On 23 Jan 2014, at 01:57, Pierz wrote:
Excellent jessem, thanks. This line from the abstract of the first
paper you cite pretty much summarises the changed understanding of
MWI I was getting at:
Measurement-type interactions lead, not to many worlds but, rather,
to many local copies of experimental systems and the observers who
measure their properties.
OK. Let us define a "universe" or "physical world" by a collection of
events close for interaction. Then the local copies determine a
spreading universe, and we get the usual (I would say) many-worlds
from this.
Some people criticize the MWI, as splitting the "universe" in a non
local instantaneous way, but nothing in QM can justify this.
Bruno
On Thursday, January 23, 2014 3:24:14 AM UTC+11, jessem wrote:
On Tue, Jan 21, 2014 at 10:34 PM, meekerdb <[email protected]>
wrote:
On 1/21/2014 4:50 PM, LizR wrote:
It seems to me that differentiation is local, and spreads slowly,
and that there is always going to be some remerging (but only in
proportion to the chances of entropy reversing). The an atom starts
in a superposition of decayed and non-decayed. Now a cat is in a
superposition of alive and dead. Now an experimenter is in a
superposition of having seen an alive and dead cat... now everyone
who reads "Nature" is in a superposition ... but none of this
affects Jupiter for a long time,
Does it? Suppose there's an electron on Jupiter that was entangled
in a singlet state with an electron on Earth and the electron on
Earth just got it's spin measured? MWI may be able to model this
with a local hidden variable, but in THIS world it looks like FTL
influence - and it can go a lot further than Jupiter, e.g. the CMB.
There's no need even for hidden variables to explain this in a MWI
context, as I understand it. Here's a pair of technical papers on
the subject by David Deutsch:
http://arxiv.org/abs/quant-ph/9906007v2
http://arxiv.org/abs/1109.6223
And a few more papers on locality in (nonrelativistic) quantum field
theory by another many-worlds advocate, Mark Rubin (p. 2 of the
first paper below has a good summary of other work by MWI advocates
on the subject of how locality is preserved):
http://arxiv.org/abs/quant-ph/0103079v2
http://arxiv.org/abs/quant-ph/0204024
http://arxiv.org/abs/0909.2673
I think the basic conceptual explanation is something like this: in
your example of the entangled electrons on Earth and Jupiter, when
an experimenter on Earth measures an electron, the experimenter
locally splits into multiple versions who may see different results
from one another, and likewise with the experimenter on Jupiter. And
there is no need for the universe to decide which version on Earth
will be part of the same "world" as which version on Jupiter until
there has actually been time for a physical message (moving at the
speed of light) to pass from one to the other.
I can illustrate this with a simple toy model. One of the various
Bell inequalities says that if experimenters at each location can
measure spin at three different detector angles, and on every trial
where they choose the same detector angle they always find opposite
spins, then on the subset of trials where they choose two different
detector angles, the probability they get opposite results must be
greater than or equal to 1/3. But in QM it's possible that they do
always get opposite results with the same detector angle, but the
probability they get opposite results when they choose different
angles is only 1/4, which violates this Bell inequality. But now
let's suppose we want to simulate this using a classical computer
simulation, using AI experimenters running on computers on both
Earth and Jupiter (call the AI on Earth "Ellen", and the AI on
Jupiter "Jim"). Suppose each AI uses a pseudorandom algorithm to
decide which choice of the three detector angles they decide to use
on each trial. Unbeknownst to the AIs, though, each time they make a
simulated measurement, the program creates 8 different copies of
that AI, 4 of which get the result "spin-up" for the measurement
axis they chose on that trial, and 4 of which get the result "spin-
down". We can assign the copies numbers to differentiate them--so
Ellen #1 got spin-up, as did Ellen #2-4, and Ellen #5-8 got spin-
down. Likewise Jim #1-4 got spin-up, and #5-8 got spin-down.
After the Ellen on Earth gets her measurement result, she wants to
communicate it with the Jim on Jupiter, so she sends a message which
travels to Jim at the speed of light, telling him both her choice of
detector angle and whether she got spin-up or spin-down at that
angle. But unbeknownst to Ellen and Jim there are actually 8
different versions of each of them, so from our point of view
outside the simulation, we see that what actually gets sent is a
bundle of 8 parallel messages, and when they arrive at Jupiter, the
simulation has some algorithm to assign one of the 8 parallel
messages to each of the 8 parallel versions of Jim. The key is that
the simulation's algorithm can work in such a way that over the
course of many trials, each copy observes statistics that violate
Bell's inequality, even though this is a purely classical simulation
(because Bell's proof assumes a unique measurement result at each
location, which is violated here by all the copies). On trials where
they both chose the same detector angle, the simulation matches up
the messages like this:
Jim #1 (spin-up) gets the message from Ellen #5 (spin-down)
Jim #2 (spin-up) gets the message from Ellen #6 (spin-down)
Jim #3 (spin-up) gets the message from Ellen #7 (spin-down)
Jim #4 (spin-up) gets the message from Ellen #8 (spin-down)
Jim #5 (spin-down) gets the message from Ellen #1 (spin-up)
Jim #6 (spin-down) gets the message from Ellen #2 (spin-up)
Jim #7 (spin-down) gets the message from Ellen #3 (spin-up)
Jim #8 (spin-down) gets the message from Ellen #4 (spin-up)
The above matching ensures that every single copy of Jim gets a
message from Ellen saying she got the opposite spin result. But on
the trials where they chose different detector angles, the
simulation matches up messages like this:
Jim #1 (spin-up) gets the message from Ellen #1 (spin-up)
Jim #2 (spin-up) gets the message from Ellen #2 (spin-up)
Jim #3 (spin-up) gets the message from Ellen #3 (spin-up)
Jim #4 (spin-up) gets the message from Ellen #5 (spin-down)
Jim #5 (spin-down) gets the message from Ellen #4 (spin-up)
Jim #6 (spin-down) gets the message from Ellen #6 (spin-down)
Jim #7 (spin-down) gets the message from Ellen #7 (spin-down)
Jim #8 (spin-down) gets the message from Ellen #8 (spin-down)
This matching ensures that 3/4 of the copies of Jim will see that
Ellen got the same spin as himself, while only 1/4 of the copies of
Jim will see that Ellen got the opposite spin. These are the
statistics that would be seen in QM, the ones that violate the Bell
inequality.
Jesse
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