On Monday, January 7, 2019 at 2:52:27 PM UTC, [email protected] wrote: > > > > On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote: >> >> On Mon, Jan 7, 2019 at 9:42 AM <[email protected]> wrote: >> >>> On Saturday, December 8, 2018 at 2:46:41 PM UTC, [email protected] >>> wrote: >>>> >>>> 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 >>>>>>> >>>>>> >>> I could use a handshake on this one. Roughly speaking, if one wants to >>> express the state of a system as a superposition of eigenstates, how does >>> one calculate the phase angles of the amplitudes for each eigenstate? AG >>> >> >> One doesn't. The phases are arbitrary unless one interferes the system >> with some other system. >> >> Bruce >> > > If the phases are arbitrary and the system interacts with some other > system, the new phases presumably are also arbitrary. So there doesn't seem > to be any physical significance, yet this is the heart of decoherence > theory as I understand it. What am I missing? TIA, AG >
Also, as we discussed, the phase angles determine interference. If they can be chosen arbitrarily, it seems as if interference has no physical significance. AG -- 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.
