On 02 May 2016, at 07:54, Bruce Kellett wrote:
On 2/05/2016 3:15 pm, Jesse Mazer wrote:
On Mon, May 2, 2016 at 12:13 AM, Bruce Kellett <[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.
The projection postulate is replaced by the FPI in Everett, and as I
explained yesterday, it is just self-entanglement, or what I call
often the contagion of superposition:
Alice * (up + down) = Alice * up + Alice * down.
If Alice look, as many times as she want at the up/down state of the
particle, she will find up (and always up) *and* down and always down.
The reason is that once she find up, Alice becomes Alice-up, and that
state does no more factor out the particle state (unless memory
erasure).
Bruno
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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