Pilot wave persistence after measurement in Bohmian entanglement

[PeterDonis]

how does the Pilot wave even know where B is being routed for measurement?

It doesn't have to. The pilot wave is just a part of the Hamiltonian that determines B's equation of motion. It doesn't have to "know" anything about B. B has to "know" what the equation of motion is, that's all.

According to your concept, that measurement setting information is then available instantaneously to the controlling Pilot wave. If that isn't a "conspiracy", I don't know what is.

It's an explicitly nonlocal realistic model, as I've said before (and as you agreed). That doesn't require any fine-tuning of the initial conditions (which is why @Demystifier said it isn't superdeterminism). It just requires instantaneous action at a distance; yes, the pilot wave updates itself instantaneously throughout the entire universe whenever anything changes that affects it.

Note, though, that I don't think Bob's measurement settings have to affect the pilot wave. The B particle and the pilot wave don't need to "know" anything in advance about those. They only need to "know" what the measurement settings are when the B particle actually goes through the apparatus. What happens while the B particle is still in mid-flight and hasn't reached the apparatus doesn't matter.

 

[PeterDonis]

What is specific for the Bohmian interpretation is that now, when the entanglement is effectively destroyed, we can say that the pilot wave associated with $A+E_A$ effectively ceases to act on the Bohmian particle associated with B.

But we can also say, knowing the result of the $A$ measurement, that only the portion of the $B$ pilot wave that is in the collapsed branch (i.e., the one associated with the $B$ measurement result that corresponds to the $A$ measurement result that was observed) will affect the motion of $B$. That is what makes it certain that, if we measure $B$ in the same basis, we must get, with certainty, the result that corresponds to the $A$ result.

 

[DrChinese]

@DrChinese
1. Here by photons A and B you mean the states in the Hilbert space (aka wave functions), and not the Bohmian particles with definite positions. Am I right? Otherwise, the text above makes no sense.

2. Now that's confusing on several levels. First, how can it occur first in all reference frames? In BM it occurs first in the preferred reference frame, not in all reference frames. Second, the pilot wave is the wave function (e.g. |HH>+|VV> or something like that). So how can the wave function act on B, which is also a wave function? There is no such action in BM. Perhaps now you changed the meaning of B and by B you mean the Bohmian particle with definite position? Fine, but you cannot speak coherently by using the same name B for two different things.

1. If you are drawing a distinction between photons as Bohmian particles versus electrons as Bohmian particles, we are veering away from the essence of this discussion. If we used the term "electron" and discuss its x/y/z spins, it's the same discussion. Same physics questions.

So if we need to discuss x/y/z spins and entanglement of electrons or other spin 1/2 systems from here on out, that's fine with me. Just let me know, it doesn't change the issues for me.

2. Certainly there are plenty of ways to position Alice and Bob such that Alice's measurement reading is before Bob's in all reference frames. And Norsen explicitly uses the same terminology/assumption/whatever you want to call it, as I quoted previously:

"One of the particles will encounter its measuring device first; the outcome of this first measurement will be determined by the random initial position of this measured particle within its wave packet; the completion of this first measurement induces a collapse in the distant particle’s CWF; this in turn determines the statistics for a subsequent measurement on the distant particle."

What difference is it to our discussion whether it is Alice or Bob we wish to identify as first?

 

[PeterDonis]

If you are drawing a distinction between photons as Bohmian particles versus electrons as Bohmian particles

He isn't. What he's emphasizing is that in BM, the wave function is not the state of the particle. The state of the particle is the Bohmian particle position. The wave function is just part of the potential in the Hamiltonian that determines the particle's equation of motion. So you have to be very careful to not talk about things in a way that implicitly assumes that the wave function describes the particle--because in BM it doesn't.

 

[DrChinese]

It doesn't have to. The pilot wave is just a part of the Hamiltonian that determines B's equation of motion. It doesn't have to "know" anything about B. B has to "know" what the equation of motion is, that's all.

1. It's an explicitly nonlocal realistic model, as I've said before (and as you agreed). That doesn't require any fine-tuning of the initial conditions (which is why @Demystifier said it isn't superdeterminism). It just requires instantaneous action at a distance; yes, the pilot wave updates itself instantaneously throughout the entire universe whenever anything changes that affects it.

2. Note, though, that I don't think Bob's measurement settings have to affect the pilot wave.

1. The point I am making: the Pilot wave cannot affect B's spin after A is measured. Anything that goes on in the rest of the universe has no net effect on B's spin (polarization) on the basis Alice measured.

Otherwise, that would go against exactly what Norsen said: "One of the particles will encounter its measuring device first; the outcome of this first measurement will be determined by the random initial position of this measured particle within its wave packet; the completion of this first measurement induces a collapse in the distant particle’s CWF; this in turn determines the statistics for a subsequent measurement on the distant particle."

Demystifier (I think!) is saying that changes to Bob's measurement setting affects the Pilot wave prior to arrival at Bob's apparatus. In his #42, he states that the Pilot wave DOES still affect B midflight. Further: "Yes, but the outcome is a property of the measuring apparatus, not a property of the measured particle." I see these posts as being quite in disagreement with Norsen's statement. Keeping in mind, of course, there is no requirement that Demystifier agree with Norsen in the first place. Nor do I assume that Norsen is "more correct" than our own @Demystifier is! After all the works I have read on BM, few actually agree on every element.

2. If fact, nothing in the universe does - no future net change to B as its H/V (or whatever) observable! At least that would need to be the situation if you follow Norsen's summary, as quoted.

 

[Demystifier]

On these matters I agree on almost everything with Norsen, as well as with @PeterDonis . On the other hand, I find very difficult to understand what exactly @DrChinese finds problematic.

 

[PeterDonis]

the Pilot wave cannot affect B's spin after A is measured.

This is not correct. The part of the pilot wave that appears in B's Hamiltonian always affects B.

What is true is that the part of the pilot wave that appears in A's Hamiltonian cannot affect B after A is measured, because of the "effective collapse" that @Demystifier described, or, to put it another way, because after A is measured, A and B are no longer entangled. It's the entanglement that makes A's part of the pilot wave affect B.

However, as I noted in post #62, the "effective collapse" based on A's measurement result means that the only part of B's pilot wave that matters is the part that's guaranteed to guide it into the appropriate measurement result that corresponds with A's measurement result. That's how the correlation between A's and B's measurement results is enforced in BM.

Otherwise, that would go against exactly what Norsen said

With the clarification I gave above, no, it wouldn't.

Demystifier (I think!) is saying that changes to Bob's measurement setting affects the Pilot wave prior to arrival at Bob's apparatus.

I don't think he is. Nor do I think this is necessary, as I explained in post #61.

 

[PeterDonis]

Further: "Yes, but the outcome is a property of the measuring apparatus, not a property of the measured particle." I see these posts as being quite in disagreement with Norsen's statement.

No, they're not. Remember that in BM, the particle is just like a classical particle obeying an equation of motion--but the equation of motion includes a term coming from the pilot wave (quantum potential).

When a particle goes through a measuring device, its equation of motion also includes terms coming from the measuring device, whose effect depends on the measuring device's settings. That's why you can't just view the measurement outcome as a property of the particle alone.

 

[DrChinese]

On these matters I agree on almost everything with Norsen, as well as with @PeterDonis . On the other hand, I find very difficult to understand what exactly @DrChinese finds problematic.

My simple problem:

a) Can anything Bob does prior to measurement nonlocally affect B? Because Norsen clearly says NO. (Again, see his quote.) If you disagree with Norsen on this, just say so.
B) Can anything anywhere else in the universe prior to B’s measurement non-locally affect B? Because Norsen clearly says NO.

And by “affect B”, I mean the basis (H/V) measurement of B and only that, and of course, assuming no other particle interaction mid flight. I just don’t see where my point is confusing. Norsen’s quoted description properly accounts for observed statistics without further embellishment, and specifically excludes action by Bob or any other agent.

———

Once you concur with my a and b above, the next question I have is whether anything can affect B as regards to other non-commuting spin observables. Say L/R polarization for a photon (or x-spin for an electron). And also commuting observables, say frequency or momentum. I would expect any reasonable interpretation/description of Bohmian mechanics to answer these basic questions for entangled pairs.

 

[DrChinese]

No, they're not.

You’re disagreeing with Demystifier’s comment, not mine. And yet again to quote Norsen on this point: "One of the particles will encounter its measuring device first; the outcome of this first measurement will be determined by the random initial position of this measured particle within its wave packet; the completion of this first measurement induces a collapse in the distant particle’s CWF [my B]; this in turn determines the statistics for a subsequent measurement on the distant particle." With this description, without embellishment, the observed statistics will be correct regardless of Bob’s choice of setting. I.e., the usual function of theta.

Norsen, on entanglement:
"In the top frame, particle 1 (on the right) encounters its SGz device first; the particle is found to be spin-up (solid trajectories) or spin-down (dashed trajectories) depending on the initial z-coordinate of the particle. 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. On the other hand, if particle 1 goes down, the collapse causes particle 2 instead to go up (dashed trajectories) regardless of its initial z-coordinate."

Add no point does Norsen invoke actions by Bob as an intermediate input for B other than the final setting, for statistical purposes (which he considers trivial at that point). In other words at no time does Bob do anything mid flight that affects particle 2 (my B). And nowhere in his paper does he say or imply otherwise.

On the other hand, if you feel I’ve misrepresented Norsen: please correct me.

 

[PeterDonis]

You’re disagreeing with Demystifier’s comment, not mine.

No, I was disagreeing with your claim that @Demystifier's posts are in disagreement with Norsen. They're not.

With this description, without embellishment, the observed statistics will be correct regardless of Bob’s choice of setting.

Yes, and nothing I or @Demystifier have said contradicts that.

At no point does Norsen invoke actions by Bob as an intermediate input for B

Nor have I, or to my knowledge @Demystifier, claimed that he did. Bob's measurement settings matter when B reaches the measuring device. Neither I nor @Demystifier have said otherwise, as far as I can tell.

 

[PeterDonis]

if you feel I’ve misrepresented Norsen: please correct me.

I don't think you've misrepresented Norsen. I'm having difficulty understanding why you seem to think @Demystifier (and possibly I) disagree with him.

 

[PeterDonis]

a) Can anything Bob does prior to measurement nonlocally affect B? Because Norsen clearly says NO.

Norsen's NO is correct. See my post #67 (and my posts #61 and #62 that it refers to).

B) Can anything anywhere else in the universe prior to B’s measurement non-locally affect B? Because Norsen clearly says NO.

If you mean anything else in the universe other than the measurement result on A and the consequent effective collapse, NO is correct. Note that this is an obvious consequence of B not being entangled with anything else except (before the A measurement is made) A.

 

[DrChinese]

I don't think you've misrepresented Norsen. I'm having difficulty understanding why you seem to think @Demystifier (and possibly I) disagree with him.

Ummm, from his post #42:

DrChinese (quoted): Is there then a Pilot wave still affecting the B spin observable
Demystifier: Of course.

But no Pilot wave (or any position of anything anywhere short of a quantum interaction) can change that observable, ergo it is NOT acting on it dynamically (saying otherwise would be a perversion of language). Assuming we are all in firm agreement (with Norsen too) that the measured (on A) spin component of B now has a fixed, static, certain, known and invariant value up to and including its measurement by Bob, regardless of anything Bob does prior to that measurement:

a) Is there a pilot wave acting on the noncommuting spin components of B? For a photon, that would be say its 1/0 polarization (i.e. 45 degrees from the H/V) and for an electron would be a perpendicular axis to z (i.e. x or y).
b) Is there a pilot wave acting on the commuting spin components of B? For a photon, that would be say its wavelength (i.e. 45 degrees from the H/V) and for an electron would be perhaps momentum (say x).

So basically: does the fact that B's spin component is known and frozen on one basis, also freeze its spin components on other bases? We know that the H/V measurement on A means that polarization entanglement ceases with B for future polarization measurements on A.

Specifically: A subsequent measurement of L/R polarization on A would NOT yield a useful prediction for a L/R polarization measurement on B. (Obviously not, since PQ<>QP and all observable variants.) So, what, is the a partial Pilot wave affecting B? Or no Pilot wave at all? More precisely: Does the measurement of one spin component on A have any effect whatsoever on the the noncommuting spin components on B?

 

[DrChinese]

This was my Q2: ...if A and B now have specific static values for their H/V polarization, does that also imply their other polarization observables are fixed and static? Or are they free variables/observables available to be measured?

Stated another way: If B was previously entangled with A, then A is measured on one spin component (say z for an electron, or H/V for my photon example), I would think the noncommuting spin components of B must change. My understanding is that any measurement that changes a spin component on A should not only affect the noncommuting spin components on A; they should also affect the same noncommuting spin components on B. (Since the measured spin components were changed on both.)

Admittedly this is getting to a level of detail that is not well explored in the literature (that I am aware of). Hopefully someone knows the answer to this. In orthodox QM, this is not much discussed because there is no explicit "action at a distance" concept as there is in the Bohmian world. (It is usually denied, if anything.) But perhaps there is more on this somewhere.

 

[PeterDonis]

DrChinese (quoted): Is there then a Pilot wave still affecting the B spin observable
Demystifier: Of course.

Yes. Now compare with what I said in post #67:

The part of the pilot wave that appears in B's Hamiltonian always affects B.

This is what @Demystifier meant when he said "of course". Then I gave more details to explain what does not affect B after the A measurement result is known:

What is true is that the part of the pilot wave that appears in A's Hamiltonian cannot affect B after A is measured, because of the "effective collapse" that @Demystifier described, or, to put it another way, because after A is measured, A and B are no longer entangled. It's the entanglement that makes A's part of the pilot wave affect B.

However, as I noted in post #62, the "effective collapse" based on A's measurement result means that the only part of B's pilot wave that matters is the part that's guaranteed to guide it into the appropriate measurement result that corresponds with A's measurement result. That's how the correlation between A's and B's measurement results is enforced in BM.

 

[PeterDonis]

So basically: does the fact that B's spin component is known and frozen on one basis, also freeze its spin components on other bases? We know that the H/V measurement on A means that polarization entanglement ceases with B for future polarization measurements on A.

Specifically: A subsequent measurement of L/R polarization on A would NOT yield a useful prediction for a L/R polarization measurement on B. (Obviously not, since PQ<>QP and all observable variants.) So, what, is the a partial Pilot wave affecting B? Or no Pilot wave at all? More precisely: Does the measurement of one spin component on A have any effect whatsoever on the the noncommuting spin components on B?

What I quoted from my post #67 in my post #76 just now should answer this. But to unpack it once more:

The "effective collapse" induced by A's measurement and its result restricts what portion of B's pilot wave affects B through B's equation of motion (namely, the portion that survives the effective collapse). How much this constrains future measurement results on B depends, of course, on what measurements you choose to make. If you measure B's spin in the same direction as A's spin was measured, it constrains B's result completely; if you measure B's spin in an exactly orthogonal direction, it does not constrain B's result at all; if you measure B's spin in some intermediate direction, it constrains B's result some, but not completely.

Of course this is just what you would expect in orthodox QM as well, which is as it should be since BM has to make the same predictions for the correlations of measurement results on A and B as orthodox QM does. The only difference is the details of what the interpretation claims is going on "behind the scenes" to enforce the correlations: in BM that's the pilot wave (quantum potential) affecting B through its equation of motion.

I'll emphasize once more that in BM, the wave function/pilot wave is not the state of the particle. It is a term in the particle's Hamiltonian. That is indeed a huge change from orthodox QM, at least the way you appear to be used to using it, in which the wave function is the state of the particle. Note, though, that in a statistical/ensemble interpretation such as Ballentine's, the wave function is not the state of the individual particle, but it still is not anything like what it is in BM.

 

[PeterDonis]

if A and B now have specific static values for their H/V polarization, does that also imply their other polarization observables are fixed and static?

This kind of reasoning implicitly assumes that the wave function is the state of the particle. As I emphasized again in post #77 just now, in BM it's not. On the BM view, where the wave function/pilot wave is a term in the particle's Hamiltonian, the question you're asking here doesn't even make sense.

 

[Demystifier]

My simple problem:

a) Can anything Bob does prior to measurement nonlocally affect B? Because Norsen clearly says NO. (Again, see his quote.) If you disagree with Norsen on this, just say so.
B) Can anything anywhere else in the universe prior to B’s measurement non-locally affect B? Because Norsen clearly says NO.

And by “affect B”, I mean the basis (H/V) measurement of B and only that, and of course, assuming no other particle interaction mid flight. I just don’t see where my point is confusing. Norsen’s quoted description properly accounts for observed statistics without further embellishment, and specifically excludes action by Bob or any other agent.

———

Once you concur with my a and b above, the next question I have is whether anything can affect B as regards to other non-commuting spin observables. Say L/R polarization for a photon (or x-spin for an electron). And also commuting observables, say frequency or momentum. I would expect any reasonable interpretation/description of Bohmian mechanics to answer these basic questions for entangled pairs.

Here Norsen considers an idealized situation, in which any interaction in the Hamiltonian (that governs the evolution of wave function through the Schrodinger equation) describes a measurement. Under this idealization, he is right. But this is an idealization. More realistically, there are always some interactions that cannot be counted as measurements, and they can affect the spin part of the B-wave function without measurement. But under the idealization Norsen considers, those can be neglected. In this way, there is no disagreement between Norsen and me.

For other observables, if you want to know what is affected without the interaction, just look at the free Hamiltonian. It depends only on the momentum, so all observables that commute with momentum (such as spin, kinetic energy and momentum itself) are conserved, that is, not affected. The wave function initially in an eigenstate of such an observable remains to be an eigenstate with the same eigenvalue. But position does not commute with the free Hamiltonian, so it is affected. The position observable changes even in the absence of interaction.

Note also that I never mentioned the Bohmian interpretation above. Bohmian and standard QM do not differ on those matters. As long as you talk only about the wave function (not about the Bohmian particle position) and don't involve collapse, there is no difference between the two interpretations.

 

[DrChinese]

The "effective collapse" ["collapse" in Norsen's terminology] induced by A's measurement and its result restricts what portion of B's pilot wave affects B through B's equation of motion (namely, the portion that survives the effective collapse). How much this constrains future measurement results on B depends, of course, on what measurements you choose to make. If you measure B's spin in the same direction as A's spin was measured, it constrains B's result completely; if you measure B's spin in an exactly orthogonal direction, it does not constrain B's result at all; if you measure B's spin in some intermediate direction, it constrains B's result some, but not completely.

Of course this is just what you would expect in orthodox QM as well...

Yes, completely agree with everything you say. But that isn't my question at all.

My question is: When B's spin component (let's call it a generic Z, so particle type doesn't matter) collapses, is there any instantaneous change to B's X or Y (also generic) noncommuting spin components? Because we know that A's collapse of Z changes changes its X and Y spin components to new random values, right? Shouldn't a change to B's Z lead to a change to B's X and B's Y as well at that same time?

Or alternately: Does B's X and Y components only get new random values at the time of measurement by Bob?

 

[DrChinese]

1. Here Norsen considers an idealized situation, in which any interaction in the Hamiltonian (that governs the evolution of wave function through the Schrodinger equation) describes a measurement. Under this idealization, he is right. But this is an idealization. More realistically, there are always some interactions that cannot be counted as measurements, and they can affect the spin part of the B-wave function without measurement. But under the idealization Norsen considers, those can be neglected. In this way, there is no disagreement between Norsen and me.

2. For other observables, if you want to know what is affected without the interaction, just look at the free Hamiltonian. It depends only on the momentum, so all observables that commute with momentum (such as spin, kinetic energy and momentum itself) are conserved, that is, not affected. The wave function initially in an eigenstate of such an observable remains to be an eigenstate with the same eigenvalue. But position does not commute with the free Hamiltonian, so it is affected. The position observable changes even in the absence of interaction.

3. Note also that I never mentioned the Bohmian interpretation above. Bohmian and standard QM do not differ on those matters. As long as you talk only about the wave function (not about the Bohmian particle position) and don't involve collapse, there is no difference between the two interpretations.

1. Everything theoretical we discuss is ideal conditions. So I'm gonna say that you should agree with this: If Bob rotates his measurement device one way by 120 degrees, then back the other way to the original setting, while B is midflight; then B is completely unaffected at all points in between. That should agree 100% with Norsen unambiguously. It goes without saying that B has no way to even know midflight in advance if Bob plans to use apparatus A1, or different apparati A2, A3, A4 etc to measure B later. That decision can be deferred. (Hopefully you won't need to invoke an-all knowing universal Pilot wave to say B does "know" what the future holds in store. Because Norsen says exactly the opposite in his Figure 6.)

2. See 3., I'm interested in the Bohmian explanation.

3. They don't differ? BM says there is an instantaneous nonlocal change to B upon measurement of A. Standard QM says no such thing. This is precisely the difference I'm hoping to gain further understanding on. For our purposes, I am hoping to take the BM position to its logical extension regarding spin.

As Norsen's paper implies simply by its existence, spin entanglement in BM is not well discussed and is often outright dismissed with a quick reference to the Quantum Equilibrium Hypothesis (QEH) and the assertion that all BM predications match those of orthodox QM (oQM). In the immortal words of the great American football commentator Lee Corso: "Not so fast, my friend!" Note that even Norsen's 2018 paper devotes a scant 2 pages to entangled spin, and discusses only the simplest of cases. But I think my questions are entirely legitimate and relevant.

My #80 above summarizes the question. My #83 adds a critical explanation of a specific difference between BM and oQM that most people are not familiar with. Thanks again for your time in looking into this, and helping me understand.

 

[PeterDonis]

When B's spin component (let's call it a generic Z, so particle type doesn't matter) collapses

What (effectively) collapses is not B's "spin component", it's the wave function. That contains information about all spin components, not just the Z component.

we know that A's collapse of Z changes changes its X and Y spin components to new random values, right?

No, it does no such thing. The wave function for B just becomes whatever corresponds to A's collapsed measurement result. In the parallel polarization case, if A's measured result is $H$, B's wave function in the Z basis will be $\ket{H}$. That is not a wave function where X and Y components have "new random values".

Note that, as @Demystifier pointed out in post #79, all this is exactly the same as orthodox QM. As long as you're only talking about the wave function, everything is the same as orthodox QM.

Shouldn't a change to B's Z lead to a change to B's X and B's Y as well at that same time?

See above.

Does B's X and Y components only get new random values at the time of measurement by Bob?

Again, as far as the wave function goes, this never happens. See above.

 

[DrChinese]

We have agreed that when A's spin is measured, entangled B is instantaneously and nonlocally updated. Entangled spin/polarization between A and B ceases at that time. And that time is as specific and unique as measurement technology allows. That would be the timestamp from the detector for A.

However, in orthodox QM (oQM), that is not the case. In oQM, there is no unique "time" at which entanglement between two particles begins, nor any particular time at which it ends. This is demonstrated in hundreds of entanglement swapping experiments, all of which indicate the following rules:

a) Particles A and B can be entangled in advance, which is my original post example.
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:

a) BM is consistent with this.
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.

Note that in both b) and c): the A and B particles are initially entangled with other partners. According to the Bohmian description provided by Norsen (his Fig. 6), that entanglement ceases as soon as A is measured. Therefore they are no longer eligible to participate in later swapping action.

So I am highlighting an unambiguous and generally accepted experimental counterexample to the Bohmian description.

 

[PeterDonis]

BM says there is an instantaneous nonlocal change to B upon measurement of A.

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.

 

[PeterDonis]

We have agreed that when A's spin is measured, entangled B is instantaneously and nonlocally updated.

No, that's not what we have agreed to. See my post #84 just now, which "crossed in the mail" with yours, so to speak.

 

[PeterDonis]

I am highlighting an unambiguous and generally accepted experimental counterexample to the Bohmian description.

Before we can even talk about the other cases you mention, we first have to be clear about the simplest case, where A and B both exist at the same time, A is measured first, and we are talking about what the effect is on B. And we're not clear about that yet. Please see my post #84.

That said, the general response to your other scenarios, where A and B never exist at the same time, or where they are both measured before any interaction happens that could be said to entangle them, has been given a while back in this thread, by @Demystifier IIRC. It is that the environment after a measurement still stores information about what the measurement result was, even though the particle itself is destroyed, and that information affects the wave function, which in turn affects the equation of motion of whatever particles still exist.

In the cases you describe, we basically have two particles, A and B, which when they are created, are entangled with two other particles, A with C and B with D. An interaction takes place between C and D that swaps the entanglement, so after the interaction C and D are entangled and A and B are entangled. In orthodox QM we account for this simply by observing that we can use the same effective wave function to describe this general setup regardless of the times at which any of the relevant events happen (A and C being created entangled, B and D being created entangled, C and D interacting and swapping the entanglement, and the measurements of each of the four particles)--even if the times are such that A and B never coexist, or are both measured and destroyed before C and D interact. The effective wave function is the same for all of these cases, so they all show the same results.

BM makes the same use as orthodox QM does of the fact that the effective wave function is the same--since, as has already been commented, if we are only talking about the wave function, there is no difference between BM and orthodox QM. Any account of how it can be that that same effective wave function works for all these cases, will have to make use of the fact noted above, that, even if a particle is destroyed when it's measured, the environment still carries information about the measurement result, and so that information continues to propagate in the wave function, in such a way that we can treat it as though the particle still existed and the effective wave function had collapsed according to its measurement result. And any such account, which orthodox QM has to have anyway, already has to account for the fact that this effective wave function works even in cases where it would seem like it can't, because the particles don't all exist at the same time. And that, all by itself, is already enough to explain what happens in BM with the particle positions--since the wave function is what appears in their equation of motion.

 

[PeterDonis]

According to the Bohmian description provided by Norsen (his Fig. 6), that entanglement ceases as soon as A is measured.

But the effect of A's measurement result on B's wave function does not cease, because of the effective collapse when A is measured, as has already been commented. And that is what's relevant for determining measurement results on B.

 

[Demystifier]

3. They don't differ? BM says there is an instantaneous nonlocal change to B upon measurement of A. Standard QM says no such thing. This is precisely the difference I'm hoping to gain further understanding on. For our purposes, I am hoping to take the BM position to its logical extension regarding spin.

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.

 

[PeterDonis]

This nonlocal change refers to the velocity of the Bohmian particles, not to the properties of the wave function (aka pilot wave).

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.

 

[Matterwave]

Not to interject too much, but as a side oberserver, my understanding would be greatly helped if folks were a bit more clear about what mathematical object they mean when they say "the wave function" (or the pilot wave).

Are we talking about the universal wave function (including measurement apparatuses), 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) or the relative wave function of A relative to B or are these concepts not applicable to BM?