From: <agrayson2...@gmail.com <mailto:agrayson2...@gmail.com>>
On Friday, April 13, 2018 at 3:10:52 AM UTC, Bruce wrote:
On Thursday, April 12, 2018 at 11:56:40 PM UTC, Bruce wrote:
On Thursday, April 12, 2018 at 10:12:58 PM UTC,
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
Does that happen spontaneously, in the absence of a
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.
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