On Friday, April 13, 2018 at 11:02:03 AM UTC, agrays...@gmail.com wrote:
> 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*

*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

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