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, agrays...@gmail.com > wrote: >> >> >> >> On Sunday, October 14, 2018 at 5:08:42 PM UTC, smitra wrote: >>> >>> On 14-10-2018 15:24, agrays...@gmail.com 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 * > > -- 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
