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 -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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