On 22/04/2016 2:46 pm, Jesse Mazer wrote:
On Thu, Apr 21, 2016 at 11:25 PM, Bruce Kellett
<[email protected] <mailto:[email protected]>> wrote:
On 22/04/2016 12:53 pm, Jesse Mazer wrote:
On Thu, Apr 21, 2016 at 9:49 PM, Bruce Kellett
<[email protected] <mailto:[email protected]>> wrote:
The point here is that some combinations of results are
forbidden. How can this happen?
By the appropriate matching rules for locally-generated copies in
different locations, as in my toy model. There's no reason you
can't have something similar in a more general model, which I
think is exactly what people like Rubin are presenting.
The best I can make of this is that you have some theory that is
not quantum mechanics. Quantum mechanics does not give any such
"matching rules"
It's important to distinguish between theories of physics and the
mathematical models used to express them--a physical theory is defined
entirely by the predictions about observable outcomes, not any
elements of the model that are not directly measurable even in
principle. For example, curved spacetime is not essential to general
relativity as a theory, though it is a feature of the most
commonly-used mathematical model (there is an alternate formulation
that only uses flat spacetime, but has a field defined on this
spacetime which varies the length of rulers and the ticking rate of
clocks at different points in the spacetime, and physicists would
still call this 'general relativity'). Likewise, a state vector in
Hilbert space is not essential to quantum mechanics as a theory. And
if one *could* come up with a model involving "matching rules" that
would be equivalent in its predictions about observable measurement
results as the existing mathematical models, this would merely be a
new mathematical model for the same physical theory.
It would seem that you are not a physicist! What you claim here about
physics is actually quite contentious. It seems to constitute an extreme
form of instrumentalism. If a physical theory is determined only by the
predictions it gives for the results of experiments, I am puzzled by why
you should have such a strong reaction against the notion of
non-locality. The non-local calculations of standard QM give a
completely straightforward mathematical model for calculating
probabilities; a model that is, in the terms of of other physical
theories, phenomenally successful. If your only concern is to get an
instrument to predict experimental results (probabilities), why should
you worry whether the theory is non-local or not? According to you, the
mathematical model has nothing to do with physical reality (whatever
that is). The anti-realist would have no worries about such trivia.
But you are clearly deeply worried about non-locality, which says to me
that you are not a thorough-going instrumentalist after all. So that you
say above about mathematical models being the only concern is all all
just so much hogwash -- you are actually concerned that your physical
theories conform to your own particular set of philosophical prejudices.
That is your concern, but you cannot expect me to share it. I take an
instrumental (or epistemic) view of the wave function of QM. That is to
say, I view it as a mathematical object that can be used to claculate
the probabilities for experimental outcomes, but it is not a real
physical thing in the same sense as chairs and tables, the earth and the
moon, are real physical things. If the wave function is not physical,
then there is no physical collapse when a measurement is made, there is
only a change in our knowledge, and the wave function changes
instantaneously to reflect this change. In just the same way, our
probability function for the outcome of a horse race, or of a lottery,
changes instantaneously once we learn the actual outcome. From this
perspective, MWI is just a ridiculously baroque construction designed to
preserve some persons' realist prejudices that the wave function is a
real physical object, like a chair or a table.
You have landed yourself in a philosophically confused position where
you are both a realist and an instrumentalist about the elements of
quantum theory. I think you should sort out your philosophy before you
attempt to argue any more about physics.
Of course, modern developments in black hole theory and cosmology render
the whole debate about locality otiose. The currently popular theory of
holography is necessarily completely non-local; and in a way that makes
EPR correlations look tame.
So I don't think I will waste more time trying to convince you that the
standard non-local quantum theory is perfectly adequate for the
explanation of all observed phenomena in its domain.
Bruce
If you disagree with any of this, please explain your disagreement.
And if you don't disagree that physics theories are defined solely in
terms of their predictions about measurement results, but you think
there is something intrinsically impossible about the idea that a
mathematical model involving "matching rules" could reproduce these
predictions, please explain the argument, because it clearly can't
just be Bell's theorem.
nor does it give any dynamics whereby such matching could be
effected. So you no longer have an interpretation of quantum
mechanics, you have a different theory. It remains for you to
develop this in a way that is convincing.
But I am not claiming I can definitely present such a model--though as
I said, my *impression* is that Rubin's paper seems to be doing
that--I'm just disputing the idea that you can state with certainty
that no such model is possible, such that you are confident that
Rubin's paper can't contain an example without actually needing to
read and understand it in detail.
Following back the train of information exchange between the
participants, and accepting that worlds, once decohered,
cannot suddenly disappear, it becomes apparent that the zero
probability branches cannot arise because they are forbidden
at the stage when A and B are still at spacelike separations.
So they are forbidden non-locally.
But that clearly isn't true in my model, so there's no reason to
think it *must* be true in more general models that reproduce
arbitrary quantum measurements. In my model *and* in more general
models of the sort that people like Rubin seem to be proposing,
until matching between Alice and Bob has happened there *are* no
"branches" containing facts about both of their results, only a
set of local branches for one region and a different unrelated
set of branches for another region. And once the two sets of
branches can interact, they can be matched up in a way that
creates zero probability of matching up a version of Alice who
got + at zero degrees and a version of Bob who got + at zero degrees.
But your model only reproduces the quantum correlations because
you have put them in by hand. That is not a viable model of physics.
I didn't claim it was, I only claimed it demonstrated that Bell's
theorem does not present any fundamental obstacle to coming up with
such a model. Remember, Bell's theorem too deals only with the
predicted quantum correlations in specific experiments, and the proof
doesn't depend at all on what mathematical theory was used to derive
those predicted correlations.
You claim that there are no branches containing facts about both A
and B until this matching takes place. The rules for this matching
presumably say that one must not match incompatible results. How
is the matching done: does one pick one result, and search about
for a match that does not violate the quantum statistics? You will
have a problem if the basic experiment on each entangled pair is
done at a recorded time. Both branches carry this timing
information, so you can only match pairs that have the same time
stamp. This means that for aligned magnets, you will have to
discard 50% of the possible matches -- giving worlds that simply
vanish for no coherent internal reason.
You don't have to discard any individual copies of Bob or individual
copies of Alice, if that's what you mean--I already gave a numerical
example showing the matching could be done in a one-to-one way between
the independently-generated copies of each, so that however many
copies of Alice got a message like "Bob used detector setting 2 and
got result +", the same number of copies of Bob would have in fact
used detector setting 2 and got result +. Do you disagree that this
sort of one-to-one matching between copies of each experimenter that
were independently generated at a spacelike separation can always
generated the correct statistics for pairs of matched results?
And of course, once you generate a given set of matches, there is no
need to later throw away some of those matched pairs either--if you
think there would be a need to do that, please explain.
Frankly, such matching is absurd, no physical law acts in this way.
I don't think "absurd" is an objection many physicist would find
meaningful, assuming a model was mathematically well-defined and
didn't obviously lead to predictions that conflicted with
observations. And the fact that no prior physics model has worked this
way doesn't seem like a physically meaningful objection either, after
all many successful new mathematical models in physics have had
features that no previous one had (like Einstein's model where gravity
was modeled in terms of geodesics in a curved manifold).
Jesse
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