On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com wrote: > > > > On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote: >> >> On Wed, Dec 5, 2018 at 10:52 PM <agrays...@gmail.com> wrote: >> >>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com >>> wrote: >>>> >>>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote: >>>>> >>>>> On Wed, Dec 5, 2018 at 2:36 AM <agrays...@gmail.com> wrote: >>>>> >>>>>> >>>>>> *Thanks, but I'm looking for a solution within the context of >>>>>> interference and coherence, without introducing your theory of >>>>>> consciousness. Mainstream thinking today is that decoherence does occur, >>>>>> but this seems to imply preexisting coherence, and therefore >>>>>> interference >>>>>> among the component states of a superposition. If the superposition is >>>>>> expressed using eigenfunctions, which are mutually orthogonal -- >>>>>> implying >>>>>> no mutual interference -- how is decoherence possible, insofar as >>>>>> coherence, IIUC, doesn't exist using this basis? AG* >>>>>> >>>>> >>>>> I think you misunderstand the meaning of "coherence" when it is used >>>>> off an expansion in terms of a set of mutually orthogonal eigenvectors. >>>>> The >>>>> expansion in some eigenvector basis is written as >>>>> >>>>> |psi> = Sum_i (a_i |v_i>) >>>>> >>>>> where |v_i> are the eigenvectors, and i ranges over the dimension of >>>>> the Hilbert space. The expansion coefficients are the complex numbers >>>>> a_i. >>>>> Since these are complex coefficients, they contain inherent phases. It is >>>>> the preservation of these phases of the expansion coefficients that is >>>>> meant by "maintaining coherence". So it is the coherence of the >>>>> particular >>>>> expansion that is implied, and this has noting to do with the mutual >>>>> orthogonality or otherwise of the basis vectors themselves. In >>>>> decoherence, >>>>> the phase relationships between the terms in the original expansion are >>>>> lost. >>>>> >>>>> Bruce >>>>> >>>> >>>> I appreciate your reply. I was sure you could ascertain my error -- >>>> confusing orthogonality with interference and coherence. Let me have your >>>> indulgence on a related issue. AG >>>> >>> >>> Suppose the original wf is expressed in terms of p, and its >>> superposition expansion is also expressed in eigenfunctions with variable >>> p. Does the phase of the original wf carry over into the eigenfunctions as >>> identical for each, or can each component in the superposition have >>> different phases? I ask this because the probability determined by any >>> complex amplitude is independent of its phase. TIA, AG >>> >> >> The phases of the coefficients are independent of each other. >> > > When I formally studied QM, no mention was made of calculating the phases > since, presumably, they don't effect probability calculations. Do you have > a link which explains how they're calculated? TIA, AG >

I found some links on physics.stackexchange.com which show that relative phases can effect probabilities, but none so far about how to calculate any phase angle. AG > >> Bruce >> >> >> > -- 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.