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


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