Quantum Decoherence and deBroglie-Bohm theory

[Demystifier]

I mean why can't we find recently published papers on dBB?

We can, if we know how to search. See e.g.
http://lanl.arxiv.org/find/quant-ph/1/ti: Bohmian/0/1/0/all/0/1
http://lanl.arxiv.org/find/quant-ph/1/ti:+AND+Broglie+Bohm/0/1/0/all/0/1
http://lanl.arxiv.org/find/quant-ph/1/ti:+AND+pilot+wave/0/1/0/all/0/1

 

[bohm2]

The particular issue is a particle in a box. Bohm's model predicts that a particle in an energy eigenstate has velocity zero (because the velocity is related to the imaginary part of the wave function, which can be taken to be zero for an energy eigenstate). But the prediction of quantum mechanics is that a measurement of momentum will yield a nonzero value. Bohm claimed that his theory makes the same prediction, but the paper doesn't reproduce the argument.

But this is just a difference in ontology between BM and Orthodox QM, but both still make the same empirical predictions.

 

[stevendaryl]

But this is just a difference in ontology between BM and Orthodox QM, but both still make the same empirical predictions.

The specific example I was talking about was an empirical prediction: The prediction of standard quantum mechanics is that if you measure the momentum of a particle in a box in the ground state, you will get $p = \pm \frac{\pi \hbar}{L}$ where $L$ is the length of the box. Bohm claimed that his theory gives the same result (although it's a lot more complicated to show this). Even though the velocity is zero according to his model, a measurement of position at two different times will give different results, because the measurement process disturbs the particle, and so will give a nonzero measured velocity.

 

[jtbell]

The prediction of standard quantum mechanics is that if you measure the momentum of a particle in a box in the ground state, you will get p=±πℏLp = \pm \frac{\pi \hbar}{L} where LL is the length of the box.

Have you ever seen the momentum-space wave functions for the infinite square well (a.k.a. "particle in a box")?

http://physicspages.com/2012/10/04/infinite-square-well-momentum-space-wave-functions/

They do not restrict the possible values of momentum to $\pm \frac{\pi \hbar}{L}$ for the ground state.

 

[Ilja]

Anyway, the major problem in dBB is the formulation of the theory for chiral fermions interacting with non-abelian gauge fields. So you can think of all papers about chiral fermions interacting with non-abelian gauge fields as secretly dBB papers (ok, maybe I went too far there, but it is my interpretation of the literature :D).

I like this idea of secretly dBB papers, and can tell you about one which is in a quite real sense "secretly dBB": http://arxiv.org/abs/0908.0591

It contains a method to describe a pair of Dirac fermions based on a scalar field with degenerated vacuum. The latter one can be handled with straightforward Bohmian field theory.

 

[Ilja]

The point is, people mostly like dBB because it preserves(at least partly) the classical nature of physical laws... But I just don't see the reason why so many people should be so insistent that nature is as people thought before QM.

I think it is more about having a reasonable picture of the whole thing. Instead of Copenhagen with its two worlds which conceptually are in conflict with each other. So you get a classical trajectory for the quantum domain too, a wave function for the classical domain too, and have no longer any need for separate collapse dynamics.

Also dBB doesn't seem to be able to make a good marriage with SR too. I know people had some attempts but things don't seem to fit nicely.
And quantum fluctuations. How can dBB account for particles coming from nothing when it doesn't accept uncertainty principles as they are in standard QM?

If you forget about fundamental relativity, which forbids the existence of hidden preferred frames, then there is no problem with relativity at all. Straightforward field theory with \(\mathcal{L} = \partial_t\varphi^2 - \partial_i \varphi^2 + V(\varphi)\) fits nicely into the standard dBB scheme (if quadratic in the momentum variables everything is fine).