From: <[email protected] <mailto:[email protected]>>
On Friday, April 13, 2018 at 11:02:03 AM UTC, [email protected]
<mailto:[email protected]> wrote:
On Friday, April 13, 2018 at 3:10:52 AM UTC, Bruce wrote:
From: <[email protected]>
On Thursday, April 12, 2018 at 11:56:40 PM UTC, Bruce wrote:
From: <[email protected]>
On Thursday, April 12, 2018 at 10:12:58 PM UTC,
[email protected] wrote:
On Thursday, April 12, 2018 at 9:26:53 PM UTC, Brent
wrote:
On 4/12/2018 12:44 PM, [email protected] 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*
It might be easier to understand if I give some equations. In the
centre-of-mass frame, after the interaction the total momentum in any
direction is zero. Consider just a one-dimensional case. The combined
wave function is:
|psi> = Sum_i |p_i>|-p_i>,
where the first ket is particle 1 and the second ket particle 2 and the
sum is over possible momenta. As you say, this is a tensor product of
individual particle states. Since there is complete correlation between
the momenta of the separate particles for all possible momenta
('possible' determined by energy conservation), this state cannot be
written as a simple product of separate states for particles 1 and 2.
Hence it is non-separable.
It is not hard to see how this comes about -- it is a direct consequence
of momentum conservation. And the non-locality comes about because a
measurement on particle 1 tells you the momentum of particle 2, no
matter how far apart the particles are.
Come on Alan. This is not really so hard, you know.
Bruce
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