Bohmian Mechanics of DCES (swaps), featuring several papers

[Matterwave]

It's not that complicated as you might think it is. See my https://arxiv.org/abs/2205.05986.

I have added this to my reading list on BM. Next to Bohm and Hiley haha. I don't know when I'll get to it.. but I will try.

 

[Demystifier]

But... I really don't think my math skills are the issue here.

There is a simple test to see if someone has math skills appropriate to understand BM. Take the Norsen's Eq. (2) and, from it, prove mathematically that particle n' does not influence particle n if the two particles are not entangled. If you can prove it, then your math skills are probably OK. If you can't prove it, then they are not. If you haven't already done that proof, I strongly recommend you to do it, because it's essential for understanding BM.

 

[Demystifier]

I have added this to my reading list on BM. Next to Bohm and Hiley haha. I don't know when I'll get to it.. but I will try.

That book also studies a field version of BM, in Chapter 11. But of course, nobody presented Bohmian QFT in such a simple form as I did.

 

[DrChinese]

I don't pick and choose anything. It's the Bohmian equation of motion that determines when the position of one particle influences the motion of the other, and when it doesn't. But there is not a good way to explain it by words. You must read the math of the Bohmian equation of motion.

It's not that complicated of a Bohmian scenario. I have 2 entangled photons 1 and 2 as part of a Bell test, while photon 2 is still midflight.

i) What is the initial influence of photon 1 on photon 2 as to polarization and momentum, while photon 1 is midflight?
ii) What is sum influence of the atoms of the PBS measuring photon 1 on photon 2 as to polarization and momentum?
iii) What is sum influence of the atoms of the detector registering photon 1 on photon 2 as to polarization and momentum?
iv) What is influence of the rest of the universe on photon 2 as to polarization and momentum?

Norsen mentions i) in his discussion (Fig. 6), but does not really mention the others. But you have mentioned ii) iii) and iv) previously. If the influence of any of these 4 is negligible, then I'd be interested to know that. Presumably, distance is not a factor. Or, if distance is a factor in the Bohmian equation of motion, just say so.

I would claim oQM says:
i) there is no influence whatsoever of Photon 1 on photon 2 while they are both midflight.
ii) there is no influence whatsoever of the individual atoms of a PBS on photon 1 or photon 2 (only the orientation - a single variable - is relevant).
iii) there is no influence whatsoever of the individual atoms of a detector on photon 1 or photon 2.
iv) there is no influence whatsoever of the rest of the universe on photon 1 or photon 2.

So... in experiment after experiment, the statistical results seems to only depend on one single variable: polarizer orientation. None of the other items you input into "the math of the Bohmian equation of motion" seem to matter at all. Why is that? If you don't pick and choose, why is it that all these inputs always seem to vanish (i.e. net to zero) in polarization experiments?

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In other words: I know that we don't know the precise particle positions, point accepted. But if you specified them exactly in an even easier example, can you tell me what the polarization results would be? In other words: If BM has deterministic features, I would think you could fabricate an example where I start with a |+> polarized photons that I will run into a H/V oriented PBS (or some other theta); and you could tell me (using Bohmian math) which specific port it would exit and be detected (H or V). You can specify whatever initial conditions you like to create the example (apparati, source, etc).

In oQM the answer is plain: This problem cannot be solved exactly, and there is only 1 variable (theta). I don't think it can be solved in BM either, but I am trying to understand how many variables are involved "under the hood" so to speak.

 

[DrChinese]

Demystifier, referencing Norsen's (2): ...particle n' does not influence particle n if the two particles are not entangled. ...

That's a new one for me, have never seen that stated elsewhere. Not sure how I missed that in other Bohmian papers. I would have thought this point might have been repeated in almost any discussion of Bohmian entanglement.

Are we talking the same "entangled" usually discussed? If so, exactly how does an entire Beam Splitter become entangled with (or due to) a single photon? And what if 2 independent photons happen to be in a Beam Splitter at the same time? And is the Beam Splitter still entangled with the same photon as it enters the Detector? Or does the entanglement now move, transfer, dissipate, or ?

Huggett: "Therefore, the particles are in some sense “pushed” around by the wave function on the configuration space – hence BM is sometimes referred to as the ‘pilot wave’ theory". On the other hand, Huggett also mentions (as you do I believe) that: "... the particle’s wavefunction evolves according to the standard Schrödinger equation (2.1), and particles’ definite positions neither appear in ψ nor feature in the Schrödinger equation, so the position variable of the wavefunction has much the same significance as before – a variable in a probability function."

 

[Demystifier]

That's a new one for me, have never seen that stated elsewhere. Not sure how I missed that in other Bohmian papers. I would have thought this point might have been repeated in almost any discussion of Bohmian entanglement.

You don't need to read this explicitly. You have to derive it by yourself from Eq. (2) in Norsen's paper. If you can't derive it, then you don't understand BM, period. And no matter how much text about BM you read, if you don't see how this text is related to the equations, then you don't understand BM.