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Classical and Quantum Mechanics via Lie algebras 
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#55
May2711, 06:11 PM

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PF Gold
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Actually, I am not able to give expert critique of Neumaier's theory. From what I do understand, I like it if it were just an interpretation. I just responded the discussion with spectracat, where both agreed that standard QM and Neumaier's theory actually made a different prediction. That makes it not just an interpretation (similar to, if you believe some of Deutch's proposals, MWI is testable). Given the difference in prediction, my physical intuition finds the standard prediction much more plausible, enough for me to bet on it. Given this I simply wanted to raise that buckyballs are not needed  just something easy to detect that is not in the receiver.
I would be very interested in strangerep commenting on the prediction difference and the feasibility of an experiment. Strangerep knows this area *much* better than I. 


#56
May2711, 06:12 PM

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I thought we were talking REAL science here. 


#57
May2711, 08:20 PM

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I would also modify (ii) to say that exactly one silver atom impacts the surface between imaging steps. Cooling the detector is easy .. I have multiple 4K cryostats in my own lab. A much bigger problem is making sure that you only have a single atom coming through at a time, I can imagine several approaches to achieving that, but they are all nontrivial, and I am not sure they would work. Even if you could achieve that, imaging a single atom is extremely hard, unless you can narrow down its position to a fairly small region. I think these experiments are doable, but would require at least a million dollars worth of equipment to achieve. As interesting as I find Neumaier's proposal, I am sad to say that I don't think there are many experimentalists out there willing to commit those kinds of resources to this project. 


#58
May2711, 09:22 PM

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#59
May2711, 09:29 PM

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#60
May2811, 01:17 AM

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in the thread http://www.physicsforums.com/showthr...Interpretation there is an unanswer message from JesseM about Neumaier Interpretation and Bell's Theorem. The last message of it points to this thread so let us continue where it left.
In message #14, Strangerep (lone known supporter of Neumaier Interpretation) states: "No. States do not consist of "definite outcomes". Although one might like to think of individual events in experiments as definite outcomes, all experiments involve some level of statistical analysis." JesseM answered: Ok. Arnold, Pls address JesseM argument that Neumaier Interpretation is not a local one. It seem you tried with superior mathematics to prove that Bell's Theorem and Aspect experiment are just local ones with hidden variable and they don't really have nonlocal correlations in spite of numerous experiments to the contrary that carries positive result of violation of Bell's Theorem. Arnold Neumaier. Are you trying to say that Bell's Theorem is not really violated. Or the violation is as a result of hidden variables? 


#61
May2811, 07:25 AM

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#62
May2811, 07:42 AM

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"Most electrons in a real material are there smeared out in a way that the particle picture is misleading. Chemists use electron densities, not electron positions to describe things. Thus a newly arriving delocalized electron is nothing very special to the detector. In an interference experiment, neither the electron nor the buckyball is a particle, since the latter is a semiclassical concept without meaning in case of interference. Since there is no particle, there is no need to explain where the particle goes. The density of the electron field or the buckyball field increases at the target  that's all that can be said, and this is enough for verifying what one can actually measure  e.g. the silver film in a SternGerlach experiment after a macroscopic amount of silver accumulated." What do you think? 


#63
May2811, 10:10 AM

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I think that the "beam" will be diffracted, and its intensity at a point on the detector will give the probability of detecting a buckyball strike at that point. For many buckyballs, this will give the density of buckyball strikes in the neighborhood of that point. If a buckyball just embeds in the detector without being destroyed, then you should be able to use an electron microscope to find it. 


#64
May2811, 06:51 PM

P: 525

Isn't it that Arnold Neumaier approach supposed to make the measurement problem nonexistent? But according to The_Duck reply in the Quantum forum about QFT and Particles that:
"The measurement problem has nothing to do with particles in particular. The measurement problem is how we get from a superposition of states to one single observed reality. QFT has superposition in exactly the same way as nonrelativistic quantum mechanics, only now it is superpositions of different possible field states instead of different possible particle positions or whatever." What really is Neumaier position about this? (btw.. I love to call him Neumaier as it is unique and like von Neumann.. both of them very skill mathematician... calling him Arnold would keep reminding me of Arnold Schwarzenegger.... a brute physical force compare to von Neumann pure intellectual might... lol) 


#65
May2911, 02:08 AM

P: 525

Therefore you can't find any single buckyball at the detector. They are smeared all over the detector. I don't know if he means the atoms of say a 430atom buckyball became become fragmentalized all over the detector or the buckyball just divides into many parts that is still interconnected. Hope others can clarify. 


#66
May2911, 03:32 AM

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I'd like to remind readers of this thread that Arnold's original purpose in opening this thread was to seek feedback on the presentation in the book prior to publication. (See opening post.) There's a LOT more in the book than just an interpretation, and much of it could benefit from feedback indicating specific areas which are unclear, or missequenced, etc, etc. I.e., the sort of feedback that helps turn a draft into a publication. Edit: One important theme in the book is already implicit in the title: "Classical and Quantum Mechanics via Lie algebras". Arnold addresses both the classical and quantum cases, also thermodynamics, and relates them with considerable insight into their common features, interwoven with Liealgebraic ideas. This commonality (once comprehended) was a real eyeopener for me when I first began to understand it. 


#67
May2911, 09:32 PM

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PF Gold
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Please clarify the situation. 


#68
May3011, 04:23 AM

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I would have expected that it depends on the details of the interaction Hamiltonian between a (quantum) buckyball field and the spatial array of atoms in the detector, i.e., whether the interaction Hamiltonian allows the formation of a bound state between the buckyball and the detector atoms (both considered as localized fields), or just some sort of excitation of the electrons of the atom(s) in a region of the detector, or maybe a combination of both. I don't see it as being a test of an interpretation though, since the detailed predictions must still be calculated using standard QM/QFT machinery once the interaction Hamiltonian is specified. 


#69
May3011, 12:18 PM

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The thermal interpretation simply gives a language for talking about the mathematical stuff in standard QM in a way free of the usual interpretational paradoxes. In the above situation (interference experiment with a _single_ particle), standard singleparticle quantum mechanics predicts only the lack of a responce at places of complete destructive interference, and nothing beyond, in agreement with the thermal interpretation. On the other hand, quantum statistical mechanics predicts a complicated (and incompletely understood) interaction between the quantum field and the detector _after_ the arrival, which leads to the actual macroscopic situation that can be measured. Whether this interaction leads (a) quickly to a state in which the field concentrated to a single point or (b) only to a state in which the field remains dispersed is completely unknown, and determines the result of an actual experiment along the suggested line: in case (a), the search (which takes some time to complete) will find a single particle somewhere, in case (b) it won't find anything. The thermal interpretation will be correct if experiment and theory both agree on (a), or if they both agree on (b). The scenario I described in detail before says only what happens until and including arrival of the quantum field, where it is obviously dispersed. About the multiparticle phase afterwards, the thermal interpretation says that the qantum field and the detector change according to the laws of statistical mechanics, which would have to be employed to do the theoretical calculation that leads to either (a) or (b). No prediction can be made before either the experiment has been performed reliably enough or a theoretical calculation decides between (a) and (b). Only if both are done and lead to a discrepancy, it would be a failure of quantum mechanics (and therefore also of the thermal interpetation) to describe the situation. 


#70
May3011, 12:33 PM

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But how do you know the effect of cooling on the behavior of a very delocalized silver field interacting with your detector? If it turns out that the only metastable configurations are those where the silver field is localized at an approximately definite position in the detector crystal and there are no energy barriers to reach such a state then no amount of cooling would prevent the delocalized silver state to concentrate somewhere before you could do the search. From the point of view of the thermal interpretation, your guess of the experimental outcome just amounts to the latter situation. It it is what really happens and if quantum mechnaics really predicts rthat then the thermal interpretation is validated by your experiment in spite of your cooling. But checking whether this situation can occur requires a complex quantum statistical mechanics calculation. I don't know how easy it is to do. Without such a calculation, there is no experimental information to say what could happen. Another question: Is it feasible to search for single silver atoms with high reliability the complete surface of your detector, if it is large enough to acrtually recieve the silver atom with high probability? 


#71
May3011, 12:39 PM

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This means that influences cannot propagate faster than light. Bell's theorem is not about influences but about correlations. There is no causal barrier against nonlocal correlations. Indeed, an ordinary local Maxwell field is causal (and local in the conventionally used terminology) but it exhibits such nonlocal feratures whenever the field is coherent enough and has a nonlocal extension. 


#72
May3011, 12:45 PM

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The particle picture is appropriate only as long as one can take the beam to be wellfocussed. The particle picture becomes meaningless once the beam goes through a narrow slit  even a single slit is enough for that. This is why in the Copenhagen interpetation one cannot say anything about the particle anymore  it no longer exists. That particles are reconstituted under certain conditions under the catalysing effect of a macroscopic detector is quite another story. 


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