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. 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.
