Timeline for Role of "hierarchic structure" in solving the Measurement Problem
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| Apr 13, 2017 at 12:39 | history | edited | CommunityBot |
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| Nov 29, 2016 at 10:54 | history | tweeted | twitter.com/StackPhysics/status/803552603862867968 | ||
| Sep 5, 2016 at 16:18 | comment | added | isometry | Thanks - you have put into words exactly what I was feeling - constructive/explicit vs mathematical-existence. I think at the moment for what I am trying to achieve I am happier with explicit even if limited. I will get the 84 paper and see if I can link it back to my question. | |
| Sep 5, 2016 at 16:02 | comment | added | yuggib | The drawback is that the result is in some sense not constructive, since it only shows that a measurement process exists but not what it is precisely. Probably the ABN paper is in that respect much more explicit. Anyways, it seems to deal with a very special situation, in particular with an observable with only discrete spectrum. That is pretty restrictive, especially because if you want to take into account repeatability of measurements the nature of the observable's spectrum plays a very important role. | |
| Sep 5, 2016 at 16:00 | comment | added | yuggib | I don't know the 98 paper, so I can't comment on that and on the state of the art of the field. However, I think you should try to get the 1984 paper. It is also not long, but pretty clear (at least in my opinion). From my point of view (that is quite mathematical), the result obtained there is satisfactory and in some sense "definitive", since it guarantees the existence of at least one measurement process for each observable that respects all the requirements of a quantum measurement. | |
| Sep 5, 2016 at 15:49 | comment | added | isometry | @yuggib A follow up comment after first read of Ozawa 98: I agree on one level he is trying to achieve a similar aim as ABN of using some Bayes principle to justify reduction. On another level ABN is 200 pages, Ozawa is 6 pages: it seems you get what you pay for - is it fair to deduce from this that quantum measurement theory has developed somewhat in 30 years? All that leaves me unsure about my initial question - I think I'll plough on with ABN - I'm finding it a good read! Final point on Ozawa: I couldn't get how he has done this without decoherence. | |
| Sep 5, 2016 at 7:38 | comment | added | yuggib | Well, the later one of 98 seems to be somewhat more complicated than the one I referred to (that unluckily is quite hard to get without paying). Concerning the initial state of the measuring device, if I recall correctly it is not assumed to be in a pure state by Ozawa, but in a general initial quantum state. | |
| Sep 5, 2016 at 7:14 | comment | added | isometry | @yuggib Thanks, this is the type of feedback I wanted to understand if ABN have done something new. I have downloaded Ozawa 1998 to study. I assume this has similar ideas. The immediate observation is that ABN stress the need to do a full realistic model of the measuring device arguing it is insufficient to describe the apparatus initial state as a pure state. | |
| Sep 5, 2016 at 5:49 | comment | added | yuggib | In the paper I just linked, Ozawa proves (in a mathematically rigorous fashion) that for every observable of (non-relativistic) QM, there exists a measurement process (à la von Neumann, consisting of the interaction with a measuring scaled apparatus) that behaves as expected by the postulates of quantum mechanics. In addition, measurements are (weakly) repeatable only if the observable has purely discrete spectrum. | |
| Sep 5, 2016 at 5:43 | comment | added | yuggib | While I cannot provide an answer concerning the paper you mention, I may say that the "measurement problem" as you describe it was solved almost 30 years before the aforementioned paper in Ozawa 1984. The paper does not mention this work, but another by the same author that is, in my opinion, less poignant. | |
| Sep 4, 2016 at 23:52 | history | edited | isometry | CC BY-SA 3.0 |
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| Sep 4, 2016 at 22:45 | history | edited | isometry | CC BY-SA 3.0 |
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| Sep 4, 2016 at 22:01 | history | edited | isometry | CC BY-SA 3.0 |
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| Sep 4, 2016 at 20:39 | history | edited | isometry | CC BY-SA 3.0 |
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| Sep 4, 2016 at 20:28 | history | asked | isometry | CC BY-SA 3.0 |