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 -- 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.
