On 27/04/2016 1:13 am, Jesse Mazer wrote:
On Tue, Apr 26, 2016 at 6:45 AM, Bruce Kellett
<[email protected] <mailto:[email protected]>> 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.
I am well aware of this, and I also thought that was probably what Rubin
had in mind. The problem is that this simply sneaks non-locality in the
back door -- neither Rubin nor you appear to realize this. This is often
the problem I find with these attempts to give a local account of EPR --
non-locality is built in unobtrusively!
That is why I said that, in any strictly local account, if A gets |+>, B
still measures the original |psi>. The measurement by A cannot /locally/
affect the state that B measures (or vice versa). So, in a purely local
account, knowing the state after it has been reduced by A's measurement
is of absolutely no help in knowing what state B measures. Strict
locality means that both A and B independently measure exactly the same
state, and both, independently, have 50% probabilities for either
result. Independence means no correlation! If there is correlation,
there is not independence.
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.
Yes, the reduction of the density matrix by the measurement (or by
decoherence) is exactly what I am talking about above. If A and B are
independent, as they must be in a local account, they both independently
reduce the density matrix, and the reduction by one observer does not
affect the measurement by the other.
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.
I think your arrogant patronizing here is a bit over the top! I have
perfectly well understood the mathematics of Rubin's paper-- that is why
I was confident that the paragraphs I quoted accurately summarized his
detailed arguments and results. The possible interpretations you discuss
above just make the same mistake as Rubin made -- you both build in
non-locality without noticing.
The basic quantum calculation of the probabilities treats the entangled
state |psi> as a unit -- there is no mention of any particular
separation between the two entangled particles, so quantum state
reduction reduces the whole state, non-locally. If this were not the
case, you would not get the traditional cos^2(theta/2) probabilities for
relative angles of theta. Try and derive that result from locally
independent measurements on each of the entangled particles if you
really believe in the possibility of a local account!
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?
No, I have no intention of replying to any of this because it is all
beside the point. If you can't follow the simple physical and conceptual
arguments that I make, numerical examples are not going to help much. If
Alice and Bob are truly local, and fully independent, then no matching
scheme can ever have the necessary information to reproduce the quantum
probabilities -- where do you find the cos^2(theta/2) basis for the
probabilities if they are truly independent?
Bruce
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