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What does the probabilistic interpretation of QM claim? 
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#1
Mar1111, 08:15 AM

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I collect here info from another thread, to have a more focussed discussion.
Nonrelativistic particles have no different interpretation than relativistic ones. Particle detectors respond to the momentum of a particle, not to its position. Scattering experiments are interpreted in the momentum picture. Nobody is interested in the position of particle tracks, only in their momentum (which tells about masses). covering the size of an uranium atom (N=92), say. This is ridiculous  such measurement devices are impossible! Whereas the form in which I stated the probability interpretation assumes nothing. it makes claims only for those projectors that are actually realizable. it is therefore much more realistic. 


#2
Mar1111, 08:27 AM

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#3
Mar1111, 08:35 AM

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#4
Mar1111, 03:19 PM

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What does the probabilistic interpretation of QM claim?
Eugene. 


#5
Mar1111, 03:42 PM

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Eugene. 


#6
Mar1111, 04:17 PM

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I also reproduce what I wrote on this point in the other thread:
Experimenters have been recording particle tracks in position space with cloud chambers, bubble chambers, spark chambers, and drift chambers for many decades. The experiments are typically done in a strong magnetic field, which allows for measuring the momentum of charged particles by measuring the curvature of a track in position space. Modern experiments also have calorimeters at the boundaries of detectors that measure energy deposited; this does give a direct measurement of a particle's energy, but not its momentum. For some recent pictures of particle tracks in position space from the LHC see http://public.web.cern.ch/press/pres.../PR15.10E.html 


#7
Mar1211, 01:50 AM

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I certainly believe that the superposition principle even applies when you can consider a quantum object in a definite state (Quantum Enigma, pg. 191; Entanglement, pg. 79; Absolutely Small, 371372). So if it is in a definite state (this is obviously determined through what you see) then you can also consider all the other states it COULD be in as potentials (as you cannot see those other states). Of course, we can only talk about what we see. Perhaps those potentials ARE really real too, we just can't see them? But such questions are pointless as what we work with is from what we see.
The Mental Universe > http://henry.pha.jhu.edu/The.mental.universe.pdf 


#8
Mar1211, 06:32 AM

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When the particles in these chambers pass the medium, they ionise their surroundings. This interaction itself causes a collapse of the wafefunction.
The resultant ionised particles of media are what is detected, the momentum can be calculated as can the energy of the particle, but since there is delay between the initial ionisation and the detectoin of the ionised media particles, the initial particle is no longer in that state and cannot be correlated with the measurement of its energy (velocity). 


#9
Mar1311, 06:13 AM

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#10
Mar1311, 06:16 AM

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If it doesn't in the most important case, there is no reason to believe it should in other cases. 


#11
Mar1311, 06:17 AM

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the particle is a spherical wave which leaves a track in the detector (according to Mott's famous analysis) in a random initial direction  the scattering direction and the particle energy (which together give the momentum) form the observables, not the position. 


#12
Mar1311, 09:02 AM

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I don't think its really correct to say that no one is interested in particle tracks. Although I'm not a particle experimentalist, I certainly think they're interesting to look at!
More seriously, detailed reconstruction of particle tracks is important for determining interaction vertices. For example, interesting unstable particles may decay after travelling some macroscopic distance, thus leading to an offset in the positions of the decay products. Deciding whether certain decay products came from a "primary vertex" or from some "secondary vertex" is critical for determining the nature of the unstable particles. For example, it helps in deciding what invariant mass to compute. At least that's my understanding from chatting with my experimentalist friends. See here: http://lhcbpublic.web.cern.ch/lhcbpublic/ for an example. The April 21, 2010 entry. 


#13
Mar1311, 01:46 PM

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#14
Mar1311, 02:58 PM

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But experimentalists do measure particle positions all the time. They use rulers, photographic plates, bubble chambers and other notsosophisticated devices to do so. Then they can specify a certain volume in space and count how many times particle passed through that volume (e.g., using a Geiger counter). So, experimentalists can calculate the probability of the particle being in that volume. Probabilistic interpretation of position measurements exists experimentally. However, for some reason, you do not allow us to do the same in theory. I would appreciate if you give an original reference to the "Wigner theorem", which, as you say, does not allow us to measure position and interpret it probabilistically. This claim sounds unbelievable to me. Eugene. 


#15
Mar1311, 03:30 PM

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I don't know what would happen if we tried to determine photon's position with the precision of, say, less than 1 Angstrom. Perhaps, in this case we would meet some difficulties that you are referring to. However, there are no experimental devices, which can measure photon's position so precisely. So, the issue of the absence of a photon's position operator is an academic issue, in my opinion. You do not deny the existence of photon's momentum eigenstates. And I can always form linear combinations of these eigenstates (with factors like exp(ipx)) which would behave *almost* like position eigenstates. For example, the linear combinations with different x and x' will be (almost) orthogonal. A space translation of an xcombination will move it to the x+acombination. So, all properties characteristic to position will be approximately satisfied. This should be sufficient for defining position measurements and related probabilities at least in our macroscopic world with micrometerorsoprecision measurements. All these problems are absent for massive particles, like electrons. So, to keep our discussion simple, let us focus on the doubleslit experiment with electrons. Eugene. 


#16
Mar1411, 05:10 AM

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#17
Mar1411, 05:33 AM

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For photons one not even has a Schroedinger picture in which photon position would be welldefined, hence clicks cannot be said to measure a photon position. Instead, the analysis in the book by Mandel & Wold shows that the clicks in the photodetector are produced by the photodetector already for a classical external e/m radiation field, showing that photodetection is a random measurement of the intensity of the incident radiation field, and nothing else. See the thread http://www.physicsforums.com/showthread.php?t=474537 For alpha particles, the corresponding analysi analysis is given in Mott's 1929 paper (reprinted in pp.129134 in: Wheeler & Zurek, Quantum theory and measurement, Princeton 1983). He shows that the tracks formed in a cloud chamber are already produced by the cloud chamber in a classical external radial charged field  in which case the quantum system considered does not contain an alphaparticle at all. Thus the tracks cannot be said to measure a particle position. Instead they form a random measurement of the intensity and direction of the incident charged field, and nothing else. 


#18
Mar1411, 05:41 AM

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