On Friday, April 13, 2018 at 12:48:11 PM UTC, Bruce wrote: > > From: <[email protected] <javascript:>> > > 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* > > > It might be easier to understand if I give some equations. In the > centre-of-mass frame, after the interaction the total momentum in any > direction is zero. Consider just a one-dimensional case. The combined wave > function is: > > |psi> = Sum_i |p_i>|-p_i>, > > where the first ket is particle 1 and the second ket particle 2 and the > sum is over possible momenta. As you say, this is a tensor product of > individual particle states. Since there is complete correlation between the > momenta of the separate particles for all possible momenta ('possible' > determined by energy conservation), this state cannot be written as a > simple product of separate states for particles 1 and 2. Hence it is > non-separable. > > It is not hard to see how this comes about -- it is a direct consequence > of momentum conservation. And the non-locality comes about because a > measurement on particle 1 tells you the momentum of particle 2, no matter > how far apart the particles are. > > Come on Alan. This is not really so hard, you know. > > *But since the momentum of either particle doesn't pre-exist the > measurement, there is a FTL influence, which IS hard to understand. In > fact, I doubt anyone does understand it. AG * >
> 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.
