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Bohm trajectories and protective measurements? 
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#73
Oct1012, 05:39 PM

P: 301

Of course, because of the relativistic background, all this on spacetime instead of space. And, once it is a many worlds variant, only with a wave function, not with a configuration itself. So, now we have a configuration space, moreover, with a structure which makes sense for a space of configurations living in a space  and all this with all the properties we would use to describe the actual configuration of the world as we see it  but without any configutions. I would say there was, in the past, some interesting research program: Is it possible to start, with only a Hilbert space and the Hamilton operator on it, to derive everything else, including all the physics? My argument was that this program fails because one needs additional structure, already in the first step where one wants to recover the configuration space from the Hamilton operator, a step which, from mathematical point of view, was the most promising, because the usual Hamilton operator, looking like $p^2 + V(q)$, looks very different for p and q. As far as I understand, the very program has been given up. The subdivision into systems, which was a central element, always had a weak point: There is no natural fundamental subdivision, and the subdivisions we have in real life, into observers, devices and so on have no fundamental origin, they make sense only in an environment of a particular configuration which contains at least the Solar system with the Earth. Maybe looking for a replacement of the subdivision into subsystems they use the subdivision into spacetime regions? That would be fine with me, it makes sense. Unfortunately not for the aim of saving relativity, because it would be an introduction of a background in a situation where the quantum gravity guys hope for backgroundindependent theories. But it doesn't seem to be the case  at other places, it sounds like all the decoherence stuff is used as it is, without worrying about the definition of subsystems. I see a circularity here: To define the real objects we observe, we have to apply this decoherence machine, which depends on the subdivision into systems. But the usual subdivisions into systems come from the real objects we observe. A problem which is absent in dBB. There we always have a configuration, and if we consider the evolution of this configuration, we have to consider its environment in the configuration space. In this environment all the visible subsystems are already present and can be used as they are. So far some ideas immediately after reading the paper, so, not very deep. 


#74
Oct2812, 01:14 AM

PF Gold
P: 691

http://philsciarchive.pitt.edu/9347...for_volume.pdf 


#75
Nov2512, 12:46 PM

PF Gold
P: 691

I'm still having some difficulty understanding the difference between weak versus protecive measurements although the authors in some of these papers seem to be suggesting that unlike weak measurements:
http://lanl.arxiv.org/pdf/0801.2761.pdf So if I'm understanding this, then, it is different than weak measurements as summarized here by Demystifier: Weak measurements in quantum mechanics and 2.6 children in an American family http://www.physicsforums.com/blog.php?b=1226 I'm still not sure if this scheme of protective measurements is universally accepted primarily because of some critical papers on the topic but in a recent paper by Gao, he suggests that protective measurements rule out ψepistemic models as per PBR: http://philsciarchive.pitt.edu/9457..._on_PRL_v9.pdf 


#76
Nov2612, 03:14 AM

Sci Advisor
P: 4,612

PM does it with a single measurement. WM does it with a large number of measurements, each on another member of an ensemble of equally prepared systems. For WM, the prepared state before the measurement may be arbitrary (but must be the same for each member of the ensemble). For PM, the prepared state before the measurement cannot be arbitrary; it must be an eigenstate of the observable which will be measured. In a perfect measurement, one would measure an observable: 1. for an ARBITRARY initial state, 2. WITHOUT DESTROYING it, and 3. with only ONE measurement performed. But in QM such a perfect measurement is not possible. Standard strong measurement violates 2, WM violates 3, and PM violates 1. EDIT: For the sake of completeness, let me also explain two additional kinds of measurement:  first kind (FK) measurement and  quantum nondemolition (QND) measurement. Both FK and QND are types of standard strong measurement, so they both destroy the initial state. However, they have a nice property if, after the measurement, you measure the same observable again; they both give the same value of the observable which you obtained by the first measurement. The difference is that FK achieves this only immediately after the first measurement, while QND achieves this at an arbitrary later time. FK measurements are measurements which can be described by a wavefunction collapse. Many (but not all !) actual measurements are FK. However, not many actual measurements are also QND. 


#77
Dec3112, 12:19 PM

PF Gold
P: 691

I don't fully understand this argument but this author tries to use protective measurement to rule out the MWI:
http://philsciarchive.pitt.edu/9494...further_v9.pdf 


#78
Mar913, 12:16 PM

PF Gold
P: 691

Another paper came out today suggesting that ψ is ontic but relying on the concept of protective measurement:
http://philsciarchive.pitt.edu/9609/1/dqs_v6.pdf 


#79
Feb814, 07:07 PM

PF Gold
P: 691

http://arxiv.org/pdf/1402.1217.pdf 


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