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Classical and Quantum Mechanics via Lie algebras 
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#127
Jun2411, 08:25 AM

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Collapse is the effect of ignoring the details of the interaction with the environment, keeping only an approximate summary in the form of a history of measurements and a POVM for the average influence of the environment upon measuring. Even in the analogy with the 2D perspecticve, one doesn't necessarily need other observers, since one notices soon that the different views the single observer gets at different times can be coherently realted only by assuming a third dimension. Once this is realized, moving around is enough to gather rthe information needed to complete the 3D picture. Therefore, in the thermal interpretation, there is no place anymore for mystery. 


#128
Jun2411, 08:48 AM

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In your Interpretation. There is no Collapse. And the behavior in the double slits can vary. For example. In Standard QM. When a Buckyball is emitted, always one hit would be detected. But in your case, since it doesn't collapse and it is alway a field, the energy of the buckyball is enough to trigger 5 or even 10 electrons at the detector. So your one Buckyball emission would result in 10 or more hits due to the energy of the Buckyball field much more than an electron. Here your interpretion obviously didn't have the same prediction as QM. 


#129
Jun2411, 09:21 AM

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#130
Jun2411, 10:18 AM

PF Gold
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#131
Jun2411, 10:59 AM

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And there is just as much collapse in my interpretation as statistical mechanics predicts. The literature contains a number of derivations of POVM's from statistical mechanics, and this captures all the observable features of (partial) collapse. 


#132
Jun2411, 11:06 AM

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#133
Jun2411, 02:40 PM

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#134
Jun2611, 06:08 PM

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#135
Jun2711, 01:53 AM

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It still leaves questions for me. The big one is, if we start with a simple system of one quantum in a definite spin state along one axis, and we use a macro instrument to measure its spin along an orthogonal axis, is there enough information in that system (perhaps including the instrument that prepared the quantum in the initial state) to determine what outcome we'll get, even though it is not practical to imagine we could ever have access to that information, or is it fundamentally necessary that we cannot have access to that information to get that probability distribution? If the latter, then how can we give meaning to information present that if we had access to it would not be present?



#136
Jun2811, 07:01 AM

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In that case, since all macro predictions are made by statistical mechanics, I doubt that one can predict more than a statistics for the resulting event.. Whether it is possible in principle is a different matter  but to be ablre to do this would mean one know every quantum detail of the macro instrument, and whether this is even knowable is questionable. 


#137
Jun2811, 07:57 AM

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Right, so my point is that if we say there is some unknowable detail that determines the outcome, then nothing science could ever do could distinguish that from something that is simply not determined. So determinism or indeterminism exits science and becomes a personal philosophical choice, and that is what I would call "the measurement problem." It just plain wouldn't qualify as a measurement if it didn't have that property, and that I think is the fundamental paradox/limitation/weirdness of physics. The thermal interpretation has not made it go away, but amazingly, it has relegated it to a completely classical problem. The measurement problem is no longer in some strange quantum/classical interface (a la Copenhagen) nor is it strictly in the quantum domain (a la deBroglieBohm), it is still perfectly classical, and applies just as well when we shuffle a deck and pick a card.



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