On Wednesday, December 5, 2018 at 10:13:57 PM UTC, [email protected] wrote: > > > > On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote: >> >> On Wed, Dec 5, 2018 at 10:52 PM <[email protected]> wrote: >> >>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, [email protected] >>> wrote: >>>> >>>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote: >>>>> >>>>> On Wed, Dec 5, 2018 at 2:36 AM <[email protected]> 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 [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.
