On Friday, April 13, 2018 at 11:02:03 AM UTC, [email protected] wrote: > > > > On Friday, April 13, 2018 at 3:10:52 AM UTC, Bruce wrote: >> >> From: <[email protected]> >> >> >> On Thursday, April 12, 2018 at 11:56:40 PM UTC, Bruce wrote: >>> >>> From: <[email protected]> >>> >>> >>> On Thursday, April 12, 2018 at 10:12:58 PM UTC, [email protected] >>> wrote: >>>> >>>> >>>> On Thursday, April 12, 2018 at 9:26:53 PM UTC, Brent wrote: >>>>> >>>>> >>>>> On 4/12/2018 12:44 PM, [email protected] wrote: >>>>> >>>>> *Let's simplify the model. Instead of a Nitrogen molecule, consider a >>>>> free electron at rest in some frame. Its only degree of freedom is spin >>>>> IIUC. Is it your claim that this electron become entangled with its >>>>> environment via its spin WF, which is a superposition of UP and DN? Does >>>>> this spin WF participate in the entanglement? TIA, AG* >>>>> >>>>> >>>>> The electron's spin dof can only become entangled with the environment >>>>> by an interaction with the environment. >>>>> >>>>> Brent >>>>> >>>> >>>> Does that happen spontaneously, in the absence of a measurement? AG >>>> >>> >>> If entanglement of a system with the environment requires measurement, >>> and if virtually everything in the physical world is entangled with the >>> environment, aka "the world" -- which seems to be the prevailing belief -- >>> what concept of measurement do we need to explain this? AG >>> >>> >>> As has been explained, entanglement is the consequence of any >>> interaction whatsoever. Measurement is just a particular kind of >>> interaction, one that is controlled and monitored, but otherwise not >>> special. >>> >> >> Is it correct to assume that once a system becomes entangled with another >> system, regardless of how it happens the two systems form a relationship >> analogous to the singlet state where non-locality applies between the two >> systems now considered non-separable? That is, does entanglement >> necessarily imply non-locality, a point IIUC which LC made earlier on this >> thread? AG >> >> >> The systems are not necessarily non-separable. In the classical situation >> I outlined below, The balls are separable after the interaction because >> each has a well-defined momentum, even though this might be unknown before >> one ball is measured. The entanglement is sufficient so that one can >> determine the momentum of one by measuring the other, but this is not >> particularly mysterious in the classical case. >> >> The quantum case is different in that the particles do not have definite >> momentum after the interaction -- they are in a superposition of an >> infinite number of different momentum states, so the particles are not >> separable -- it requires both particles to specify the overall state. >> > > *I suppose you mean that each particle is represented as a wave packet and > you're treating the interaction as a scattering problem where EM and > gravity are not involved, but rather as a "mechanical" interaction where > momentum is preserved. If the particles become entangled due to the > interaction, and are now not separable, what exactly does "not separable" > mean in this context and how does it come about? TIA, AG* >
*I think entanglement here means that somehow, through the interaction, the scattering process, the wf of the total system consists of sums of tensor states, each a product of the subsystem states, analogous to the wf of entangled singlet state. Hard to see how this comes about, and its relation to non-locality. TIA, AG* > > > >> I suspect that it is a case like this that Bruno is thinking of when he >> claims that there is no non-locality in Everettian QM. Each possible >> momentum of one of the particles after the interaction is matched by the >> corresponding momentum of the other, given overall momentum conservation. >> Each momentum of the overall superposition would be though to exist in a >> separate world, so that there is no non-locality in the determination of >> one momentum by measuring the other particles -- one is just locating >> oneself in one of the infinity of separate (pseudo-classical) worlds. (This >> does not work, however, because the separate particles are measured >> independently, and generally in different worlds. See below.) >> >> The trouble is that this treatment of elements of the superposition as >> separate classical worlds does not work for the case of spin entanglement >> in the spin singlet case. Prior to any measurement, one could view the >> orientation of the spin axis of each individual spin-half particle as a >> superposition of an infinite number of different spin states, one for each >> possible orientation. These would then be paired with corresponding spin >> states in the same orientation for other particle. One could then view this >> as an infinite number of worlds, in each of which the two particles have >> definite spin orientations. The idea would then be that by selecting a >> measurement orientation for one particle, one is simply selecting the world >> in which one is located. >> >> It sounds as though this would eliminate the non-locality in the same way >> as definite momentum states for each particle eliminates the non-locality >> for the classical billiard balls. The trouble, though, is that the two ends >> of the system are independent, so that while choosing a measurement >> orientation at one end locates you in the world in which that particle is >> spinning along that axis, that does not select the world in which the other >> particle is measured. The measurement of the second particle is, by >> construction, independent of the measurement of the first, so that >> measurement of the second particle locates you in the world in which the >> spin is oriented along the second measurement axis. Since the two >> measurement axes are chose independently, in general the second measurement >> will not be in the world in which the first measurement was made. And since >> the worlds are, by definition, non-interacting and independent, the >> separate results can never be compared in the same world, again, >> contradicting experiment. >> >> The net result of this picture is that there will be no correlation >> between the spin measurement results of the two particles -- each >> measurement was made in a world in which the results are 50/50 for up/down. >> Since there is no interaction between the measurements, they are not made >> in the same world, so they cannot be correlated -- contradicting with >> experimental results. So even if you view the particles in the entangled >> singlet state as defining an infinity of worlds, one for each element of >> the superposition of possible spin axes, you still have non-locality in >> that the experiment shows that the second independent measurement must have >> been made in the *same* world. That requires a non-local influence from one >> measurement to determine the world in which the other measurement is made. >> In fact, this whole analysis in terms of a superposition of worlds >> corresponding to different spin axes is rather silly, because the spin axis >> is not actually set by the measurement. What the orientation of the S-G >> magnet, or the polarizer, determines is the spin component that will be >> measured, not the axis along which the particle is spinning. >> >> Bruce >> >> >> Consider a scattering interaction between two billiard balls. If you >>> know their initial momenta, and you know that momentum is conserved, then >>> because of the entanglement, if you measure the momentum of one particle, >>> you immediately know the momentum of the other, no matter how far away it >>> is (provided there have been no intervening interactions). Entanglement is >>> not just a quantum phenomenon, though quantum entanglement does have some >>> non-classical features. (Such as violating the Bell inequalities.) >>> >>> Bruce >>> >> >> -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
