SQM vs Pilot Waves - Potential issue with Pilot Waves?

[tomdodd4598]

Hey there. I'm not a expert in quantum mechanics, although have some experience with it, but I'm certainly far from being an expert when it comes to the pilot wave interpretation. For whatever reason, pilot waves have been mentioned quite a lot recently, and so I decided to take a closer look at it. I've seen many people claim that it makes the same predictions as standard quantum mechanics (Schrödinger equation, etc.), but I was pointed to this paper which seems to show that there is actually an issue with the predictions of the pilot wave theory:

Deficiencies of Bohm Trajectories in View of Basic Quantum Principles

Of course, it is possible that the people who have wrote this have made a mistake, but I don't have the ability to see it if it is there. Is this result not a serious issue for supporters of the pilot wave interpretation?
Thanks in advance.

 

[dextercioby]

I am by no means expert on these issues, but I know that Hagen Kleinert is a smart guy. @Demystifier is the greatest fan/expert of Bohmian Mechanics on PF, so he is welcome to review this paper.

 

[A. Neumaier]

The equivalence holds only after averaging over the ensemble of all possible Bohmian trajectories - not for a fixed collection of N trajectories of an N-particle system.

There are more discrepancies of the naive Bohmian picture [i.e., working with one fixed collection of N Bohmian particles]; see, e.g., the introduction of https://arxiv.org/abs/1610.03310 which mentions the above paper on p.2 as [4]. In principle, everything can be discussed away, but note also the fact that one needs to change the ontology when going from one model to another (e.g. from particles to fields) and other strange things such as that in a universe consisting of a single electron in the ground state of a central field, the Bohmian particle stands still no matter how close or far it is from the center (https://arxiv.org/abs/quant-ph/0001011).

 

[Demystifier]

I am by no means expert on these issues, but I know that Hagen Kleinert is a smart guy. @Demystifier is the greatest fan/expert of Bohmian Mechanics on PF, so he is welcome to review this paper.

Kleinert is one of the most prolific writers of QFT books. However, he is not an expert on quantum foundations, i.e. on topics such as measurement problem, decoherence, quantum nonlocality, interpretations, etc. But let us not use ad hominem arguments. Let us concentrate on the content of the paper.

I have several minor objections on the paper, but let me concentrate my attention on the one major objection. Chen and Kleinert do the same mistake that many others have done before them: They do not study the process of measurement! Indeed, it is well known in Bohmian mechanics that BM and standard QM do not have the same predictions when the process of measurement is not taken into account. It is only when the process of measurement is taken into account that the two theories have the same predictions. Therefore, their results are neither surprising nor relevant for consistency of BM with standard QM.

 

[PeterDonis]

It is only when the process of measurement is taken into account that the two theories have the same predictions.

Can you elaborate on this? In particular, is what you are saying consistent with what A. Neumaier says in the post just before yours? This:

The equivalence holds only after averaging over the ensemble of all possible Bohmian trajectories - not for a fixed collection of N trajectories of an N-particle system.

 

[Justintruth]

Two things always steered me away from the images I imagine of a wave somehow guiding a particle maybe like a surfer or something similar.

The first was a simple particle in a square well. it's energy is quantized by the geometry of a standing wave in the well. Now some standing waves have nodes with zero amplitudes that divide the well into sections. so how does the particle get from one side of a node to another or how do you "guide" a particle through an area with zero probability of it being.

The second was the Bhor atom. How do guide waves guide an electronic from one orbit to another with zero probability of the electronic being in between.

These are very crude models but they illustrate the fact that the images of "guiding" become so different than we normally think that we might as well do away with them.

 

[tomdodd4598]

They do not study the process of measurement! Indeed, it is well known in Bohmian mechanics that BM and standard QM do not have the same predictions when the process of measurement is not taken into account. It is only when the process of measurement is taken into account that the two theories have the same predictions. Therefore, their results are neither surprising nor relevant for consistency of BM with standard QM.

Interesting - I did not know about that. The fact is, I really don't know much when it comes to the ins and outs of this formulation, as unlike the standard formulation, I've found it difficult to find any notes that explain and go through it from the ground up. Would you happen to know a good place to learn about it - perhaps at a roughly undergraduate level?

 

[secur]

The first was a simple particle in a square well. it's energy is quantized by the geometry of a standing wave in the well. Now some standing waves have nodes with zero amplitudes that divide the well into sections. so how does the particle get from one side of a node to another or how do you "guide" a particle through an area with zero probability of it being.

The second was the Bhor atom. How do guide waves guide an electronic from one orbit to another with zero probability of the electronic being in between.

According to Bohm in the first case the particle doesn't move. It holds still, presumably at a place of max probability. Only when measurement disturbs the system might it be found elsewhere. A perfect example showing you must take the measurement process into consideration with pilot wave interpretation. Similar answer for second case (although admittedly I don't recall that exactly).

Would you happen to know a good place to learn about it [.e. Bohmian Mechanics] - perhaps at a roughly undergraduate level?

I doubt you can do better than "The Undivided Universe" by Bohm and Hiley.

 

[Demystifier]

Can you elaborate on this?

A short elaboration: the Appendix in https://arxiv.org/abs/quant-ph/0208185
A longer (and better) elaboration: Sec. 2 in https://arxiv.org/abs/1112.2034

For a generalization to the degenerate case see also
https://www.physicsforums.com/threads/spin-in-bohmian-mechanics.861549/#post-5406709

In particular, is what you are saying consistent with what A. Neumaier says in the post just before yours? This:

It's unrelated.

 

[Demystifier]

Would you happen to know a good place to learn about it - perhaps at a roughly undergraduate level?

See my recommendations in post #9.
For even more details, see also Sec. VI of https://arxiv.org/abs/1206.1084
or the book recommended by secur.

 

[tomdodd4598]

See my recommendations in post #9.
For even more details, see also Sec. VI of https://arxiv.org/abs/1206.1084
or the book recommended by secur.

Thanks very much!

 

[bohm2]

Interesting - I did not know about that. The fact is, I really don't know much when it comes to the ins and outs of this formulation, as unlike the standard formulation, I've found it difficult to find any notes that explain and go through it from the ground up. Would you happen to know a good place to learn about it - perhaps at a roughly undergraduate level?

Try these lecture slides by Towler (Univ. of Cambridge):
http://www.tcm.phy.cam.ac.uk/~mdt26/pilot_waves.html

 

[muscaria]

Would you happen to know a good place to learn about it - perhaps at a roughly undergraduate level?

The textbook called "The Quantum Theory of Motion" by Peter Holland is a very clear exposition of it.