Bohmian Mechanics: Recent Readings & Experimental Evidence

[George Isaac]

Recently, I read Bohm's articles explaining his interpretation of Quantum Mechanics. I did not find anything "bad" with it, so why didn't anybody pursue it further? Any experimental evidence against its predictions?

 

[humanino]

Did you not notice the central role of the position representation ? In Copenhagen interpretation, there is no well-defined trajectory, because one cannot speak about objects by themselves outside measurement. Bohm attempts to keep classical concepts valid, which is very questionable ! Do you not think that QM teach us that the microworld is very different from the macroworld ? In the same context, the process of decoherence is well understood in Copenhagen interpretation, but quite artificial in Bohm's theory. The worse IMHO, is the fact that this interpretation is in conflict with elementary Lorentz invariance (which is due to the central role of non-locality. In Copenhagen interpretation, non-locality is also here but limited to EPR-like phenomena). Bohmian mechanics cannot be formulated in a Lorentz-invariant way, which is not the case for Copenhagen interpretation.

For instance : http://en.wikipedia.org/wiki/Bohm_interpretation

 

[Doc Al]

There's still quite a bit of interest in it. You might want to take a look at Shelly Goldstein's review article (Stanford Encyclopedia of Philosophy) here:
http://plato.stanford.edu/entries/qm-bohm/

 

[humanino]

Yes, Doc Al is right. Plus the fact that Stanford Encycl. Phil. is such a great ressource. Actually it is quoted in the wikipedia link. Wikepedia is more scientific : less discussion (which is bad) but more equations (which is useful)

I also wanted to add a welcome for you George Isaac

 

[jtbell]

Recently, I read Bohm's articles explaining his interpretation of Quantum Mechanics. [...] Any experimental evidence against its predictions?

As I recall, Bohm's version of QM doesn't make any experimental predictions that distinguish it from "standard" QM, so there isn't even a possibility of experimental evidence one way or the other.

 

[zhangpujumbo]

What's your opinions about Landau's work on QM?

 

[seratend]

BM is only an equivalent model of QM (formally). Only the interpretations of BM are questionable (as well as the QM interpretations ;).

BM is the explicit display of the QM statistics through the Q observable. we replace the schroedinger equation (evolution of the state |psi(t)>) by 2 equations : the rho(q,t) time evolution (probability conservation law) and the v(q,t) time evolution (the Hamilton-jacobi equation).
As long as we stay with these two variables, we always recover the QM results (including the measurement postulate). However, to solve the rho(q,t) and v(q,t), we almost always need to solve the schroedinger equation first. Thus, this model is not much useful to get initial results. This may explain why this model is not much used today (even if some experts are using it).

The questionable interpretation of BM concerns the v(q,t) field: you can attach an extra equation "the bohmian particle path": dq/dt=v(q,t). However, this path cannot be measured (included in the statement of the BM). Therefore, it is quite a philosophy to accept or not its "reality" (no testable results of QM depends on the existence of this path).

The Lorentz invariance is more hidden in BM but we still have it as a formally equivalent QM model. It is analogue to the Lorentz invariance of EM field with either the coulomb gauge (you have an instantaneous V pontential) or the lorenz gauge (we can view BM as QM with “the coulomb gauge”, ie the Q observable).

However, in my humble opinion, BM model is a very interesting tool to understand how QM works. It also helps in demystifying the measurement problem of QM and some paradoxes.

Seratend.

 

[sifeddin]

Dear George:
I think Bohm's Mechanics is the last resort to those who needs particle trajectory. I would like to show you (one of these papers in that directory http://hume.iet.unipi.it/iannaccone/publications/ ) in which the author finally says if one needs to calculate the tunelling time without the debate about larmor times then turn your sight to BM in which you can navigate the electron in defined path with a defined propagation time. Unfortunately (as you know about me from myself my friend) I do not practice BM so I do not "know" how to calculte such thing in BM. I hope someone else give us more info

 

[caribou]

The decoherent histories interpretation actually allows you to describe paths for any particles at any times in the history of the universe from just after the big bang. There are some restrictions, however, that distinguish the paths from classical ones.

If you choose to describe particle positions, then you can't describe particle momenta at the times you describe positions, and you need to course-grain these fine-grained particle descriptions by only looking at some particles at some times to get useful probabilities. Also, if a particle lacks sufficient entanglement with the rest of the universe then the particle histories interfere, as in the two particle paths in the two-slit experiment.

Other than that, you can talk of a particle going from here to there in almost a classical sense.

 

[sifeddin]

What's your opinions about Landau's work on QM?

And he said ... what? would you explain or give link(s) to what the legendary Landau said?

 

[humanino]

And he said ... what? would you explain or give link(s) to what the legendary Landau said?

AFAIK, the work of Landau in his famous lectures is a (very good) restatement of Bohr's work and the Copenhagen interpretation.

 

[Eye_in_the_Sky]

In Bohm's words ...

Recently, I read Bohm's articles explaining his interpretation of Quantum Mechanics. I did not find anything "bad" with it, so why didn't anybody pursue it further? Any experimental evidence against its predictions?

Here are Bohm's own words on the subject, written around the time of his retirement in 1987:

These proposals did not actually 'catch on' among physicists. The reasons are quite complex and difficult to assess. Perhaps the main objection was that the theory gave exactly the same predictions for all experimental results as does the usual theory. I myself did not give much weight to these objections. Indeed, it occurred to me that if de Broglie's ideas had won the day at the Solvay Congress of 1927, they might have become the accepted interpretation; then, if someone had come along to propose the current interpretation, one could equally well have said that since, after all, it gave no new experimental results, there would be no point in considering it seriously. In other words, I felt that the adoption of the current interpretation was a somewhat fortuitous affair, since it was affected not only by the outcome of the Solvay Conference but also by the generally positivist empiricist attitude that pervaded physics at the time. This attitude is in many ways even stronger today, and shows up in the fact that a model that gives insight without an 'empirical pay-off' cannot be taken seriously.

I did try to answer these criticisms to some extent by pointing out that the enriched conceptual structure of the causal interpretation was capable of modifications and new lines of development that are not possible in the usual interpretation. These could, in principle, lead to new empirical predictions, but unfortunately there was no clear indication of how to choose such modifications from among the vast range that was possible. And so these arguments had little effect as an answer to those who require a fairly clear prospect of an empirical test before they will consider an idea seriously.

In addition, it was important that the whole idea did not appeal to Einstein, probably mainly because it involved the new feature of non-locality, which went against his strongly-held conviction that all connections had to be local. I felt this response of Einstein was particularly unfortunate, both during the Solvay Congress and afterwards, as it almost certainly 'put off' some of those who might otherwise have been interested in this approach.

 

[yanniru]

IMHO, BM is just another interpetation of QM. Personally, I like the idea that in time, particle trajectories then to collapse. That theory, using time as a parameter, can vary all the way from the Copenhagen Interpetation to the Bohm Interpetation.
I should find that reference- about 6 months ago in www.arXiv.com.

Personally, I think it just points out how little we are really sure about in physics. Avtually that just justifies how little I know.

Richard

 

[yanniru]

Today www.arXiv.org has posted a reasoned paper review by Oliver Passon of BM. Turns out that there are two relevant equations: the potential equation and the guidance equation. Bohm and his followers emphasized the potential equation as fundamental; whereas Durr and his school emphasized the guidance equation as fundamental, and called that approach "Bohmian Mechanics"-- hence some confusion about what BM means.

An essential part of BM is a distribution of initial particle positions given by the squared modulus of the eigenfunctions. Given that, then Passon concludes that there is no experimental way to discern BM from ordinary QM.

Here is the link to the paper:
http://www.arxiv.org/PS_cache/quant-ph/pdf/0412/0412119.pdf

Ten pages long, it is the most concise review I am aware of.

Richard