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? AGAs 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? AGThe 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 packetand you're treating the interaction as a scattering problem where EMand gravity are not involved, but rather as a "mechanical" interactionwhere momentum is preserved. If the particles become entangled due tothe interaction, and are now not separable, what exactly does "notseparable" 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.`

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