On Saturday, November 3, 2018 at 9:33:54 PM UTC, Philip Thrift wrote: > > > > On Saturday, November 3, 2018 at 3:50:30 PM UTC-5, [email protected] > wrote: >> >> >> >> On Thursday, November 1, 2018 at 11:22:46 PM UTC, Pierz wrote: >>> >>> >>> >>> On Monday, October 15, 2018 at 9:40:39 PM UTC+11, [email protected] >>> wrote: >>>> >>>> >>>> >>>> On Sunday, October 14, 2018 at 5:08:42 PM UTC, smitra wrote: >>>>> >>>>> On 14-10-2018 15:24, [email protected] wrote: >>>>> > In a two state system, such as a qubit, what forces the >>>>> interpretation >>>>> > that the system is in both states simultaneously before measurement, >>>>> > versus the interpretation that we just don't what state it's in >>>>> before >>>>> > measurement? Is the latter interpretation equivalent to Einstein >>>>> > Realism? And if so, is this the interpretation allegedly falsified >>>>> by >>>>> > Bell experiments? AG >>>>> >>>>> It is indeed inconsistent with QM itself as Bell has shown. >>>>> Experiments >>>>> have later demonstrated that the Bell inequalities are violated in >>>>> precisely the way predicted by QM. This then rules out local hidden >>>>> variables, therefore the information about the outcome of a >>>>> measurement >>>>> is not already present locally in the environment. >>>>> >>>>> Saibal >>>>> >>>> >>>> What puzzles me is this; why would the Founders assume that a system in >>>> a superposition is in all component states simultaneously -- contradicting >>>> the intuitive appeal of Einstein realism -- when that assumption is not >>>> used in calculating probabilities (since the component states are >>>> orthogonal)? AG >>>> >>> >>> I think because of interference. Consider the paradigmatic double slit, >>> with the single electron going through it. It sure looks like the electron >>> was in two place at once, doesn't it? >>> >> >> *Yes, that's my assessment how the erroneous interpretation took hold, >> but only if you restrict yourself to the particle interpretation. If the >> electron travels as a wave, it can go through both slits simultaneously and >> interfere with itself. This is my preferred interpretation; the only one >> that makes sense. AG* >> >> I'm not sure what you mean by "that assumption is not used in calculating >>> probabilities". >>> >> >> *If the operator whose eigenvalues are being measured has a well defined >> mathematical form -- e.g., not like |alive> -- it has specific eigenvectors >> and eigenvalues, and the state function can be written as superposition of >> these eigenvectors. It can be shown that eigenvectors with distinct >> eigenvalues are orthogonal, meaning the Kronecker delta applies to their >> mutual inner products. Therefore, to calculate the probability of observing >> a particular eigenvalue, one must take the inner product of the wf with the >> eigenvector which has that eigenvalue. Due to the orthogonality, all terms >> drop out except for the term in the superposition which contains the >> eigenvector whose eigenvalue you want to measure. As you should see, there >> is nothing in this process of calculating probabilities that in any way >> implies, assumes, or uses, the concept that the system is simultaneously in >> ALL component states of the superposition (written as a sum of >> eigenvectors). AG* >> >> >>> If you take a sum-over-histories approach it's explicitly assumed the >>> electron went via all possible paths. >>> >> >> *I don't know that method, but offhand POSSIBLE PATHS might have nothing >> to do with, and possibly independent of SUPERPOSITIONS OF STATE. AG* >> >> I don't see what the orthogonality of the basis vectors (and hence >>> component states) has to do with the question of interpretation of >>> superposition. >>> >> >> *Explained in detail above. AG* >> >> Clearly the system will be measured in only one state, and this is what >>> the orthogonal vectors represent. However the quantum state itself >>> typically spans more than one dimension of the vector space - that's what a >>> superposition is. However I think when physicists say that the >>> superposition is in all states simultaneously, it's only in a manner of >>> speaking - a way of conveying the mathematical situation in natural >>> language that is inherently classical. >>> >> >> >> *It's a totally misleading way to discuss the quantum superpositions. >> Even classically, say for the vector space of "little pointy things" in a >> plane, each vector can be expressed in uncountably many bases, both >> orthogonal and non-orthogonal. So to claim that one basis is somehow >> preferred, and the vector being expressed as a sum or superposition in that >> basis, is simultaneously in all components of that particular basis, make >> no sense whatsoever. AG* >> >> Reading Born's exchange of letters with Einstein (I'm proud to say Born >>> was my great grandfather), it's clear that Born had a conception of QM that >>> was still very realistic in the Einstein sense. Though they disagreed >>> significantly and somewhat heatedly, Born still seems to have regarded QM >>> probabilities as classical probabilities in disguise. >>> >> >> *Einstein realism seems to have been falsified due to Bell experiments. >> If that's the case, it would mean that BEFORE measurement of a quantum >> system, it is not only NOT in all states of a superposition simultaneously >> for the reasons I have argued (nothing to do with Bell), but ALSO has no >> local preexisting value. AG* >> >> I don't think he would ever have endorsed the notion that a particle is >>> truly in all of the states of the superposition simultaneously. >>> >> >> *Thanks for your input. AG * >> > > > > The (complex-number-weighted) "path"s of the path integral > (sum-over-histories) formulation are all that are needed to define > superpositions. >
*Can you flesh that out? How can complex numbers be weighted and result in superpositions? AG* "Einstein realism" is restored if *retrocausality* (the path futures can > *stochastically* influence the path pasts) is allowed. > *I don't believe it. I think it has hugely absurd implications. AG * > > - pt > > > -- 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.
