On 2/05/2016 1:31 pm, Jesse Mazer wrote:
On Sun, May 1, 2016 at 8:49 PM, Bruce Kellett
<[email protected] <mailto:[email protected]>> wrote:
On 2/05/2016 7:52 am, Jesse Mazer wrote:
On Fri, Apr 29, 2016 at 8:32 PM, Bruce Kellett
<[email protected] <mailto:[email protected]>>
wrote:
That is a semantic matter. There is a problem if one insists
that "non-local" means the propagation of a real physical
influence (particle of wave) faster-than-light. But
"non-locality" in standard quantum usage means the above --
the entangled state acts as a single physical unit even when
its components are widely separated.
I agree it's a semantic matter, but your description of the
"standard quantum usage" doesn't seem to be accurate. Among
physicists, the standard understanding of "local" and "non-local"
in the context of Bell's theorem and relativity is the one I
cited earlier--a theory is "local" if and only if the function
that gives you the value of local variables at any given point P
in spacetime (or gives the best possible probabilistic prediction
about their values, in the case of a non-deterministic theory)
only requires as input the values of local variables at other
points that lie within P's past light cone, whereas a "non-local"
theory would be one where the function requires knowledge of
variables at a spacelike separation from P to generate the best
possible prediction. As I mentioned, I think this is explained
most clearly in Bell's paper "La nouvelle cuisine" which you can
find in the collection "Speakable and Unspeakable in Quantum
Mechanics", and you can also find it discussed in other sources,
http://arxiv.org/abs/0707.0401 for example. As for "acts as a
single physical unit", that seems like a decidedly
non-mathematical definition which physicists would steer clear
of, unless you can provide a mathematical formalization or what
you mean, or cite a mainstream source that provides one.
I don't see any paper of the title you mention in my copy of
"Speakable and Unspeakable in Quantum Mechanics", could you give a
page number reference?
It's on p. 232 of the 2nd edition, chapter 24.
I have now looked at the paper by Norsen. It seems that the more
detailed definiton of locality does little more than remove the notion
of "superdeterminism" from the equation -- the idea that things in the
common past of A and B could conspire to give rise to the correlations.
Bell rules this out:
“An essential element in the reasoning here is that [aˆ] and [ˆb] are
free variables. One canenvisage then theories in which there just are no
free variables for the polarizer angles to be coupled to. In such
‘superdeterministic’ theories the apparent free will of experimenters,
and any other apparent randomness, would be illusory. Perhaps such a
theory could be both locally causal and in agreement with quantum
mechanical predictions. However I do not expect to see a serious theory
of this kind. I would expect a serious theory to permit ‘deterministic
chaos’ or ‘pseudorandomness’, for complicated subsystems (e.g.
computers) which would provide variables sufficiently free for the
purpose at hand. But I do not have a theorem about that.”7
Quoted from the "La nouvelle cuisine" paper.
Bell is quite clear in his opinion that orthodox QM is not a locally
causal theory:
“The theory requires a perfect correlation of [results] on the two
sides. So specification of the result on one side permits a 100%
confident prediction of the previously totally uncertain result on the
other side. Now in ordinary quantum mechanics there just is nothing but
the wavefunction for calculating probabilities. There is then no
question of making the result on one side redundant on the other by more
fully specifying events in some space-time region 3. We have a violation
of local causality.”7
I don't think there is any case for me to answer - my informal
definition of locality is perfectly adequate for the current purposes.
Bruce
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