On Mon, Apr 25, 2016 at 10:16 PM, Bruce Kellett <bhkell...@optusnet.com.au> wrote:
> On 26/04/2016 5:52 am, Jesse Mazer wrote: > > On Mon, Apr 25, 2016 at 2:58 AM, Bruce Kellett <bhkell...@optusnet.com.au> > wrote: > >> >> >> I think you may have missed a salient feature of my little story about >> mismatching. The point to which I wish to draw attention is that Alice and >> Bob do not know that they are in an impossible world until after they have >> compared their experimental notes. In general, in order to do the matching >> in a way that will preserve the quantum correlations, you have to know the >> probabilities of the combined worlds in advance. But these probabilities >> can be calculated only after Alice and Bob exchange notes. >> > > What do you mean by "in advance"? There is no need to do any matching at > all until you look at a patch of spacetime that is in the overlap of the > future light cone of Alice's measurement and the future light cone of Bob's > measurement; and at that point, of course information about what detector > setting each one used can be available without violating locality. > > > That, of course, is the issue. How is that information available? It only > becomes available when Alice and Bob exchange notes -- there is no external > indication of that information before that time. > Available to who? The human experimenters? Of course in a general mathematical reformulation of quantum physics it would not actually be necessary for any humans to be aware of some information for it to have a physical effect. Any explicitly local model of physics should work a bit like a cellular automata--imagine a tiny computer at each point in spacetime, which receives information about the values of local variables (Bell's 'beables') at points in the past light cone, and uses them to determine what the value of the local variables at that point should be. The twist here would just be that the local variables at a given point would be a superposition of different possible values--the "copies"--and we can imagine the tiny computer at a given point C may need to do some matching of copies of events at A and copies of events at B in order to determine the set of copies at C. > So you need to know the relative orientations and results in order to >> calculate the probabilities required to get consistent matchings, but these >> probabilities become available only after the matching is complete. In >> other words, the model as proposed is incoherent. >> > > To do the matching, you only need the statistics of the fraction of copies > of Alice that used each setting, and the fraction of copies of Bob that > used each setting, which were determined at the time each one made their > measurement. > > > The matching must be made separately for each copy of Alice and Bob. > Overall statistics are relevant for matchings over repeated runs of the > experiment, but not otherwise. > I don't know what you mean by "made separately for each copy". Say for example a measurement made by Alice at one point in spacetime resulted in 3 copies A1, A2, A3 and a measurement made by Bob at a different point in spacetime resulted in 3 copies B1, B2, B3. And say each copy sends a causal influence (like a photon or some other particle) towards a third point P that lies in the future light cone of both of these points, with the exact nature of this causal influence being slightly different for each copy (for example, A1 might send a photon with a different frequency than A2, and A3 might send a photon with a third different frequency). The computer at P then receives the 3 slightly different copies of a causal influence from Alice, and the 3 slightly different copies of a causal influence from Bob. Then to determine the effect of the causal influences on copies P1,P2,P3 of some physical system located at P, it uses some kind of matching rule; let's say for example that it decides P1 was causally influenced by the matched pair (A1,B2), P2 was influenced by the matched pair (A2,B1), and P3 was influenced by the matched pair (A3,B3). Does this fit your criteria for a matching "made separately for each copy", and if not what part of this account violates it? >> > Well, if they have some ideal perfect shielding that perfectly prevents > any information from getting to a given point in the overlap of the future > light cones, then by definition the probabilities for physical events at > that point in spacetime won't depend on what result each got, so there's no > need to do any matching up of their measurement results at that point. > > > In which case their shielding has thwarted the quantum predictions. > I disagree, but if you think so, please present a specific quantum experiment whose predictions you think would be thwarted by my above claim--for example, perhaps you are imagining something like a three-particle entangled system, with the third particle being measured at this point? Keep in mind that when I talk about "the probabilities for physical events at that point in spacetime" in this context, that's meant to be synonymous with the fraction of copies at this point that show one result for a local measurement vs. another result for that same local measurement. If for example this point contains a third experimenter "Chuck" who is using a stern-gerlach magnet at a particular angle to measure the spin of an electron, then the fraction of Chuck-copies that see spin-up and the fraction that see spin-down can be determined solely from the results of past measurements on this same electron (or the system that emitted it), the fraction won't depend on what measurement angles Alice and Bob chose to use for their own stern-gerlach magnets on other members of an entangled triplet. And as long as there is no local measurement that could tell Chuck what angles had been used by Alice and Bob, there is not as of yet any need for copies of Chuck to be matched to any specific copies of Alice and Bob. There may be some *later* point where local measurements would tell a fourth observer Doug about all three detector settings and the measurements obtained with those settings (and if Doug could learn this info from local measurements, that must mean his region is *not* shielded from particles emitted by Alice and Bob), and at that later point of course the matching does need to be done, but there doesn't need to be at the shielded point where Chuck made his measurement. If you're not convinced, again please provide a specific experiment with specific known probabilities for all combinations of results at different locations, and I can show how a local-copies-plus-matching-when-needed can generate the correct observed statistics. > > Only when there is some physical event C whose local probability depends > on the results of both prior events A and B is there a need to do any > matching--and by definition, such a physical event C must have had some > nonzero probability of getting a "signal" from both measurement-events. > > > By definition!!!!!! Whose definition? That is just unphysical nonsense. > I think you misunderstand what I mean by "local probability", see above about local copies based solely on different possible observable outcomes in that particular region (not facts about distant regions which would be unknowable to anyone in that region). Or if you want an elaboration that doesn't depend on talking about copies, just note that it's provably impossible to use entanglement to transmit messages faster than light, so the probability that a result is observed in one local region of spacetime can't depend on detector settings used for any other measurements made at a spacelike separation. > > > And in the many-worlds interpretation, C would actually be receiving a > cluster of copies of different possible signals whose statistics would > reflect the statistics of different measurement results. > > > In the case of interest, there are only two possible results for each > observer. Multiplying observers and results serves only to obfuscate. > If one is interested in the possibility of a nice frequentist model where probabilities are determined by ratios of numbers of copies, then in any case where the probabilities aren't 50/50, more than two copies will be needed to make it work (for example, if the probability of some event is 1/3, at least 3 copies are needed). Besides, we are also discussing cases where a given experimenter may first make a measurement of their own and then later receive a signal about the results of one or more other experimenters' measurements, in which case there are more than 4 possible experiences at the end. > The real problem is that any theory which enables the gathering of such >> information from the results of environmental decoherence would have to >> involve radically new physics, of a kind that has never been seen before. >> This would have to be universal physics -- we can't just dream up an ad hoc >> theory that applies only to the correlations of entangled particles! >> > > > You still haven't given a clear answer the basic question I've been > persistently asking you about: do you claim there is any airtight argument, > akin to Bell's theorem (or perhaps based on Bell's theorem itself), which > would allow us to prove mathematically it's not *possible* to come up with > a local theory of copies and matching which is "general" in the sense of > reproducing the correct quantum predictions for *arbitrary* experiments? > > > Yes. The argument is the one given. The necessary matching information is > simply not available to any proposed "matching algorithm". This is based on > general physical principles -- nothing more complicated is necessary. > Your verbal argument is not clear to me. Numerical examples are always more clear than words--if you are really confident, you should be able to present an example of a specific experiment where the correct observed statistics would not be reproduced by a local model involving copies and matching. > > > Or are you just skeptical/incredulous based on your personal intuitions > about what such a theory would need to look like, without claiming it's > possible to rule out absolutely in the same way Bell's theorem absolutely > rules out a local realist theory (with the conditions he assumes, which > include unique measurement outcomes and no 'conspiracy' in initial > conditions) that reproduces the statistics of quantum experiments with > entangled particles? > > If the latter, I wonder how you can be so confident that Mark Rubin's > paper at http://arxiv.org/abs/quant-ph/0103079 doesn't qualify as just > this sort of "local theory of copies and matching which generally > reproduces the correct quantum predictions for arbitrary experiments", > given that you said you hadn't actually read through the paper. > > > I have looked more closely at the paper now, and Rubin makes a number of > elementary mistakes, and his argument certainly does not support the > conclusion you wish to draw. > > I quote: > "Measurement-type interactions (20) transform the operators for the states > of awareness of observers into sums of operators, each corresponding to a > distinct state of awareness of the observer, and each labelled with factors > corresponding to the system which the observer measured, as well as to > other systems with which *that* system has previously interacted. These > labels control the subsequent results of measurement involving the labelled > operators, including in particular measurements of correlations between the > states of awareness of observers who have measured particles which have > previously interacted with each other." > > And also: > "When one of the observers performing, say, an EPRB experiment with both > analyzer magnets oriented in the same direction measures the spin of one of > the paired particles, that observer splits into noninteracting copies, each > copy labeled with information corresponding to the state of the observed > particle as well as to the state of the other particle." > > I think the trouble here is that the particle each observer measures may > have interacted with the other, but only *before* the other particle's > interaction with a measuring magnet. So that operator cannot carry > information about that *other* interaction. The second quote seems to > suggest that after A's measurement, A's state carries information about the > state of the particle that went to B for subsequent measurement. > These words don't clearly indicate the interpretation you suggest, I would guess that "the state of the other particle" refers to the quantum state that would be assigned to B given only knowledge of the state of A (as well as knowledge of how they were entangled originally). Anyway, if you want to confidently accuse him of an "elementary mistake", I think you should have something a little more solid than just a speculation about what his ambiguous verbal summary "seems to suggest" to you (and keep in mind this paper did end up making it through peer review, see http://link.springer.com/article/10.1023%2FA%3A1020477902039 ). Jesse -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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