On Sunday, November 4, 2018 at 1:42:49 PM UTC-6, [email protected] wrote: > > > > 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* >
My theory, it's a sort of Darwinian struggle: *In this sum-over-histories-and-futures interpretation, “decoherence” is defined as all histories/futures but one die. (In a Darwinian”survival-of-the-fittest analogy, selection is made from a “fitness” probability distribution.)* - https://codicalist.wordpress.com/2018/03/16/mirror-mirror/ - cf. https://codicalist.wordpress.com/2018/09/25/retrosignaling-in-the-quantum-substrate/ This may be a sort of version of quantum Darwinism [ https://en.wikipedia.org/wiki/Quantum_Darwinism ]. - 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.
