am able. I thought I was meeting Bohmians halfway by calling spin an “observable”.

But let’s be realistic: all of the experiments I want to discuss involve spin/polarization! They are real, objective, and cannot be simply ignored by denial. Is spin at least an observable? How else can we discuss if we can’t agree on this?

 

[Demystifier]

One entangled particle’s outcome completely dictates the other’s, nothing else does which is not entangled.

Dictating is not changing. I have explained the difference in the first post in this thread on the example with cards.

Photon B is midflight with a certain measurement outcome, say |+>. Does it/can it change polarization midflight prior to measurement, or is it static in the Bohmian view as Norsen says/implies? That photon might participate in a future swap with photon C (say on the H/V basis), or it might be measured on the same original basis as photon A. That’s our thread.

The photon, as a particle in a Bohmian sense, does not even have polarization prior to measurement. What does have a polarization is the effective wave function (pilot wave) guiding this photon. In principle, this polarization can change even without the measurement. But in the experimental setup we are discussing it doesn't change.

 

[Demystifier]

I will gladly discuss an actual experiment with you, but discussions of hypothetical cats are outside my field.

Ok, then answer this. Suppose that we prepare one particle with spin in the superposition of the form
$$|+\rangle + |-\rangle$$
Then we measure it with the measuring apparatus $M$, in the $\pm$ basis. Prior to collapse, do you agree that the state of the full system (apparatus + particle) is of the form
$$|M_+\rangle|+\rangle +|M_-\rangle |-\rangle ?$$
Do you agree that this state is entangled?

 

[DrChinese]

The photon, as a particle in a Bohmian sense, does not even have polarization prior to measurement. What does have a polarization is the effective wave function (pilot wave) guiding this photon. In principle, this polarization can change even without the measurement. But in the experimental setup we are discussing it doesn't change.

I hope you’re talking about our entangled photon B.

In oQM, we would also rebel against assertions about unperformed measurements. So that’s fair, although I think it goes diametrically against what Norsen said. I understood observables to have definite values.

But thank you for stating that it doesn’t change in the experiment we are discussing.

 

[DrChinese]

Ok, then answer this. Suppose that we prepare one particle with spin in the superposition of the form
$$|+\rangle + |-\rangle$$
Then we measure it with the measuring apparatus $M$, in the $\pm$ basis. Prior to collapse, do you agree that the state of the full system (apparatus + particle) is of the form
$$|M_+\rangle|+\rangle +|M_-\rangle |-\rangle ?$$
Do you agree that this state is entangled?

The future measurement apparati are not in any way involved in an entangled pair any more than human observers in the lab are. You can label that however you like. And post measurements, the measurement apparati are no more entangled than those same observers are.

Not sure what this has to do with this thread. What, you’re giving me test questions now?

 

[Matterwave]

No authors you mention really touch on modern experiments though. They are mostly about 30+ years behind.

Well the paper from Norsen I quoted is from 2013. Do you mean you specifically want a BM treatment of a modern (delayed) entanglement swap experiment? I am not aware of any, but if I come across one I'll post it here.

I thought I was meeting Bohmians halfway by calling spin an “observable”.

Is spin at least an observable? How else can we discuss if we can’t agree on this?

I have a feeling, and please tell me if I'm wrong, that when you say "observable" and you are referring to e.g. spin as viewed through the lens of Bohmian Mechanics, you are thinking of "a thing which has a definite value at all times" and for which a subsequent measurement will reveal this value. Is that so? Only talking Bohmian mechanics here.

 

[Motore]

The future measurement apparati are not in any way involved in an entangled pair any more than human observers in the lab are.

I think you are completely wrong here. From this paper:
https://arxiv.org/html/0905.4036v1

First, the definition of a physical system in BM does not include just the particles whose behaviour is under observation, but also the measurement apparatus – in the case of entanglement exchange, a device that we’ll call the “Bell-ometer”.

They mathematically show that the trajectories of particles 1 and 4 change contextually depending on how particles 2 and 3 interact with the macroscopic device.

In Bohmian mechanics, you can't just leave out the apparatus. It's the actual physical evolution of the device's particles that chops up the pilot wave and forces those distant particles into their new entangled states.

 

[Demystifier]

The future measurement apparati are not in any way involved in an entangled pair any more than human observers in the lab are. You can label that however you like. And post measurements, the measurement apparati are no more entangled than those same observers are.

Not sure what this has to do with this thread. What, you’re giving me test questions now?

Yes, I am testing your understanding of the concept of entanglement. More precisely, of the entanglement of apparatus with something else. This is extremely important for this thread because I (and others) emphasized a million times that it is the apparatus which is entangled with something, which you denied. And now, you didn't give me a straight answer, is it entangled or not? Yes or no? Without a straight answer to that question, I claim, it is impossible to understand BM in general, and BM explanation of entanglement swapping in particular.

 

[Demystifier]

Roughly, this whole thread can be summarized as follows.
1) BM explains entanglement swapping by emphasizing the role of entanglement with the measuring apparatuses.
2) @DrChinese cannot accept that entanglement with the apparatus is a meaningful concept.
3) Therefore DrChinese thinks that BM cannot explain entanglement swapping.

 

[Morbert]

Remember that it was previously established that @DrChinese does not accept basic quantum theory, which is a prerequisite for a Bohmian accounting (or any accounting) of any quantum-related experiment.

 

[Demystifier]

I think you are completely wrong here. From this paper:
https://arxiv.org/html/0905.4036v1

They mathematically show that the trajectories of particles 1 and 4 change contextually depending on how particles 2 and 3 interact with the macroscopic device.

In Bohmian mechanics, you can't just leave out the apparatus. It's the actual physical evolution of the device's particles that chops up the pilot wave and forces those distant particles into their new entangled states.

That's all correct, but note that this paper considers the case in which the joint measurement of B and C (called 1 and 3 in this paper) is performed before the independent measurement of A and D, while in this thread we are more interested in a more puzzling case where this joint measurement is performed after. This is more puzzling because in this case the photons A and D don't even exist (they are destroyed) at the time of joint measurement of B and C, and yet A and D show entanglement before this joint measurement, conditioned on the result of that measurement that will happen in the future. For that version of the experiment the role of the apparatus is even more important. Namely, even though photons A and D don't exist in the future, some remnant of them still exists. In unitary quantum theory, quantum information is never really destroyed. This remnant carrying the relevant quantum information is the two apparatuses that measured and absorbed the photons A and D. Hence, in the future just before the joint measurement of B and C is performed, it is those two apparatuses that are entangled with B and C. To put it metaphorically, even though the photons A and D are no longer with us, their spirit still lives in the apparatuses that measured and destroyed them.

 

[Demystifier]

Remember that it was previously established that @DrChinese does not accept basic quantum theory, which is a prerequisite for a Bohmian accounting (or any accounting) of any quantum-related experiment.

Remind me, what aspect of basic QM he does not accept?

 

[Morbert]

Remind me, what aspect of basic QM he does not accept?

He does not accept the expansion of pure states. E.g. He rejects equation (2) as an expression of the initial preparation in Ma's entanglement swapping experiment. https://arxiv.org/pdf/1203.4834

As such, questions like:

$$|M_+\rangle|+\rangle +|M_-\rangle |-\rangle ?$$
Do you agree that this state is entangled?

Have no hope of a reasonable answer.

 

[Motore]

Remind me, what aspect of basic QM he does not accept?

See post #204 and prior, future posts.