From: <agrayson2...@gmail.com <mailto:agrayson2...@gmail.com>>

On Friday, April 13, 2018 at 3:10:52 AM UTC, Bruce wrote:

    From: <agrays...@gmail.com>

    On Thursday, April 12, 2018 at 11:56:40 PM UTC, Bruce wrote:

        From: <agrays...@gmail.com>

        On Thursday, April 12, 2018 at 10:12:58 PM UTC,
        agrays...@gmail.com wrote:


            On Thursday, April 12, 2018 at 9:26:53 PM UTC, Brent wrote:


                On 4/12/2018 12:44 PM, agrays...@gmail.com 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*

"Non-separable" means what it says: neither particle that participated in the interaction has a definite quantum state that can be specified without including the other state. That is why measuring one of the particles gives you information about the other, widely separated particle. It comes about from momentum conservation in the interaction. Any interaction involving a conserved quantity (and most interactions are subject to conservation laws) leads to an entanglement. That is why entanglement is ubiquitous. Of course, any particular entanglement becomes diffused through interactions with other particles, so the pure two state entanglement with momentum is fairly short lived. However, particle spin, or the polarization of a photon, is not so easily disturbed, and angular momentum conservation can lead to long-lived entanglements between spin states, such that the spin of neither particle can be specified in isolation, but the combined state of both particles must be considered.

Bruce

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