On Mon, May 2, 2016 at 12:13 AM, Bruce Kellett <[email protected]> wrote:
> > No, I disagree. The setting *b* has no effect on what happens at a remote > location is sufficiently precise to encapsulate exactly what physicists > mean by locality. In quantum field theory, this is generalized to the > notion of local causality, which is the statement that the commutators of > all spacelike separate variables vanish -- as you mention below. > And if you used full quantum description of the measuring apparatus and experimenter, and didn't assume any collapse on measurement, then there would in general be no single "setting b" in the region of spacetime where one experimenter was choosing a setting, but rather a superposition of different settings. Do you think your preferred definition can be meaningfully applied to this case, and if so how? > > My qualitative definition of non-locality is not non-standard -- it is the >> definition frequently used by Bell, and (almost) everyone else. Your >> definition seems to want to take account of some sort of hidden variables, >> such that the quantum state as written does not contain all the information >> about that state. >> > > > There are no hidden variables in the MWI (though the definition of > locality should be general enough to cover theories with hidden variables > as well as ones with no hidden variables, since Bell's theorem is meant to > rule out local realist theories of either type). The "quantum state as > written" does not give any definite outcomes of measurements, only a set of > amplitudes on different eigenvectors associated with particular > eigenvalues, which are understood as possible measurement results. > > > True, but not relevant for these purposes. I am not ruling out an > Everettian interpretation of the state vector -- my definition of locality > simply rules out faster than light (FTL) transfer of information. Given the > standard quantum treatment of the entangled singlet state, non-locality is > unavoidable. > Without any assumption of "collapse", the *amplitudes* assigned to local measurements on either member of an entangled pair could be determined solely from amplitudes on locally-measurable variables in the past light cone--do you disagree? > That does not mean that there is actually a physical transfer of particles > or waves FTL, it simply means that the state is a unity, and changing one > part changes the whole state. That is the nature of quantum non-locality -- > it does not have a local explanation, even a FTL explanation. > There are no non-mathematical "explanations" for anything whatsoever in physics (obviously there can be explanations in words, but these are understood as shorthand for arguments that could be formalized mathematically). And in terms of mathematical physics, the "explanation" for a local physical fact about what's happening in one point in spacetime is just the mathematical function representing the "laws of physics" along with whatever initial boundary conditions have to be fed into the function to generate the prediction about that local physical fact. If the boundary conditions are all confined to the past light cone, I would say there is nothing FTL in this mathematical explanation--you may disagree, but so far you have been unable to provide any alternate precisely-defined conditions for distinguishing locality from non-locality, ones which we could still obviously make sense of even if we didn't assume a unique real-valued measurement setting and measurement outcome. > And if you just want the amplitudes for locally-measurable quantities in a > given region of spacetime, in quantum field theory my understanding is that > you can determine this using only knowledge of amplitudes for > locally-measurable quantities in the past light cone of that region (I > don't understand the details, but this is supposed to have to do with the > fact that the commutators for spacelike-separated points always vanish). > Only if you assume there is an objective "collapse" of the wavefunction at > the point of measurement does the quantum formalism become incompatible > with locality in the light cone sense. > > > That is not correct. You have not given a local account in MWI either. > What does "account" mean? A mathematical description, or a conceptual explanation in the English language? > Your "light cone sense" of locality would only add something to the > traditional sense if the quantum state were not a complete description of > the system. In other words, a hidden variable theory. > I have no idea why you think this, and you haven't made any argument for it. Your traditional sense seems to be simply ill-defined if we assume a superposition of different detecter settings in a single location in spacetime, and a superposition of measurement results at another location, whereas the "light-cone sense" is still well-defined here since it can cover local variables of any kind, including a bundle of complex amplitudes assigned to different possible results. So, unless you think your traditional sense *can* handle this case, it seems the light cone definition is more broad and useful here, even though there are no hidden variables being discussed. Jesse -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
