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What does the probabilistic interpretation of QM claim? 
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#19
Mar1411, 06:05 AM

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#20
Mar1411, 06:25 AM

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Do you deny that the position of an electron can be measured by letting it fall on a photographic plate?



#21
Mar1411, 08:51 AM

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The plate responds to the field strength of the beam containing the electrons: Random atoms are ionized, with a rate proportional to the field strength. This effect that is subsequently magnified and becomes visible. What is measured is therefore the field strength, although because of the randomness involved, the measurement becomes reliable only if the exposure is sufficiently long. 


#22
Mar1411, 09:45 AM

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Mr Neumaier,
I'm also suprised to read such a statement! (That the tracks in a bubble chamber are not a position measurement). I dont deny this immediately, i just want to understand what you're saying. Let me say first how i would define a position measurement. If the incident field/particle has a state Ψ>, and expand this state on the basis of position eigenstates, then i would call a position measurement something that would make the wavefunction of the particle in the position representation "gather" around a point. So that, we will be able to say that it was here, in that box, and not in the andromeda galaxy. Knowing that the field/particle is located in a subregion of space, i think defines a position measurement. When charged fields/particles interact with the bubble chamber we see a trajectory. This trajectory has dimension, for example 0.5x0.5 mm^2 and that defines a subregion of space. I agree that what we see is the effect of the interaction of the particle with the atoms of the liquid, but there can be an interaction only if the paticle's wavefunction is nonzero at the point of the interaction with an atom. The fact that we see only a small trajectory to my mind means that the wavefunction of the particle is nonzero only in that subregion of space. It doesnt interact with the rest of the chamber, and its not in my house either. So, that fits my definition of position measurement, the wavefunction is 'gathered' in a subregion of space. Am i wrong? John 


#23
Mar1411, 09:59 AM

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On Wigner's nogo theorem for exact measurement:



#24
Mar1411, 10:43 AM

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The position is of course a field label, since the quantum field is essentially the position version of momentum mode creation operators. But why does that imply that the position of an electron cannot be measured? As far as I know, the fact that momentum is a label of the creation operators for momentum modes does not imply that the momentum of an electron cannot be measured, so what's the difference? 


#25
Mar1411, 10:46 AM

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In my opinion, we should first define what we mean by a 'position measurement' and then see if the tracks in a bubble chamber, for example, qualify.



#26
Mar1411, 10:48 AM

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Things start to get semiclassical (where the particle concept begins to be applicable) only when field concentrations are so large that their density peaks at reasonably welldefined locations in phase space. At this point, these peaks behave like particles, and position and momentum of the peak behaves approximately classically. 


#27
Mar1411, 10:50 AM

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#28
Mar1411, 10:56 AM

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#29
Mar1411, 11:01 AM

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#30
Mar1411, 11:16 AM

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That's why information about microsystems is always collected via scattering experiments described by the Smatrix, which connects asymptotic preparation at time t=inf with asymptotic measurement at time t=+inf. 


#31
Mar1411, 11:31 AM

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The problem with this is that there is no known mechanism for causing the collapse. (Decoherence reduces the pure state to a mixture, but we don't observe a mixture of tracks  only a single one. This accounts correctly for the longterm average, but not of the collapse at each single instance.) The quantum field picture doesn't need to assume a collapse; ordinary randomness is enough. 


#32
Mar1411, 03:19 PM

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You would possibly object that the Fock space is not valid for interacting particles. But this has no relevance, because we've been discussing the measurements of position of a single electron, which is not interacting with anything. Another point is that refusing the measurability of positions you are are not saving yourself from the "weird" quantum collapse. You've mentioned elsewhere that the momentumspace wavefunction [tex] \psi(p) [/tex] does have a measurable probabilistic interpretation. So, it does require a collapse. This time in the momentum space. If I understand correctly, your position is that the blackened grain of photoemulsion or the formed bubble is not a proof that the particle really hit that spot. You invoke a (rather strange, in my opinion) detection theory from Mandel & Wolf, where they represent the particle by an extended continuous field. Then creation of the local photographic image or a small bubble is "explained" by a sequence of nontrivial condensation events happening in the bulk of the detector. These events require migration of charge to macroscopic distances, entanglement, and other complicated and not fully explained things. If I understand correctly, your motivation for applying these nontrivial models of particle detection is to avoid using the quantummechanical wave function collapse. So, you replace the collapse with some chaotic and yet mysteriously choreographed (condensation of the originally distributed particle energy at one fixed but random point) processes inside the macroscopic detector. Eugene. 


#33
Mar1411, 09:37 PM

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tracks by charged particles) in more detail... There's an extended treatment in Schiff's textbook, pp335339. He uses 2ndorder perturbation theory to consider the probability of a fast electron participating in an ionizing interaction with the electrons in two separate atoms. The result is that the probability is very small unless the atoms are on a line parallel to the momentum of the incident electron (approximated as an incident plane wave field). Thus, Mandel & Wolf are not the only ones who treat the subject in this more careful way. 


#34
Mar1511, 01:39 AM

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I agree that some aspects of particle detection can be explained by Mandel & Wolf type arguments. However, there are situations, where these arguments fail completely. I think the most spectacular failure is related to electrons registered by a photographic plate. If you describe the incident electron by a plane wave or other continuous charge density field, you will have a hard time to explain how this distributed charge density condenses to a single location of one emulsion grain. I think it is well established that after "observation" the entire electron charge is located in the neighborhood of the blackened emulsion grain. Apparently, there should be a mechanism by which the distributed charge density condenses to a point and overcomes a strong Coulomb repulsion in the process. This doesn't look plausible even from the point of view of energy conservation. Eugene. 


#35
Mar1511, 06:58 AM

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#36
Mar1511, 11:22 AM

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Nevertheless, even in a track, one only has a measurement of the projection of the position on the plane transversal to the momentum. But before the detector is reached, there is just a radially expanding quantum field for each particle kind involved in the decay (before and after), and Mott's analysis applies. The secondary bubble traces start at random positions along the track, for the same reason that the primary trace start at a random position anywhere at the surface of the detector where the field density is large enough and continues inside the detector. 


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