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Classical and Quantum Mechanics via Lie algebras 
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#37
May1311, 10:36 PM

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#38
May1311, 10:56 PM

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So finally the double slit experiment mystery is finally solved after 80 years?? 


#39
May1411, 01:15 AM

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So what has been gained by adopting your model rather than standard QM? 


#40
May1411, 12:32 PM

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kinda like paintballs but not exactly.... i..e there are no electron (from the detector side) involved here......how would Neu's hypothesis explain the patterns of molecules on such a primitive detector.....? or let's make it even simpler....instead of detector we have a white sheet of paper.....coated with some chemical....that...reacts with the bucky ball to create a tiny black dot....... after say a million/billion molecules have passed through the slits and touched the detector.....we would see a (interference/noninterference pattern depending upon our setup) a pattern......is there a way to explain this via Neu's hypothesis? 


#41
May1411, 01:31 PM

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The particle concept loses its meaning when applied outside its domain of applicability. Trying to keep the concept then leads to all sorts of weird things. and discussed in the thread http://www.physicsforums.com/showthread.php?t=480072 


#42
May1411, 01:51 PM

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The analogous question of what happens if a delocalized drop of water (in the form of a faint mist) reaches a detector. It just stays there delocalized and is virtually unmeasurable at the resolution of typical water drops. There is no conceptual problem. The quantum case is essentially the same. On the other hand, after the slits, there are no particles in any meaningful sense. Only an empty label ''particle'' without any discernible meaning persists. W. Sandhas, Definition and existence of multichannel scattering states, Comm. Math. Phys. 3 (1966), 358374. to see how fields for bound states are constructed rigorously in the nonrelativistic case (sufficient for buckyballs). The relativistic case is similar, and figures under the heading of HaagRuelle scattering theory. 


#43
May1411, 02:40 PM

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I said: "The interaction of the molecule with the surface is certainly strong enough to disrupt that delicate superposition, resolving the molecule at a single location. That is the standard interpretation and it is far more consistent and believable (at least to me) than your suggestion that there is somehow another form of "smeared out" molecule that can survive interaction with a detector and remain in its smeared out form." You said: "You imagine that this is the case, but to give it the label ''certainly'', you need to provide a proof for your assertion, which you can't give. Thus what you say is pure speculation." and "No. it is your ad hoc invention. The standard interpretations are silent about the situation." Is that really true? Because I am certain that standard QM says that measurements of observables can only yield eigenvalues. Thus for a position measurement, as is carried out by the detector, we should observe a wellresolved position, rather than the superposition of position states reflected by your "smeared out" version. This is often called the measurement problem, and is sometimes interpreted as "wavefunction collapse" ... I think all of that is pretty "standard" and is certainly not "my ad hoc invention". Also, I again ask you, where is the experimental evidence of massive particles existing in the sort of "smeared out" state you describe while interacting with a macroscopic surface? A simple google search will provide hundreds of examples of images of welllocalized versions of massive particles interacting with macroscopic techniques. There is even a famous one where IBM spelled out their corporate logo with single atoms (I think it was using Xenon on gold). 


#44
May1411, 03:29 PM

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 measurements of half lives, spectral frequencies, or of the anomalous magnetic moment of the electrons are not eigenvalues of observables in any relevant sense.  standard QM is silent about anything unobserved. But nobody has performed your experiment.  the projective measurements that you have in mind are applicable only to discrete observables whose spectrum is known in advance. Not to the position of a particle.  what constitutes a measurement of the position of a particle is not even welldefined. Regarding heavier particles, I count the interference experiments for buckyballs as such evidence. 


#45
May1711, 02:49 AM

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A bucky ball if went in wave from, would have more than a single quanta of energy.
Thus when it hits the screen, per Neu's hypothesis, we should see a couple of electrons (out of the billions) being triggered and not just one. Thus if we go with the dam with one hole analogy, a couple of electrons would come out of the hole. 


#46
May1711, 02:01 PM

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(How much energy it brings depends on its momentum, hence on the preparation. Thus what was argued before by both sides about energy should have in fact been argued about mass.) 


#47
May2611, 07:59 PM

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Come on PF members. If Neumaier was right. Others would have figured this out already for more than a century. Why only he figured this out. I hope other critics can put hole in his theory. If it is really wrong. Let's not let it drag on and make it disturb us who search for the right interpretation. I'll start with Camboy criticism (A. Neumaier, pls. comment on it):
"I'm sorry  this sounds like nonsense to me. He says only 1 electron in the detector responds because of conservation of energy. What happens when the screen is the inner surface of a hollow sphere a lightyear across, and the emitter is a point source dead in the middle emitting a spherical moving quantum field? How is the energy transported across space via the quantum field? Across the whole wave front? In which case, what kind of process involving conservation of energy takes place around the whole surface of the sphere instantaneously when the wave hits the screen? How does this work? if you wish to provide an 'interpretation' one must do more than simply state something happens." Well? 


#48
May2611, 08:53 PM

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I would literally bet a million dollars that the outcome would be consistent with conventional interpretations and falsify Neumaier's. 


#49
May2611, 10:17 PM

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#50
May2711, 04:56 AM

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The whole point about interpretations is that every interpretation predicts the same things for any given experimental setup. If they didn't, then interpretations would be experimentally decidable, and those in contradiction with experiment would be discarded. Arnold's interpretation is just that  an interpretation. It does not contradict experimental results, but rather offers a more rational way of thinking about QM. And others did "figure it out" (in related forms). Arnold already said elsewhere that his initially naive views about particles in QM were improved considerably after discussions with experts in quantum optics years ago. If you want to search for a "right" interpretation, first master the most essential and basic interpretation, i.e., "shut up and calculate". Everyone with an interpretation must master "shut up and calculate" first, since that's what decides whether QM is or isn't in contradiction with experiment. Regarding buckeyballs, atom interferometry, etc, the generic features of the "shut up and calculate" interpretation for a field incident on a doubleslit were explained in post #73 of this thread: http://www.physicsforums.com/showthr...82#post3171882 with an additional bit in post #78. The more accurate calculations with a relativistic quantum field instead of a classical field do not change the gross features significantly. (Mandel & Wolf give details.) 


#51
May2711, 07:13 AM

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So an extremely tiny amount of energy arrives at any place of the hollow sphere, integrating over the sphere to the energy of one electron. Thus energy is conserved. The probability of response anywhere is extremely tiny, too, so that uncertainties in the sphere by far dominate the effect, and nothing can be concluded. 


#52
May2711, 07:21 AM

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(i) the absorbing surface is completely silverfree, (ii) one and only one silver atom is emitted by the source, (iii) The silver field at the absorber had no time to redistibute itself during the procedure it takes to search the absorber for a single silver atom. 


#53
May2711, 05:55 PM

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#54
May2711, 05:59 PM

P: 525

Others pls. join scrutinize Neumaier's Interpretation and either support it doesn't violate some known principles or have theoretical flaws or point out the flaws if you can so Neumaier would be aware of them too, and can either improve them or just call it a day. 


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