Re: Non-locality and MWI

```On Tue, Apr 26, 2016 at 6:45 AM, Bruce Kellett <bhkell...@optusnet.com.au>
wrote:
>
>
> You think that "the state of the other particle" refers to the quantum
> state that would be assigned to B given only knowledge of the state of A
> (as well as knowledge of how they were entangled originally). Actually,
> that is the interpretation I gave the words, except I teased out what that
> actually meant. From the entangled state, given A's state (result, say
> |+>), you would assign a state |-> to B. But this is wrong for spacelike
> separations -- the state B actually measures is exactly the same as the
> state A measured: |psi> = (|+>|-> - |->|+>)/sqrt(2).
>```
```
You use the full state if you just want to generate the total probabilities
for various possible *joint* outcomes. But if you want a conditional
probability of various outcomes *just for B* given knowledge of what
measurement A got, this can be done in QM, in the Schroedinger picture you
could project |psi> onto on eigenstate that corresponds to whatever
definite outcome was measured on A, resulting in a different state vector
for the combined system |psi'> which may lead to different probabilities of
getting various results for B, but which does not assume any knowledge of
what measurement was actually performed on B. I assume something similar is
possible in the Heisenberg picture which Rubin is using, so I was
speculating that he meant something like this when he talked about a label
on one particle which says something about the state of the other particle.

There is also another possibility along the same lines, which is that for
any entangled system in a pure state, you can construct a "reduced density
matrix" for some subsystem, which gives the probabilities of various
outcomes for measurements just on the subsystem alone (and the subsystem
could just be one particle in a multiparticle entangled system). This is
important in the analysis of decoherence, for example, where the approach
apparently involves treating both the subsystem and its environment as
being in a pure state, and then looking at how interactions between
subsystem and environment change the reduced density matrix for the
subsystem.

That is clearly wrong, so the details are irrelevant. If you think like a
> physicist, rather than as a mathematician, you look for the physics of what
> a paper is saying.
>
>
It isn't obviously wrong in my interpretation above, and I think it's
wrongheaded to imagine you can be confident about the interpretation of any
verbal statement by a physicist if you don't have a detailed grasp on the
mathematics of the model the physicist is talking about--if you don't you
may miss possible interpretations, like the ones above that you don't seem
to have considered.

Also, do you plan to respond to the rest of my comment? In particular, do
you think you can come up with any simple numerical examples that show a
local-copies-with-matching model can't correctly reproduce some observed
statistics at a given location if we assume that location has been
"shielded" from any physical influences from Alice or Bob (and assuming
'matching' between copies of Alice and copies of Bob can only be done in
regions that have received measurable physical signals from them), as you
seemed to claim earlier?

Jesse

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