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Tangential comment: if you are interested in quantum mechanics then you may be interested to read about "Bohmian Mechanics". I became interested in Bohmian Mec

by shoo 12y ago

Tangential comment: if you are interested in quantum mechanics then you may be interested to read about "Bohmian Mechanics". I became interested in Bohmian Mechanics after reading an email exchange between Sheldon Goldstein & Steven Weinberg [1]. It contains a few quite entertaining quotes, in particular: > And since Bohm’s equations make exactly the same > predictions as those of ordinary quantum mechanics, > it is not clear what is accomplished by adding the > complication of guiding waves, except to restore a > sense of sanity to the whole affair. Scott Aaronson has a brief introduction to Bohmian Mechanics at the end of his notes on decoherence and hidden variables [2]: > Again, the amazing thing about this theory is that it's > deterministic: specify the "actual" positions of all the > particles in the universe at any one time, and you've specified > their "actual" positions at all earlier and later times. Scott's perspective is particularly interesting because he points out some limitations of Bohmian Mechanics. To paraphrase badly, the deterministic particle trajectories obtained from Bohmian Mechanics rely upon dealing with actual particles, position, momentum, in infinite dimensional spaces. It doesn't give you deterministic behaviour in the finite dimensional spaces that computer scientists prefer. Some proponents of Bohmian Mechanics point out that the theoretical predictions of deterministic particle trajectories for the famous double-slit experiment agree with recent experimental results. Theoretical predictions: see Figure 1, page 14 of [3], which is an adaptation of a figure from [4]. Experimental results: see Figure 3, page 1171 of [5]. Note that [5] carefully frame their experimental results as "Using weak measurements, however, it is possible to operationally define a set of trajectories for an ensemble of quantum particles". For further reading, please see [6] for links to introductory writing about Bohmian Mechanics. [1]: http://inference-review.com/article/on-bohmian-mechanics http://inference-review.com/article/on-bohmian-mechanics [2]: http://www.scottaaronson.com/democritus/lec11.html http://www.scottaaronson.com/democritus/lec11.html [3]: http://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/files/Introduction.pdf http://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/fil... [4]: "Quantum interference and the quantum potential" -- Philippidis, Dewdney, Hiley -- Il Nuovo Cimento B, 1979; [paywalled article] -- http://link.springer.com/article/10.1007/BF02743566 http://link.springer.com/article/10.1007/BF02743566 [5]: "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer" -- Kocsis, Braverman, Ravets, Stevens, Mirin, Shalm, Steinberg; Science, 2011 -- [PDF] http://materias.df.uba.ar/labo5Aa2012c2/files/2012/10/Weak-measurement.pdf http://materias.df.uba.ar/labo5Aa2012c2/files/2012/10/Weak-m... [6]: http://www.bohmian-mechanics.net/whatisbm_introduction.html http://www.bohmian-mechanics.net/whatisbm_introduction.html

UhUhUhUh 12y ago
And the recent pilot-wave experiments. Determinism not dead yet...
ajkjk 12y ago
I don't find Bohmian mechanics any more satisfying than regular QM. In an effort to formulate a 'hidden state' that makes QM make.. sense.. you add a guiding wave equation that depends on the state of the universe? That's not better at all. I'm all for trying to formulate QM in a way that doesn't offend basic sensibility, but I'm not convinced this is it. I don't think deterministic-but-nonlocal is better than nondeterministic-but-local.
- jostylr 12y ago
  Standard quantum mechanics only has the wave function. The thing you object to in Bohmian mechanics is the wave function. Both are nonlocal. You should object to both. In particular, standard quantum mechanics gets results of experiments by collapsing the wave function. That is, it takes something which is universe spanning and it collapses it to something, with the collapse based on what a physicist does in a laboratory. That, of course, should seem rather absurd. To get around that, you have to add something either particle positions, a matter density, flashes, etc. You need results to experiments in a theory. Without something (and collapse from experiments is adding the collapse mechanism + external experiments, whatever that means), you do not get results. So the theory is a complete failure. Only many worlds is not non-local (it adds a matter density by integrating the wave function appropriately), but they escape it by not having results of experiments at the time that history records there were results. I think. That theory makes me a little dizzy at times. Also, the hidden state of BM is not hidden. We have a basic sense that stuff has positions. That may be an illusion, but Bohmian mechanics says that we can choose a theory that does not have that be an illusion. The thing that is hidden, that is deduced from the behavior of stuff which we see, is the wave function. What BM explains is why it seems that our world is particle-like and why we have singular outcomes to experiments. All done naturally. Sure, the nonlocal nature is a problem that we are still trying to understand, but so what? No one has got the full story yet and so BM is viable and gives a great intuition about QM (the standard QM (operators, collapse) is a derivable formalism, like thermodynamics from Newtonian Mechanics).

by shoo 12y ago

UhUhUhUh 12y ago

And the recent pilot-wave experiments. Determinism not dead yet...

ajkjk 12y ago

I don't find Bohmian mechanics any more satisfying than regular QM. In an effort to formulate a 'hidden state' that makes QM make.. sense.. you add a guiding wave equation that depends on the state of the universe? That's not better at all. I'm all for trying to formulate QM in a way that doesn't offend basic sensibility, but I'm not convinced this is it. I don't think deterministic-but-nonlocal is better than nondeterministic-but-local.

jostylr 12y ago
Standard quantum mechanics only has the wave function. The thing you object to in Bohmian mechanics is the wave function. Both are nonlocal. You should object to both. In particular, standard quantum mechanics gets results of experiments by collapsing the wave function. That is, it takes something which is universe spanning and it collapses it to something, with the collapse based on what a physicist does in a laboratory. That, of course, should seem rather absurd. To get around that, you have to add something either particle positions, a matter density, flashes, etc. You need results to experiments in a theory. Without something (and collapse from experiments is adding the collapse mechanism + external experiments, whatever that means), you do not get results. So the theory is a complete failure. Only many worlds is not non-local (it adds a matter density by integrating the wave function appropriately), but they escape it by not having results of experiments at the time that history records there were results. I think. That theory makes me a little dizzy at times. Also, the hidden state of BM is not hidden. We have a basic sense that stuff has positions. That may be an illusion, but Bohmian mechanics says that we can choose a theory that does not have that be an illusion. The thing that is hidden, that is deduced from the behavior of stuff which we see, is the wave function. What BM explains is why it seems that our world is particle-like and why we have singular outcomes to experiments. All done naturally. Sure, the nonlocal nature is a problem that we are still trying to understand, but so what? No one has got the full story yet and so BM is viable and gives a great intuition about QM (the standard QM (operators, collapse) is a derivable formalism, like thermodynamics from Newtonian Mechanics).