Bohmian Mechanics: When Does Pilot Wave Action Cease?

[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.