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? What I did find was chapter 8, "Locality in quantum
mechanics: reply to critics" (pp. 63-66). In that chapter, Bell says:
"...now we add the hypothesis of l/ocality/, that the setting *b* of a
particular instrument has no effect on what happens, A, in a remote
region, and likewise that *a* has no effect on B..... With these /local/
forms, it is /not /possible to find functions A and B and a probability
distribution /rho/ which give the correlations <AB> = -*a.b*."
This is an informal statement of exactly the notion of locality or
non-locality that I have been using all along. Your more convoluted
statement may bear some relation to Bell's theory of local beables
(chapter 7 of his book), but the complications are unnecessary -- the
informal definition is the one most physicists would use in practice.
Bruno should be aware that in the discussion you and I had earlier,
you used this sort of qualitative non-standard definition to argue
even if the function giving values of physical variables at each point
*does* depend solely on data from the past light cone, that is
"irrelevant" to deciding whether the theory is "local" in your sense,
presumably because you think there can be qualitative features of the
function itself that can make it "non-local" for reasons unrelated to
the question of what data the function takes as input.
My qualitative definition of non-locality is not non-standard -- it is
the definition frequently used by Bell, and (almost) everyone else. Your
definition seems to want to take account of some sort of hidden
variables, such that the quantum state as written does not contain all
the information about that state. Since the quantum state is taken to be
a complete description, its past history over the whole of its light
cone is truly irrelevant.
Bruce
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