On Thursday, December 6, 2018 at 5:46:13 PM UTC, [email protected] wrote: > > > > 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 >
Here's the answer if anyone's interested. But what's the question? How are wf phase angles calculated? Clearly, if you solve for the eigenfunctions of some QM operator such as the p operator, any phase angle is possible; its value is completely arbitrary and doesn't effect a probability calculation. In fact, IIUC, there is not sufficient information to solve for a unique phase. So, I conclude,that the additional information required to uniquely determine a phase angle for a wf, lies in boundary conditions. If the problem of specifying a wf is defined as a boundary value problem, then, I believe, a unique phase angle can be calculated. CMIIAW. 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.
