On Sunday, November 4, 2018 at 3:01:50 PM UTC, Philip Thrift wrote: > > > > On Sunday, November 4, 2018 at 7:27:12 AM UTC-6, [email protected] > wrote: >> >> >> >> On Sunday, November 4, 2018 at 1:05:36 AM UTC, Philip Thrift wrote: >>> >>> >>> >>> On Saturday, November 3, 2018 at 6:21:18 PM UTC-5, [email protected] >>> wrote: >>>> >>>> >>>> >>>> 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 >>>>> >>>>> >>> The paths (histories) in a path integral (sum over histories) >>> formulation have complex numbers assigned to them. (That's their >>> "weights".) >>> >>> >>> http://muchomas.lassp.cornell.edu/8.04/Lecs/lec_FeynmanDiagrams/node3.html >>> >>> The Feynman formulation of Quantum Mechanics builds three central ideas >>> from the de Broglie hypothesis into the computation of quantum amplitudes: >>> the probabilistic aspect of nature, superposition, and the classical limit. >>> This is done by making the following three three postulates: >>> >>> >>> 1. *Events in nature are probabilistic with predictable >>> probabilities P.* >>> 2. *The probability P for an event to occur is given by the square >>> of the complex magnitude of a quantum amplitude for the event, Q. The >>> quantum amplitude Q associated with an event is the sum of the >>> amplitudes [image: tex2html_wrap_inline1605] associated with every >>> history >>> leading to the event.* >>> 3. *The quantum amplitude associated with a given history [image: >>> tex2html_wrap_inline1605] is the product of the amplitudes [image: >>> tex2html_wrap_inline1609] associated with each fundamental process in >>> the >>> history.* >>> >>> ... >>> >>> Postulate (2) specifies how probabilities are to be computed. This item >>> builds the concept of superposition, and thus the possibility of quantum >>> interference, directly into the formulation. Specifying that the >>> probability for an event is given as the magnitude-squared of a sum* >>> made from complex numbers*, allows for negative, positive and >>> intermediate interference effects. This part of the formulation thus builds >>> the description of experiments such as the two-slit experiment directly >>> into the formulation. A *history* is a *sequence* of fundamental >>> processes leading to the the event in question. We now have an explicit >>> formulation for calculating the probabilities for events in terms of the >>> [image: >>> tex2html_wrap_inline1605] , quantum amplitudes for individual >>> histories, which the third postulate will now specify. >>> ... >>> >>> - pt >>> >> >> *Thanks for that. I have a few basic questions about Feynman's >> path-integral formulation of QM. Firstly, IIUC, Bruce wrote that Feynman >> initially believed in a particle-only formulation of QM. but later realized >> this was not possible. Is this true or false? Personally, as I wrote above, >> I don't see how a particle-only theory of slit experiments makes any sense. >> Only using a wave model can we imagine that the "particle" goes through >> both slits simultaneously to produce interference. Secondly, in his >> particle only, or path integral formulation, how does he choose which paths >> to use, given that there exists an uncountable number of direct paths, and >> an uncountable number of paths which loop, go backward, then forward, and >> so on. How does he choose which paths to use? Thirdly, how does he define a >> "fundamental process", which is required to define a "history"? TIA, AG* >> > > > This has been written about by the late Victor J. Stenger, Huw Price, Ken > Wharton, ... and me, of course. > > All are some sort of reification of Feynman paths. > > There is the zig-zag particle that goes back and forth in time > ("eventually"going through both slits). There is the reflective path > integral (paths in one time direction mirrored with paths going in the > opposite time direction), etc. > > - pt >
*Seems like a desperate grasping at straws. How does Feynman choose which paths to use, or are all equally required for the theory to make correct predictions? 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 [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.
