On 18/04/2016 5:00 pm, Jesse Mazer wrote:
On Mon, Apr 18, 2016 at 1:37 AM, Bruce Kellett
<[email protected] <mailto:[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] <mailto:[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]
<mailto:[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.
2) The QM state describing an entangled singlet pair does not refer to,
or depend on, the separation between the particles.
3) The quantum calculation of the joint probabilities depends on the
relative orientation between the separate measurements on the separated
particles.
4) This quantum calculation is the same for any physical separation,
since the singlet state itself does not depend on the separation.
5) The quantum calculation is, therefore, intrinsically non-local
because it does not depend on the separation, which can be arbitrarily
large.
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.
You appear to be disagreeing with step 5 here -- by relying on a
non-standard notion of locality.
Bruce
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