On Wed, Apr 20, 2016 at 7:51 PM, Bruce Kellett <[email protected]> wrote:
> On 21/04/2016 1:34 am, Jesse Mazer wrote: > > On Tue, Apr 19, 2016 at 8:54 PM, Bruce Kellett <[email protected]> > wrote: > >> So, the fact that these simulated results were supposed to have come from >> an entangled singlet pair has not been used anywhere in your simulation. It >> has only ever been used to link the copies of Alice and Bob, the statistics >> that they observe come entirely from what you happen to put in you >> accumulator for each setting of the relative orientations. >> > > Saying the idea of a singlet pair "has not been used anywhere in your > simulation" and then saying it has "been used to link the copies of Alice > and Bob" seems like a contradiction--isn't the linking itself part of the > simulation? > > No, there is no contradiction. You have used the fact that they are > measuring parts of an entangled system only to link the sets of results. > Nowhere have you used the quantum properties of the entangled singlet pair > in the simulation to calculate the probabilities: you have imposed those > probabilities from outside by fiat. > Sure, it's a toy model so I just tailor it to give the correct statistics for a single type of quantum experiment. But if I were to try to do the same thing in a scheme where there *weren't* multiple copies of Alice and Bob, so that each had to get a unique result *at the place and time they make a measurement* (not just later when they compare results), then Bell's theorem absolutely rules out doing this in any classical setup that respects locality, even toy models. So, the toy model is just mean to illustrate the principle that Bell's theorem isn't applicable to situations where measurements don't yield unique outcomes but just yield a bunch of different copies of a system at a given location in space at a given time. Once you accept this general principle, you can see that Bell's theorem doesn't offer any fundamental obstacle to reformulating the general laws of quantum mechanics in a way that yields the same predictions about *all* observations using purely local equations, of the kind that could be simulated on a computer where you have a bunch of separate computers calculating how physical variables are evolving in a confined region of space, and each computer can only get data from other computers representing neighboring regions, in a locality-respecting way. As I said, my reading of the non-mathematical parts of Mark Rubin's paper suggests that the paper is coming up with exactly such a model, albeit one that is only equivalent to a non-relativistic quantum field theory (perhaps the math of doing it for a relativistic field theory would be more difficult). You seem to be saying this is impossible in principle, and you're confident enough of this to dismiss the possibility Rubin's paper has done this without apparently understanding the mathematical details either. So, given what I said above, should I take this to mean you think you have an argument for the impossibility which is entirely independent of Bell's theorem? If so you could you try to spell it out in a more detailed, step-by-step way? > No, I am simulating the system as it stands after Alice and Bob have > communicated, written their results on the tokens, and put them in the > appropriate urns. All completely local. > But then you are not simulating the observations each one gets at arbitrary times in a local way (the condition I mentioned earlier about all results being generated by the computers in realtime), your method is limited to a specific time after they have communicated. Bell's theorem is specifically about the impossibility of a local theory in which the results of each measurement must be generated when neither measurement result (or choice of detector setting) can have had a causal influence on the other (a spacelike separation in the context of relativity), and getting the correct statistics on the joint results. My toy model is meant to illustrate the point that Bell's theorem depends on the implicit assumption that each measurement yields a single unique result, and if you relax this and allow multiple copies, then you can have a theory which is still local and still generates the initial measurements at a spacelike separation, and also yields the correct joint outcomes for a randomly-selected copy of the experimenter once there's been time for the results to be communicated. > > Since you are accumulating joint results according to the statistics that > you have calculated on the basis of standard quantum mechanics, completely > independently of the properties of the actual singlets states that Alice > and Bob measure, my example is exactly equivalent to yours. > My example is relevant to Bell's theorem for the above reasons, while yours is not. Again, Bell is restricting his attention to the class of local theories in which it's true in *every* local patch of spacetime that the values of the "beables" in that patch (which should include any physically measurable result that is localized in space and time) are influenced only by the beables at points in the past lightcone of the patch. And as long as you add the implicit assumption that measurements yield unique outcomes, the theorem does prove it's impossible to have a local theory that can generate the correct observations on *arbitrary* local patches of spacetime (as opposed to only considering a pair of patches where the experimenters have already communicated with their results to one another, in which case it's trivial to impose the right statistics just for those patches using a local theory). But if you allow beables in each patch to include multiple parallel versions of physical systems inside the patch, then the model I suggest would have this feature of giving the correct observational results (for this one particular experiment) on *arbitrary* patches, while yours has no way of generating the results in the patches where each experimenter makes their own individual measurement prior to learning about the other's measurement. > > But that is precisely what you toy model does. It has absolutely no >> connection with EPR or real experiments. One could generate any arbitrary >> set of statistics to satisfy any theory whatsoever by this method. You have >> demonstrated absolutely nothing about the locality or otherwise of EPR. >> > > > Would you agree that in my toy model the results at each location can be > generated in realtime (each experimenter finds out their own result before > finding out the other one's result, and before they have any way of knowing > what detector setting the other one used), and in a local way (the rule > that generates a result that appears at a particular position and time > doesn't depend on anything outside the past light cone of that event), and > that the subjective probabilities for each experimenter match those of the > EPR experiment? > > > No, I don't agree with this. You have not used the quantum properties of > the singlet state in your simulation, so there is no way that you can > reproduce the quantum probabilities. All you can get is repetitions of the > four possibilities (++), (+-), (-+), (--), with equal probabilities. > Are you saying that even if we consider the matching rule used by the computer, the matched results must assign equal probabilities to all combinations regardless of detector settings? If so that's clearly not true, and I provided a numerical example proving it (I can repost if you're not clear on which email in the thread I'm talking about). Or are you ignoring the matching (even though it is clearly part of the rules of the simulation), and just pointing out that if we pick a copy of Alice and a copy of Bob at random (regardless of whether the computer has matched them), we will find all combinations with equal probability? But that would be irrelevant to what is actually experienced by a randomly-selected copy of Alice living inside the simulated world, assuming for the sake of the argument that she is a conscious computer program like a mind upload. 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