On 2/05/2016 1:31 pm, Jesse Mazer wrote:
On Sun, May 1, 2016 at 8:49 PM, Bruce Kellett
<bhkell...@optusnet.com.au <mailto:bhkell...@optusnet.com.au>> wrote:
On 2/05/2016 7:52 am, Jesse Mazer wrote:
On Fri, Apr 29, 2016 at 8:32 PM, Bruce Kellett
<bhkell...@optusnet.com.au <mailto:bhkell...@optusnet.com.au>>
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 only have access to the first edition -- this must refer to a later
paper of Bell's.
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.
I disagree, physicists generally only use informal definitions if it's
obvious they could be formalized, or if they are *implied* by some
more precise technical definition (the looser definition you mention
above would be implied by the more precise one I mentioned, *if* one
assumes there is a unique truth about the setting at b and the
measurement A).
No, I disagree. The setting *b* has no effect on what happens at a
remote location is sufficiently precise to encapsulate exactly what
physicists mean by locality. In quantum field theory, this is
generalized to the notion of local causality, which is the statement
that the commutators of all spacelike separate variables vanish -- as
you mention below. If quantum mechanics is complete, then the current
quantum state contains all the information about the system that is
either available or relevant. Sure, if you include hidden variables,
then you are saying that QM as currently formulated is incomplete. That
may be the case, but even so, the given definition of locality still
holds -- it is about FTL propagation of information, nothing else.
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.
There are no hidden variables in the MWI (though the definition of
locality should be general enough to cover theories with hidden
variables as well as ones with no hidden variables, since Bell's
theorem is meant to rule out local realist theories of either type).
The "quantum state as written" does not give any definite outcomes of
measurements, only a set of amplitudes on different eigenvectors
associated with particular eigenvalues, which are understood as
possible measurement results.
True, but not relevant for these purposes. I am not ruling out an
Everettian interpretation of the state vector -- my definition of
locality simply rules out faster than light (FTL) transfer of
information. Given the standard quantum treatment of the entangled
singlet state, non-locality is unavoidable. That does not mean that
there is actually a physical transfer of particles or waves FTL, it
simply means that the state is a unity, and changing one part changes
the whole state. That is the nature of quantum non-locality -- it does
not have a local explanation, even a FTL explanation.
And if you just want the amplitudes for locally-measurable quantities
in a given region of spacetime, in quantum field theory my
understanding is that you can determine this using only knowledge of
amplitudes for locally-measurable quantities in the past light cone of
that region (I don't understand the details, but this is supposed to
have to do with the fact that the commutators for spacelike-separated
points always vanish). Only if you assume there is an objective
"collapse" of the wavefunction at the point of measurement does the
quantum formalism become incompatible with locality in the light cone
sense.
That is not correct. You have not given a local account in MWI either.
Your "light cone sense" of locality would only add something to the
traditional sense if the quantum state were not a complete description
of the system. In other words, a hidden variable theory.
Bruce
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