On 02 May 2016, at 06:13, Bruce Kellett wrote:
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
> 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
> 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.
It is not in my book "speakable and unspeakable", but it is in my book
" John S. Bell on The Foundations of Quantum Mechanics". edited by M.
Bell, K. Gottfried, & M. Veltman, page 216 (published by World
Scientific 2001, published originally in 1990).
It seems to me that his argument that QM cannot be embedded in a local
close theory relies on the assumption of definite unique outcomes for
the measurement, instead of the Everett FPI. But I just glanced to it,
and I will reread it.
Bruno
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 locality, 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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