Does Decoherence Solve the Measurement Problem Completelyby Prathyush Tags: measurement, quantum mechanics 

#19
Nov2612, 01:43 AM

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#20
Nov2612, 02:02 AM

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What do you mean by "both"? Both dead and alive?




#21
Nov2612, 02:26 AM

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#22
Nov2612, 02:29 AM

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but this does not follow mathematically from decoherence but is a (one of many) philosophical interpretation; and therefore decoherence does not fully solve the measurement problem




#23
Nov2612, 08:12 AM

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#24
Nov2612, 09:55 AM

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a) the "mathematical entities" (subspaces, ...) describing the dead cat and the alive cat are both "present" after decoherence in the density matrix  I agree b) it is not a matter of physics but of philosophical interpretation whether this corresponds to something "ontologically real" in the sense of MWI, whether you want to add a "collapse" or whatever; physically this is a matter of taste b/c there is no experimental prediction to distinguish between all these interpretations, so it's philosophy or metaphysics (Ockhams razor is philosophy, not physics) As a platonist believing in some abstract sense in the reality of the wave function and the specific cat as its realization I may also believe in MWI. As a positivist I will not believe in any reality but only in the results of my calculation and whether they agree with experimental results or not; they agree with experiments  fine  endofstory (it is interesting that there are positivists arguing for MWI and against a collapse  which is a selfcontradictory position). Not even Ockhams razor is sufficient to decide b/c there are two choices: 1) add complexity to the ontological level in order to reduce the complexity of the interpretation => MWI 2) add complexity to the (not fully understood) explanation or interpretation in order to reduce complexity of the ontological level => collapos (b/c there is only one world = the observable world) Ockhams razor doesn't tell you whether (1) or (2) is the correct reasoning b/c Ockhams razor is applied two different 'categories', namely 1) to 'interpretation' 2) to 'ontology' So decoherence as a purely physical phenomenon cannot tell us anything regarding the metaphysical level. In order to deduce a metaphysical reasoning you have to have some metaphysical input  which is not present in the formalism of QM and decoherence. Compare the following positions: 1) There are two branches of reality, both real in the same sense, one containing the dead cat and one containing the alive cat; and there are two observers in these two branchens ... In that sense everything that is present in the density operator does exist in the above mentioned sense. 2) blablabla regarding collaps ... 3) There is a density operator describing the probability to find a dead cat; but b/c w/o any observation of both cats at the same time  which we don't have  we do not have any indication whether they both exist in some still to be defined sense, so we decide not to ascribe any ontological meaning to the density operator (nor to wave functions etc.) We use the QM formalism as a model which approximately represents a subset of aspects of "reality" but which allowes us to predict results of a certain class of experiments 3) is an agnostic position. It does not allow us to explain in any sense why (!) physics (based on mathematics) is a successful description of reality  b/c neither do we make any statement regarding the relation between physics and reality, nor do we make any attempt to define 'reality'. But it still allowes us to use quantum mechanics including decoherence to derive experimentally testable and accurate predictions. Any position that goes beyond (3) like MWI in the sense of (1) or collapse (2) adds some metaphysical reasoning beyond decoherence as a pure mathematical fact. 



#25
Nov2712, 06:45 AM

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I wonder if detailed study of the line between "in principle" and "in practice" might reveal something here (based on limited information storage capacity in the universe). 



#26
Nov2712, 08:56 AM

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In the formalism of QM there is neither a collapse nor a branching into many worlds; there's only a single wave function with unitary time evolution (or a density matrix; but taking all d.o.f. into account there is not even the need to consider density matrices)
But when a human observes a pointer in an apparatus the pointer is not in any superposition, so there must be something like a collaps, a branching or whatever; and this is beyond the formalism of QM. 



#27
Nov2712, 05:05 PM

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PF Gold
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As Schlosshauer says it transforms a superposition into an 'improper' mixed state. Here improper means it mathematically looks exactly the same as a mixed state and no experiment can tell it from one but in reality it isn't. But it is this 'mimicking' of a mixed state that allows it to be interpreted as one, and as an interpretational thing solve the measurement problem. It doesn't by itself solve the measurement problem but by allowing the improper mixed states to be interpreted as proper ones does for all practical purposes. The wavefunction collapse issue is still there but swept under the rug so to speak. Thanks Bill 



#28
Nov2712, 06:36 PM

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I'd appreciate the reference. TIA. jimgraber 



#29
Nov2712, 07:12 PM

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#30
Nov2712, 10:04 PM

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Thanks
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#31
Nov2712, 10:24 PM

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Thanks Bill 



#32
Nov2812, 12:43 AM

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So QM doesn't tell us how potential results become actual (real) results. Even decoherence doesn't. 



#33
Nov2812, 01:04 AM

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QM is a probability calculus based on classical wave mechanical concepts of the reality underlying instrumental behavior which are inferred from the instrumental behavior. Quantum superposition is a mathematical representation, based on classical wave mechanics, of the extent of our knowledge of possible instrumental behaviors. Quantum superposition has the nonclassical character it does precisely because of our ignorance of the reality underlying instrumental behavior. That is, quantum superposition is, in a most important sense, an expression of our ignorance of deep reality. There is currently no extension or interpretation of QM (including decoherence) which explains instrumental behavior to the extent that that behavior can be predicted in any way other than assigning probabilites to the possiblities associated with any particular instrumental preparation. Why there's only one observed experimental outcome rather than the multiple ones that might be entailed in a particular superposition isn't the question, imo. The question is, rather, eg., why was there a detection (as opposed to no detection) recorded during a certain interval. Decoherence can't answer this question, because the mathematics of decoherence doesn't tell us any more about the reality underlying instrumental behavior than can be inferred without applying the mathematics of decoherence. Quantum amplitudes are superposed in accordance with the requirements of any consistent wave mechanical representation. Philosophical pseudoproblems and paradoxes arise due to assuming that quantum states are real ontological states, which is an assumption that has no direct evidentiary support. The current state of affairs is that the math of quantum decoherence doesn't solve the real measurement problem. Imho, there will never be a solution to the real measurement problem. It seems likely to me that some form of QM, ie. a probabilty calculus regarding instrumental behavior, is the best that can be hoped for  and that the real quantum measurement problem will remain unsolved. 



#34
Nov2812, 01:26 AM

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nanosiborg, great, thanks.
A view comments: The case of decoherence tells us that (partially !!) we can solve the measurement problem. And there's some hope  so we don't stop. Perhaps the whole discussion is misguided b/c decoherence adds a pseudosolution in introducing the incoherent (classical) environment. It seems as if adding a classical environment could solve the quantum measurement problem (the discussion shows that it doesn't). But even if decoherence applies to most experiments (fapp) we must not forget about experiments which we could construct in principle, namely measurements where the apparatus is perfectly isolated from the environment and where the branching or collaps is not due to decoherence + XYZ. In that case we still have to deal with a small number of entangled d.o.f. and decoherence simply doesn't apply! 



#35
Nov2812, 01:47 AM

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Thanks tom.stoer. I think I should reread your and others' comments and think about this some more.




#36
Nov2812, 02:51 AM

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