On 2/05/2016 3:15 pm, Jesse Mazer wrote:
On Mon, May 2, 2016 at 12:13 AM, Bruce Kellett
<[email protected] <mailto:[email protected]>> wrote:
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.
And if you used full quantum description of the measuring apparatus
and experimenter, and didn't assume any collapse on measurement, then
there would in general be no single "setting b" in the region of
spacetime where one experimenter was choosing a setting, but rather a
superposition of different settings. Do you think your preferred
definition can be meaningfully applied to this case, and if so how?
I do not know what you here mean by "collapse on measurement"? It seems
that you might be confusing a collapse to a single world after
measurement with the projection postulate of standard quantum theory.
The projection postulate is essential if one is to get stable physical
results -- repeated openings of the box in Schrödinger's cat experiments
would result in oscillations between dead and alive cats. This is ruled
out by decoherence -- extended entanglement with the environment is
irreversible, so the result after a completed measurement is that the
system is in the eigenstate corresponding to the observed eigenvalue.
This says nothing about whether or not the other eigenvalues are
observed in the disjoint worlds of the MWI.
It seems, if fact, that whether there is a particular setting of b in
the remote region or not is not really an issue. Bob is measuring the
same entangled pair as Alice, and he only ever has one setting: Alice
may not know this setting until later, but this could scarcely be
called a superposition of different settings -- this is not part of the
standard quantum formalism, even in MWI. To Alice, before she exchanges
notes with Bob, she merely knows that the quantum state of Bob's
particle can be expressed in any number of possible bases, but that does
not mean that there is a superposition over all of these alternative
bases. Try writing such a superposition our in standard form if you need
to convince yourself of this fact.
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.
Without any assumption of "collapse", the *amplitudes* assigned to
local measurements on either member of an entangled pair could be
determined solely from amplitudes on locally-measurable variables in
the past light cone--do you disagree?
No, I don't disagree. But I also don't see the point -- the preparation
of the singlet state is all that can be known about the states that
either Alice or Bob have available for measurement. Addition information
from the past light cone need be considered only if you want to pursue a
"superdeterministic" theory in which A and B are not actually free to
determine their measurement angles.
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.
There are no non-mathematical "explanations" for anything whatsoever
in physics (obviously there can be explanations in words, but these
are understood as shorthand for arguments that could be formalized
mathematically). And in terms of mathematical physics, the
"explanation" for a local physical fact about what's happening in one
point in spacetime is just the mathematical function representing the
"laws of physics" along with whatever initial boundary conditions have
to be fed into the function to generate the prediction about that
local physical fact.
Exactly, and the relevant physical laws to be applied here are the laws
of quantum mechanics operatio=g on the defined singlet state.
If the boundary conditions are all confined to the past light cone, I
would say there is nothing FTL in this mathematical explanation--you
may disagree, but so far you have been unable to provide any alternate
precisely-defined conditions for distinguishing locality from
non-locality, ones which we could still obviously make sense of even
if we didn't assume a unique real-valued measurement setting and
measurement outcome.
I have, several times. Local means the absence of superluminal
influences -- Commutators of all variables vanish for spacelike
separations. Nothing more is necessary.
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.
What does "account" mean? A mathematical description, or a conceptual
explanation in the English language?
An "account" means applying the known laws of physics to a well-defined
initial state. This can be either mathematical or descriptive - these
are not necessarily incompatible.
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.
I have no idea why you think this, and you haven't made any argument
for it. Your traditional sense seems to be simply ill-defined if we
assume a superposition of different detecter settings in a single
location in spacetime,
Any such notion is incompatible with the laws of quantum mechanics. Just
write me out a superposition in an infinity of different bases
simultaneously.....
and a superposition of measurement results at another location,
whereas the "light-cone sense" is still well-defined here since it can
cover local variables of any kind, including a bundle of complex
amplitudes assigned to different possible results. So, unless you
think your traditional sense *can* handle this case, it seems the
light cone definition is more broad and useful here, even though there
are no hidden variables being discussed.
Ruling out (local) hidden variables was not my intention - that is the
work of Bell's theorem. Your broader sense of locality is not actually
doing any work here. It seems that Bell discussed this simply to obtain
more precision, and to give sense to the notion of "superdeterministic"
theories. Although 't Hooft may favour such theories, I don't, and I
don't think think you do either.
Bruce
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