Pilot wave persistence after measurement in Bohmian entanglement

[DrChinese]

Write down the initial wavefunction of the entangled particles and observing environment. $|\Psi(0)\rangle = |\psi,M_\mathrm{ready}^A,M_\mathrm{ready}^B\rangle$ and evolve it unitarily, yielding some form $|\Psi(t')\rangle=|0\rangle^A|0\rangle^B\sum_{\alpha,\beta}c_{\alpha\beta}|M_\alpha^A,M_\mathrm{\beta}^B\rangle$. This pilot wave is over all systems.

And I am saying that logically, after Alice's measurement, nothing in the universe has any net effect on the evolution of B's polarization during the time prior to Bob's measurement.

 

[DrChinese]

Norsen provides a nice summary which fits my example nicely:

"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."

This makes sense as the Bohmian perspective, and accounts correctly for entangled photon correlations in my example. I can now see answers here for my Q1, Q3, and more of less Q4 too. Yay! I'm not sure anyone so far would particularly contradict Norsen on this, but I can't be sure. Hopefully readers will let me know their thoughts.

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But now we get into some really hairy territory regarding my Q2 (italics below, from post #1). This area can be complicated (at least to me) in orthodox QM. What changes on B's other polarization bases (1/0, L/R) when an H/V measurement is performed on A? The analogy with an electron would be a z-component measurement: what happens to the remote particle's x- and y-components? Are they disturbed? Do they take on random values different than what they had before the first measurement? Do they remain sync'd in some manner?

Admittedly, there are no direct tests that can fully answer these questions (or maybe there are!). What does theory say?

Q2) A photon can be polarized in at least 3 mutually unbiased manners: H/V, 1/0, L/R. Does a measurement on the H/V basis of A fix the photon's unmeasured value on the 1/0 or L/R bases? Ditto for B photon? This is confusing to me, because presumably under BM: particles have definite values for all observables simultaneously - which is different than most other interpretations. So... 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?

 

[Matterwave]

On the other hand: There are experiments that instantaneous action cannot easily explain. An example would be entangling particles that have never co-existed. Or entangling particles after they cease to exist. If you want references on these, just let me know.

I would certainly like to see some of these references. My reading list is very long but I'll try my best haha. It seems interesting.

 

[Matterwave]

Honestly, trying to say that a simple Alice/Bob entanglement setup cannot be described by Bohmian Mechanics kinda makes my point.

I would like to see the NRQM discussion of entangled photon polarization experiments where at detection photons gets annihilated. Would you have a reference?

I will try to look into Peter's reference to chapter 19 of Ballentine later today.

 

[Matterwave]

...this in turn determines the statistics for a subsequent measurement on the distant particle.

Hopefully readers will let me know their thoughts.

I don't find anything objectionable (at least at first impression) in what Norsen says. But do note that he says "statistics" for a subsequent measurement.

What changes on B's other polarization bases (1/0, L/R) when an H/V measurement is performed on A?

This is my feeling from reading your post (I could be totally off base with this): I feel like you are still implicitly assuming Bohmian mechanics is at some level non-contextual. That it assumes all possible observables (not just position) have ontological status independent of how they are measured. You mentioned in one of your posts that you agree BM is contextual. But when I read your questions or arguments it really reads to me like you assume it is not contextual

Again, I might be totally off base here.

Could it not be that the action on B's wave function is done upon A being measured and yet it still depends on how you make that future L/R measurement on B to know its value? <-- I would love to be corrected on this.

 

[DrChinese]

I would certainly like to see some of these references. My reading list is very long but I'll try my best haha. It seems interesting.

Photons that never coexisted (A measured before B created):
https://arxiv.org/abs/1209.4191

Photons entangled after they (both A and B) have been measured:
https://arxiv.org/abs/1203.4834

 

[DrChinese]

I would like to see the NRQM discussion of entangled photon polarization experiments where at detection photons gets annihilated.

The two references I provided in the previous reply are non-relativistic QM. Literally, there is nothing whatsoever about relativistic QM or QFT that has anything to do with the predictions in normal optical polarization tests featuring entanglement. No theoretical considerations regarding reference frame figure into the testing. That will be obvious when you read those papers.

 

[Matterwave]

Nice, thanks for the references! I'll take a look.

 

[DrChinese]

This is my feeling from reading your post (I could be totally off base with this): I feel like you are still implicitly assuming Bohmian mechanics is at some level non-contextual. That it assumes all possible observables (not just position) have ontological status independent of how they are measured. You mentioned in one of your posts that you agree BM is contextual. But when I read your questions or arguments it really reads to me like you assume it is not contextual

Again, I might be totally off base here.

Could it not be that the action on B's wave function is done upon A being measured and yet it still depends on how you make that future L/R measurement on B to know its value? <-- I would love to be corrected on this.

As with many things, precise definitions of things like “contextuality” make the difference.

The reason I agree with Demystifier on this subject (we’ve discussed previously at length) is that I don’t believe there are predetermined outcomes for every possible measurement basis. That isn’t necessary if you follow the description Norsen gives. Which is pretty similar to what you are saying in your last paragraph.

 

[Matterwave]

As with many things, precise definitions of things like “contextuality” make the difference.

The reason I agree with Demystifier on this subject (we’ve discussed previously at length) is that I don’t believe there are predetermined outcomes for every possible measurement basis. That isn’t necessary if you follow the description Norsen gives. Which is pretty similar to what you are saying in your last paragraph.

Hmmm fair enough. Then it seems my read was wrong and I'm just not understanding what the objection is. I don't think I have much more to add to this discussion~

I will read the associated materials (if only for my own curiosity). :)

 

[Demystifier]

However, you gotta admit: If an experiment is performed on B at any point in time after A is measured, then it would be an odd thing to now assert that the universe knew all along exactly when and where (and how!) the future B was to be measured

I see nothing odd with that, once I accept determinism. And this is not superdeterminism, because superdeterminism involves also a fine tuning of initial conditions, while in BM initial conditions are typical.

 

[Demystifier]

Is there then a Pilot wave still affecting the B spin observable

Of course.

 

[Demystifier]

So I believe Norsen would agree with you (at least in some respects) that my B must have a static H/V outcome after the collapse induced by the Alice measurement.

Yes, but the outcome is a property of the measuring apparatus, not a property of the measured particle.

 

[Demystifier]

The reason I agree with Demystifier on this subject (we’ve discussed previously at length) is that I don’t believe there are predetermined outcomes for every possible measurement basis.

You mean - disagree?

 

[Roberto Pavani]

I have a few questions that I hope the experts here can clarify:

1. On the foliation in practice: In a real experiment, Alice and Bob measure at irregular intervals with timing jitter.
The temporal separation between the two measurements differs from pair to pair.
Wouldn't a preferred foliation that renders the two measurements "simultaneous" need to change for each pair?
If so, is it still a geometric property of spacetime, or does it become dependent on the experimenters' free choices?

2. On the relevance of the ordering: The experimental correlations are $-\cos(a-b)$ regardless of who measures first, how much later the second measurement occurs, or whether the ordering fluctuates randomly from pair to pair. If the result is independent of the ordering, what physical work is the causal story ("the first measurement collapses the CWF of the distant particle") actually doing?

3. On what changes at B: Is there any operationally observable change at B's location upon measurement of A, before we condition on A's results? If the correlations only become visible through post-selection on coincidences, how do we distinguish "A causes a change at B" from "the correlations were already in the shared source and are revealed by conditioning"?

4. On delayed-choice and "never coexisted" experiments: In entanglement swapping, the correlations between photons 1 and 4 are only visible in the subensemble selected by Victor's Bell-state measurement on 2 and 3.
Without that selection, no correlations appear. Doesn't this suggest that Victor's measurement acts as a statistical filter on pre-existing variables rather than retroactively creating entanglement?

I'm not claiming these points refute anything, I'm genuinely trying to understand how BM, or other interpretations, address them.

 

[Demystifier]

Wouldn't a preferred foliation that renders the two measurements "simultaneous" need to change for each pair?

No. In BM the preferred foliation is preferred for all particles in the whole universe.

 

[Demystifier]

The two references I provided in the previous reply are non-relativistic QM. Literally, there is nothing whatsoever about relativistic QM or QFT that has anything to do with the predictions in normal optical polarization tests featuring entanglement. No theoretical considerations regarding reference frame figure into the testing. That will be obvious when you read those papers.

Except that, at some moment of time, you have to assume that one photon has been destroyed. How would you describe photon destruction with ordinary nonrelativistic QM?

 

[Roberto Pavani]

No. In BM the preferred foliation is preferred for all particles in the whole universe.

This confuses me, especially the part "for all particles in the whole universe". This seems to me like to say "there is no preferred foliation"

 

[Demystifier]

This confuses me, especially the part "for all particles in the whole universe". This seems to me like to say "there is no preferred foliation"

I have no idea why it looks so to you.

 

[Roberto Pavani]

Probably I'm misreading the definition, so let me rephrase. In BM there is a family of parallel spacelike hypersurfaces (one for each "absolute time" instant), so for any pair of measurements on A and B, one can always say which happened first. Fair enough.

My remaining question is: since the experimental correlations are the same regardless of which measurement comes first according to that ordering, what role does the ordering play in the physics?

 

[Demystifier]

@DrChinese I see several misconceptions already in your first paragraph of your first post, so let me try to deconstruct them one by one.

Under the Bohmian Interpretation (BM or BMI):
Suppose we have a traditional pair of polarization entangled photons A and B going to Alice and Bob, who will test their polarizations in the same reference frame. To be specific, let's say A and B are entangled |HH> + |VV>.

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.

In the traditional view of this interpretation, a measurement of A by Alice occurring first (in all reference frames) instantaneously leads to an update of B due to action of a pilot wave. This is action at a distance as a way to explain entangled systems.

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.

 

[Demystifier]

Probably I'm misreading the definition, so let me rephrase. In BM there is a family of parallel spacelike hypersurfaces (one for each "absolute time" instant), so for any pair of measurements on A and B, one can always say which happened first. Fair enough.

My remaining question is: since the experimental correlations are the same regardless of which measurement comes first according to that ordering, what role does the ordering play in the physics?

It depends on what you mean by "physics". If by physics you mean making measurable predictions and nothing else, then you don't need BM at all. Standard QM is enough.

But if by physics you mean real stuff existing out there irrespective of whether we measure it or not, then standard QM is not enough. The ordering in BM tells you what "really" happens in nature, irrespective of whether we measure it or not. It tells you what "really" happened first, rather than what appears to be happening first to this or that observer.

There is also a third intermediate interpretation of BM. You may think of Bohmian trajectories not as a real stuff, but as an auxiliary mathematical object similar to the gauge potential in classical electrodynamics. To define the gauge potential you must fix a gauge, which often involves fixing a Lorentz frame (in Coulomb gauge). All measurable predictions are still Lorentz invariant, and yet the description of physics in terms of gauge potentials is not Lorentz invariant. Still, you may imagine that the potential is a real stuff, for example because otherwise it's difficult to understand the Aharonov-Bohm effect.

 

[Roberto Pavani]

Thank you, this is very clear and gives me a useful way to think about it. The gauge analogy is particularly helpful.

 

[Demystifier]

He also uses the term "Pilot wave" in much the same sense I have in my questions: that is, the Pilot wave includes elements that cannot be solely attributed to the Schrödinger wave function. That is explicit stated in his first paragraph:

Norsen: "As a so-called “hidden variable theory” the pilot-wave theory adds something to the state descriptions of ordinary quantum mechanics: in addition to the usual wave function Ψ obeying the usual Schrodinger equation..."

The bold part above is wrong. The pilot wave is the Schrodinger wave function. Bur perhaps you meant the pilot wave theory, because the pilot wave theory involves the pilot wave itself (which is the same as Schrodinger wave function) and something additional on which this wave acts as a pilot.

 

[Demystifier]

Note that for our purposes, this thread discussion, it really doesn't matter whether we are discussing entangled photons, entangled electrons, or any other particle type. The essential Bohmian concepts must apply to all entangled particle systems. Hopefully there is no problem with this statement.

I could agree with this statement if you could reformulate your question such that there is no destruction of A. (Otherwise, I cannot.) But if there is no destruction of A, then I don't see any reason to ask when does the action of the pilot wave cease. It never ceases.

 

[Demystifier]

He uses the term "collapse", which I think is appropriate. Further, it is clear from his description that he views this as physical - not merely an update of knowledge. There is no question that this is instantaneous action at a distance.

Ah, I think I understand now what's the main source of confusion. In BM there is no collapse, and yet one can talk about collapse in BM. How can that be?

The key, made particularly clear by Bell, is that, in BM, one needs to distinguish exact statements from FAPP (for all practical purposes) statements. In BM there is no real exact collapse, but there is an effective FAPP collapse. Namely, even though there is no real collapse, under certain conditions the motion of particles can approximately be described by a collapsed wave function. In other words, for practical purposes it looks as if the wave function collapsed, even though it really didn't. This happens whenever a sufficient amount of decoherence happened due to interaction with the environment, which is just another way to say that the environment performed a measurement. That is how measurement in BM explains an effective collapse, without involving a real collapse.

And now we can answer the central question of this thread. Suppose that initially two particles, A and B, are entangled. Now if A strongly interacts with the environment $E_A$, that effectively destroys entanglement of B with and A. Instead, now B is entangled with the composite system $A+E_A$. But this kind of entanglement cannot be measured because $E_A$ is a complex system with a huge number of degrees of freedom, so effectively (FAPP) it looks like a classical system, even though it is really a quantum system. Thus it looks as if now B is no longer entangled with anything. All that is valid for both the standard and the Bohmian interpretation. 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 it's only an effective approximative description, akin to to the effective collapse, while on the exact level the action did not realy cease.

I want to believe that this is all consistent with the things that @DrChinese had in mind, but I hope I made all this more explicit.

 

[PeterDonis]

No theoretical considerations regarding reference frame figure into the testing.

It's worth nothing, though, that when you use the words "before" and "after", as I understand it, those are relativistically invariant in the experiments being described (i.e., the events in question are timelike separated, so even in a relativistic model their time ordering is independent of any choice of reference frame).

 

[DrChinese]

I see nothing odd with that, once I accept determinism. And this is not superdeterminism, because superdeterminism involves also a fine tuning of initial conditions, while in BM initial conditions are typical.

How is this not the same as Superdeterminism? Of course the precursor conditions are not typical in your description because the Pilot wave can "read" Bob's measurement device in advance (if the Pilot wave is still changing B's spin to match).

In the Weihs et al experiment, for example, measurement settings are changed randomly mid-flight. 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.

And your point is not even needed for the description in my example anyway - although it could be an important point later on. There could be determinism without it requiring the Pilot wave to know how Bob is planning to measure B. You supply that explanation via the unknown position. I.e. if you knew the precise position of B, when B is entering the measurement apparatus, that would conceivably allow the outcome to be determinate.

So I want to be sure I understand what you are saying: You are saying: If Bob changes his measurement setting midflight, the Pilot wave has an interim effect on B even if Bob returns his measurement setting to the original by the time B arrives?

I mean, how does the Pilot wave even know where B is being routed for measurement? I could send B through an intricate maze of mirrors, fiber and lenses so complex it would be difficult for anyone to know where it will end up. Keeping in mind here that the issue in play is whether B is further affected midflight by a Pilot wave after A's outcome occurs.

 

[DrChinese]

It's worth nothing, though, that when you use the words "before" and "after", as I understand it, those are relativistically invariant in the experiments being described (i.e., the events in question are timelike separated, so even in a relativistic model their time ordering is independent of any choice of reference frame).

Exactly.

And note that in Norsen's paper, he explicitly states that one particle of an entangled pair will always be measured before the other. So he assumes a similar scheme as I intend. Even in QFT, there is no relevant difference to the analysis of an entangled system due to ordering of measurements.

 

[DrChinese]

You mean - disagree?

Yes, but the outcome is a property of the measuring apparatus, not a property of the measured particle.

Haha, I guess there is plenty of room to disagree on the meaning of words like "contextual".

You have stated BM is contextual: "The values of observables in BM are contextual, meaning that they are not defined without a measuring apparatus. If there is no measurement, than there is no value." I agree with that as calling BM contextual, as I said: "I don’t believe there are predetermined outcomes for every possible measurement basis." Norsen says: "the measurement cannot be thought of as passively revealing a pre-existing value." I would call the outcome being determined per the "combination of system being measured plus measurement device" as being contextual. And that could be determinate in BM without difficulty, although standard QM implies (but only implies) it might be totally random and therefore indeterminate.

You also say that every possible outcome could, in principle, be calculated if you knew which observable was being measured (along with the hidden position of course). I'm silent on that point, so that's where we diverge. I am saying there is no counterfactual information in existence. (It would run afoul of Bell if it did, IMHO.)