Can the Quantum Potential Exert Pressure on a Classical Particle in a Box?

[Mentz114]

In P. Hollands book "The Quantum Theory of Motion" there is a detailed discussion of this situation. As I understand it, dBB predicts that the particle can be stationary ( v=0) in which case its energy ( and momentum ?) go into the quantum potential.

I have a question about this. A classical particle in a box will exert pressure on the walls of the box. Is the quantum potential able to exert this pressure ?

 

[vanesch]

I would think so. Let's not forget that the quantum potential in BM is non-local: as such, the particle doesn't need to be "in contact" with the wall to exert a force on it. But I admit never having looked at the details.

 

[Demystifier]

I have a question about this. A classical particle in a box will exert pressure on the walls of the box. Is the quantum potential able to exert this pressure ?

This question has nothing to do with the Bohmian interpretation. Namely, the quantum potential is completely described by the standard Schrödinger equation. So the correct question is: Does the wave function described by the Schrödinger equation exerts pressure on the walls? The answer is that it depends on details of the interactions described by the Schrödinger equation. In practice, the walls are usually assumed to be fixed non-dynamical objects, so in this case there is no such pressure. This, of course, may be merely a not completely realistic approximation.

 

[Demystifier]

I would think so. Let's not forget that the quantum potential in BM is non-local: as such, the particle doesn't need to be "in contact" with the wall to exert a force on it. But I admit never having looked at the details.

This is an misinterpretation of BM nonlocality. BM nonlocality only means that motion of one particle depends nonlocally of the positions of the other particles. Thus, only if the wall is also described by quantum particles entangled with the particle in the box, such a force would take place. In practice, one usually does not describe the wall as made of quantum particles.

 

[Mentz114]

Dr Nikolic,

This question has nothing to do with the Bohmian interpretation

Eh ?

However, the rest of your reply explains it, thank you, you are most kind to take the trouble.

 

[Demystifier]

However, the rest of your reply explains it, thank you, you are most kind to take the trouble.

Well, I just like to demystify things.

 

[vanesch]

This is an misinterpretation of BM nonlocality. BM nonlocality only means that motion of one particle depends nonlocally of the positions of the other particles. Thus, only if the wall is also described by quantum particles entangled with the particle in the box, such a force would take place. In practice, one usually does not describe the wall as made of quantum particles.

Well, I was of course assuming that the walls were quantum objects, otherwise - as you point out - it is meaningless to talk about any "pressure" which can only follow from the interaction between the particle and the wall. For that interaction to exist, both must be objects in the physical description.

I thought the OP had some problem with the "particle being at rest somewhere within the volume" and nevertheless there being a pressure on the walls.

 

[Demystifier]

Well, I was of course assuming that the walls were quantum objects, otherwise - as you point out - it is meaningless to talk about any "pressure" which can only follow from the interaction between the particle and the wall. For that interaction to exist, both must be objects in the physical description.

I thought the OP had some problem with the "particle being at rest somewhere within the volume" and nevertheless there being a pressure on the walls.

I agree. I was thinking in terms of the usual technical description of "walls" in QM, while you were thinking in terms of actual physical objects in nature.

 

[Mentz114]

I thought the OP had some problem with the "particle being at rest somewhere within the volume" and nevertheless there being a pressure on the walls.

That's it.
So if the walls were included in the description then the quantum potential would be trying to move them, thus exerting pressure ?.