On 26/04/2016 5:52 am, Jesse Mazer wrote:
On Mon, Apr 25, 2016 at 2:58 AM, Bruce Kellett
<bhkell...@optusnet.com.au <mailto:bhkell...@optusnet.com.au>> wrote:
I think you may have missed a salient feature of my little story
about mismatching. The point to which I wish to draw attention is
that Alice and Bob do not know that they are in an impossible
world until after they have compared their experimental notes. In
general, in order to do the matching in a way that will preserve
the quantum correlations, you have to know the probabilities of
the combined worlds in advance. But these probabilities can be
calculated only after Alice and Bob exchange notes.
What do you mean by "in advance"? There is no need to do any matching
at all until you look at a patch of spacetime that is in the overlap
of the future light cone of Alice's measurement and the future light
cone of Bob's measurement; and at that point, of course information
about what detector setting each one used can be available without
violating locality.
That, of course, is the issue. How is that information available? It
only becomes available when Alice and Bob exchange notes -- there is no
external indication of that information before that time.
So you need to know the relative orientations and results in order
to calculate the probabilities required to get consistent
matchings, but these probabilities become available only after the
matching is complete. In other words, the model as proposed is
incoherent.
To do the matching, you only need the statistics of the fraction of
copies of Alice that used each setting, and the fraction of copies of
Bob that used each setting, which were determined at the time each one
made their measurement.
The matching must be made separately for each copy of Alice and Bob.
Overall statistics are relevant for matchings over repeated runs of the
experiment, but not otherwise.
These fractions can depend arbitrarily on what rule each one used to
pick their setting--for example, Alice could have used a deterministic
pseudorandom algorithm in which case all copies of Alice will have
chosen the same detector setting, or she could have used some
independent quantum experiment (say, one involving radioactive decay)
to choose her setting randomly with whatever probabilities she wanted,
like 1/19 chance of setting 1, 5/19 chance of setting 2, and 13/19
chance of setting 3, in which case those will be the fraction of
copies of Alice that chose each of those settings. Regardless of what
the fractions were for each of Alice and Bob individually, once you
reach the first point in spacetime where the future light cones of
their measurements overlap, that point *can* have access to each one's
statistics without locality (though it doesn't necessarily have to,
see below), and given that information
If that information is available. But in general it is not.
it's always possible to match them in a one-to-one way that gives the
correct quantum statistics. Do you disagree with this, and if so which
point?
Again, Alice and Bob might try to thwart such a scenario by
careful shielding of their apparatus and not communicating with
anyone. Once more, I don't think quantum mechanics can be stymied
by silence and lead shielding.
Well, if they have some ideal perfect shielding that perfectly
prevents any information from getting to a given point in the overlap
of the future light cones, then by definition the probabilities for
physical events at that point in spacetime won't depend on what result
each got, so there's no need to do any matching up of their
measurement results at that point.
In which case their shielding has thwarted the quantum predictions. I
give you odds of 10,000,000 to 1 that that does not happen -- the
correlations predicted by QM will be observed whatever shielding
precautions are taken
Similarly, in the idealized Schroedinger's cat thought-experiment
where the inside of the box is perfectly shielded from leaking any
information to the outside, there is no need to match up copies of the
experimenter outside with copies of the cat inside, even if the
experimenter is in the future light cone of the event of the cat
having been saved/killed.
Schroedinger's cat is not a measurement on an entangled system of the
requisite kind.
Only when there is some physical event C whose local probability
depends on the results of both prior events A and B is there a need to
do any matching--and by definition, such a physical event C must have
had some nonzero probability of getting a "signal" from both
measurement-events.
By definition!!!!!! Whose definition? That is just unphysical nonsense.
And in the many-worlds interpretation, C would actually be receiving a
cluster of copies of different possible signals whose statistics would
reflect the statistics of different measurement results.
In the case of interest, there are only two possible results for each
observer. Multiplying observers and results serves only to obfuscate.
The real problem is that any theory which enables the gathering of
such information from the results of environmental decoherence
would have to involve radically new physics, of a kind that has
never been seen before. This would have to be universal physics --
we can't just dream up an ad hoc theory that applies only to the
correlations of entangled particles!
You still haven't given a clear answer the basic question I've been
persistently asking you about: do you claim there is any airtight
argument, akin to Bell's theorem (or perhaps based on Bell's theorem
itself), which would allow us to prove mathematically it's not
*possible* to come up with a local theory of copies and matching which
is "general" in the sense of reproducing the correct quantum
predictions for *arbitrary* experiments?
Yes. The argument is the one given. The necessary matching information
is simply not available to any proposed "matching algorithm". This is
based on general physical principles -- nothing more complicated is
necessary.
Or are you just skeptical/incredulous based on your personal
intuitions about what such a theory would need to look like, without
claiming it's possible to rule out absolutely in the same way Bell's
theorem absolutely rules out a local realist theory (with the
conditions he assumes, which include unique measurement outcomes and
no 'conspiracy' in initial conditions) that reproduces the statistics
of quantum experiments with entangled particles?
If the latter, I wonder how you can be so confident that Mark Rubin's
paper at http://arxiv.org/abs/quant-ph/0103079 doesn't qualify as just
this sort of "local theory of copies and matching which generally
reproduces the correct quantum predictions for arbitrary experiments",
given that you said you hadn't actually read through the paper.
I have looked more closely at the paper now, and Rubin makes a number of
elementary mistakes, and his argument certainly does not support the
conclusion you wish to draw.
I quote:
"Measurement-type interactions (20) transform the operators for the
states of awareness of observers into sums of operators, each
corresponding to a distinct state of awareness of the observer, and each
labelled with factors corresponding to the system which the observer
measured, as well as to other systems with which /that/ system has
previously interacted. These labels control the subsequent results of
measurement involving the labelled operators, including in particular
measurements of correlations between the states of awareness of
observers who have measured particles which have previously interacted
with each other."
And also:
"When one of the observers performing, say, an EPRB experiment with both
analyzer magnets oriented in the same direction measures the spin of one
of the paired particles, that observer splits into noninteracting
copies, each copy labeled with information corresponding to the state of
the observed particle as well as to the state of the other particle."
I think the trouble here is that the particle each observer measures may
have interacted with the other, but only /before/ the other particle's
interaction with a measuring magnet. So that operator cannot carry
information about that /other/ interaction. The second quote seems to
suggest that after A's measurement, A's state carries information about
the state of the particle that went to B for subsequent measurement.
That might well be the case -- if A measures
|psi> = (|+>|-> -|->|+>)/sqrt(2)
and gets |+>, it follows that only the |-> part remains for B to measure
(|-> in A's orientation, that is). But that is not sufficient. B
measures at some arbitrary angle at a spacelike separation from A's
measurement, so no matter what piece of the singlet state is left after
A's measurement, that cannot get to B at sub-light speeds before B makes
his measurement at some independent angle. So simply knowing from A's
measurement that |-> went to B is of no help in determining the joint
probabilities. Spacelike separations are the reason this experiment is
said to demonstrate non-locality, after all. And Rubin's argument
appears to have simply overlooked this crucial fact.
My other comment stand.
Bruce
Again, if you haven't read through it because you lack the expertise
to evaluate the mathematical details, then I'm in the same boat, so I
can't definitely claim it *does* given an example of a mathematical
formulation of QM with the above properties, I can only note that it
sure *sounds* like it from the descriptions of the model that appear
in the paper. For example, from the abstract:
'Measurement-type interactions lead, not to many worlds but, rather,
to many local copies of experimental systems and the observers who
measure their properties. Transformations of the Heisenberg-picture
operators corresponding to the properties of these systems and
observers, induced by measurement interactions, "label" each copy and
provide the mechanism which, e.g., ensures that each copy of one of
the observers in an EPRB or GHZM experiment will only interact with
the "correct" copy of the other observer(s). The conceptual problem of
nonlocality is thus replaced with a conceptual problem of
proliferating labels, as correlated systems and observers undergo
measurement-type interactions with newly-encountered objects and
instruments'
Whatever the nature of this new theory, it would by in addition to
quantum mechanics, so you will not have solved the problem of
non-locality in quantum mechanics, you will have abandoned quantum
mechanics in favour of your new theory.
It wouldn't be *in addition to quantum mechanics" as a physical theory
if it made identical predictions about all empirically measurable
results, see my last message with the comment from Kip Thorne about
the difference between physical claims and philosophical ones. And the
central question I ask you to answer above does specify that I'm
asking whether you can rule out the possibility of a mathematical
model involving local copies and matching that gives rise to
predictions about arbitrary measurable results that are identical to
those of existing formulations of QM (and as I pointed out in my last
message, there are already several mathematically distinct
formulations of QM, like the 'Schroedinger picture' vs. the
'Heisenberg picture', that are considered different formulations of
the same theory, not distinct theories).
Jesse
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