On 18 Apr 2016, at 09:45, Bruce Kellett wrote:
On 18/04/2016 5:00 pm, Jesse Mazer wrote:
On Mon, Apr 18, 2016 at 1:37 AM, Bruce Kellett <[email protected]
> wrote:
On 18/04/2016 2:53 pm, Jesse Mazer wrote:
On Sun, Apr 17, 2016 at 9:19 PM, Bruce Kellett <[email protected]
> wrote:
On 18/04/2016 10:11 am, Jesse Mazer wrote:
On Sun, Apr 17, 2016 at 7:34 PM, Bruce Kellett <[email protected]
> wrote:
The future light cones of the observers will overlap at a time
determined by their initial separation, regardless of whether
they send signals to each other or not.
Of course, I never meant to suggest otherwise. Imagining a
central observer who receives messages about each experiment was
just conceptually simpler than imagining an arbitrary system that
is affected in some unspecified way by each experimenter's
results along with every other part of that system's past light
cone. But you certainly
don't *need* to use that particular example.
The issue is to find a local explanation of the correlations:
appealing to some arbitrary system that is affected in some
unspecified way. But my example shows that no exchange of
information after the separate worlds of the two experimenters
have fully decohered can ever explain the quantum correlations.
Why do you think it shows that? Does "explain" mean something more
than giving a mathematical model that generates the correct
correlations, or is that sufficient?
Have you not understood my argument? The specified experiment
results in four possible combinations of results: |+>|+'>, |+>|-'>,
|->|+'>, and |->|-'>. It is relatively easy to show, either by
looking at special cases, or by consideration of a repeated
sequence of such experiments, that the probabilities are different
for each of the four sets of results. The differences in
probability depend only on the relative orientations of the
measuring magnets. Conveying this angle information after the
experiment has been completed, and each of the measurements has
totally decohered, cannot explain these correlations.
What is required is an account of how these correlations can arise
before A and B speak to each other, because once they have their
results in hand, it may be weeks before they actually communicate.
Rubin's argument (following from Deutsch) does not achieve this.
But as I said, you can achieve it if there is no fact of the matter
about *both* results except in the overlap region of the future
light cone of both measurements, where a single localized system
may be causally influenced by both measurements (see below for more
on what I mean by this if you're unclear).
This so-called "matching up" is pure fantasy. Who does this
matching? If the central umpire is to do the matching, he has to
have the power to eliminate cases that disagree with the quantum
prediction. Who has that power?
The laws of physics would do the matching in some well-defined
mathematical way.
I agree that the laws of physics will 'prevent' the formation of
any worlds in which the laws of physics are violated. That is not
the issue. The issue is: how do the laws of physics act in order
to achieve this. Do they act locally or non-locally? If they act
locally, then you are required to provided the local mechanism
whereby they so act. You are not doing this at the moment.
Similar to my question above, what do you mean by "mechanism" ? Do
you mean something more than simply "mathematical rule that gives
you the set of possible outcomes (with associated probabilities or
at least probability amplitudes) at each local region of
spacetime, given only the set of possible outcomes at regions in
the past light cone"?
The mathematical rule that gives the differing probabilities for
each outcome depending on the relative angle of the magnets is just
quantum mechanics. But that is intrinsically non-local
I specified that I was talking about a local mathematical rule--I
said the rule would give out the outcomes at one
location in spacetime "given only the set of possible outcomes at
regions in the past light cone". Did you miss that part, or do you
disagree that if I mathematically determine the state of some
region of spacetime using *only* information about the states of
regions in the past light cone, that is by definition a local theory?
The local mathematical rule in this case, say for observer A, is
that measurement on his own local particle with give either |+> or |-
>, with equal probability. It does not matter how many copies you
generate, the statistics remain the same. I am not sure whether your
multiple copies refer to independent repeats of the experiment, or
simply multiple copies of the observer with the result he actually
obtained. The set of outcomes on the past light cone for this
observer is irrelevant for the single measurement that we are
considering. Taking such copies can be local, but the utility
remains to be demonstrated.
You are claiming to have a local account. But I have not yet seen
it. Published attempts fail for the reasons given.
Can you actually follow the detailed math of Rubin's argument in a
step-by-step way, and identify the first step that's an error? Or
are you just saying that your conceptual argument is sufficient to
show that any such attempt is impossible, regardless of the
details? If you're making an impossible-in-principle argument, I
think a simple toy model like the one I described is sufficient to
show your argument must be wrong.
The conceptual argument is sufficient to show that Rubin must fail.
Your toy model makes no impact on my argument.
In this type of toy model, the idea is not to simulate arbitrary
quantum systems with full generality, but just to simulate the
results that will be seen by a set of experimenters at different
locations in space, given that they are running some specific
experiment that is known to violate some Bell inequality (like
measuring the spin of pairs of entangled particles with something
like a Stern-Gerlach device, with each experimenter choosing
randomly which of three possible axes to measure along). For
concreteness you could imagine that each experimenter has a piece
of paper which has written down all the results the experimenter
knows about at that time (obviously they will know about their own
results up till then, and they can also know about
results seen by distant experimenters if there's been time for them
to have received a light signal the other experimenter sent out
communicating their result, in which case the paper can also record
the *correlations* between one of their own past results and
another experimenter's result at the same time).
OK, but the past results are irrelevant here.
Given that this is the type of physical scenario we want to
simulate, I'm specifically talking about a simulation that
continually creates multiple copies of experimenters at each
location, with the computer having a purely local mathematical rule
for determining how many copies of a given simulated experimenter
will have a given set of results written on their own piece of
paper. You could even imagine that the simulation is being run on a
set of networked computers, with each physical computer solely
devoted to simulating multiple copies of a single experimenter at a
single location in space, and the computers are forbidden to
communicate with one another in a way that would be FTL in the
context of the simulated world. My claim is that it's possible to
have a purely local simulation rule of this type that has the
property that if you *randomly* select one of the copies of a given
simulated experimenter at any given moment, the probability that
copy will have a given set of results written on their paper will
match up with the probability the corresponding real-world
experimenter would have recorded the same results, assuming the
real-world experimenter's probabilities are determined by the laws
of quantum mechanics.
So the copies are running separate measurements on the same
particle: so 50% get |+> and 50% get |->. A random selection then
simply reflects these probabilities.
Do you dispute that it would be possible to have a purely local and
algorithmic copy-spawning rule with this property of reproducing
the statistics of the real-world experiment, even knowing the real-
world experiment would violate Bell inequalities? Or would you
acknowledge this could be done but say it's irrelevant to whatever
argument makes you confident Rubin's paper fails to do something
analogous but with more generality? Or do you think that even if my
approach succeeds at doing what I describe above and Rubin's might
succeed in an analogous way, any local mathematical rule that deals
solely with "copies" of systems at each location in space, without
assigning copies at different locations to any common "world", is a
failure as a local "mechanism" or "explanation"?
Even if your local copy model succeeds in doing what you claim, it
cannot reproduce the quantum correlations.
Let me reduce this to simple steps:
1) MWI is an interpretation of QM only. I.e., it reproduces all the
results of QM without adding any additional structure or dynamics.
What do you mean by QM? I am not sure I agree with you. Everett did
not talk about a new intepretation of QM, but about a new formulation
of QM. And he is right in the sense of the logician. Before Everett:
QM was formulated roughly SWE + Collapse + an implicit dualist theory
of mind or of scale (mircro/macro). Everett's QM is SWE, the abandon
of collapse, + a mechanist theory of mind, with the implicit use of
the FPI.
For a logician, if QM (without collapse) is formalized, you get an
"Herbrand minimal model" which contains already all relative state
(like we get them already in the sigma_1 arithmetic with the Mechanist
Hypothesis in the Cognitive Science).
Given the linearity of the tensor product and the evolution, we can
only abstract away the self-superposition, although we would have to
take them into account if we get a quantum brain (and here the SWE
give non ambigous result where a collapse theory has to first make
more precise how the (non local) collapse is made physically.
2) The QM state describing an entangled singlet pair does not refer
to, or depend on, the separation between the particles.
OK. But the singlet state describe an infinity of Bob and Alice with
their spin correlated, yet both of them see their own particles with a
random result, as none of them know in which universe they are. They
know only one thing for sure: their spin are correlated, and remains
so independently of the distance.
3) The quantum calculation of the joint probabilities depends on the
relative orientation between the separate measurements on the
separated particles.
No problem.
4) This quantum calculation is the same for any physical separation,
since the singlet state itself does not depend on the separation.
No problem.
5) The quantum calculation is, therefore, intrinsically non-local
because it does not depend on the separation, which can be
arbitrarily large.
This does not follow. It would be if the state |psi> = (|+>|-> - |->|
+>) would be interpreted by We know that Alice has a particle in
state |+> or in state |-> and Bob the opposite. But the state (|+>|->
- |->|+>) means eaxctly that neother Alice nor Bob know in which
universe they are. It could be one with |+'> or |-'> or whatever.
6) Since MWI does not add anything to standard QM, and standard QM
gives a non-local account of the probabilities we are considering,
any MWI account must also be intrinsically non-local.
Proof?
Don't invoke Bell's theorem, because it assumes Alice and Bob are in
the same reality, where without collapse, the measurement of Bob and
Alice propagate only locally from multiple Alice to mutiple Bob, as
describe by the superposition singlet state (in any base).
If I find some time, I might try to describe this with the density
matrix formalism, which I think can make this more obvious.
One physical reality, and/or hidden variables specifying unqiueness of
state + Violation of Bell's inequality entails non-locality. That is
shown by Bell's inequality violatin.
But without "collapsing" a wave at a distance, the apparent non-
locality comes only from Alice or Bob determining in which universe
they are. There are just no reason they found themsleves in the same
universe. If they can compare the results, it is only after the
contagion of their superposed state with each other, and in that case,
the statistics implies the Bell correlations, without any physical
action at a distance. You need to transform the pure state in some
mixture, before the measurement to get non-locality, but such mixture
are local and different for each Alice and Bob in the superposition
state, so you cannot take them as definite like if Alice or Bob could
know that in advance.
It is "shocking" because it is really the self-multiplication which
explains the apparent non-locality, but then that was also the case
for the apparent indeterminacy.
Put in a different way: when Alice and Bob make their measurement,
they might get result violating the correlation, but that would make
their belonging to different cross-product term of the final
superposition, so they would not been able to compare those forbidden
results.
Bruno
You appear to be disagreeing with step 5 here -- by relying on a non-
standard notion of locality.
Bruce
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