On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote: > > On Wed, Dec 5, 2018 at 10:52 PM <[email protected] <javascript:>> 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 > > 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.
