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* -- 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.
