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. "Einstein realism" is restored if *retrocausality* (the path futures can *stochastically* influence the path pasts) is allowed. - 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.
