> On 10 Jan 2019, at 21:33, [email protected] wrote: > > > > On Thursday, January 10, 2019 at 11:07:51 AM UTC, Bruno Marchal wrote: > >> On 9 Jan 2019, at 07:58, [email protected] <javascript:> wrote: >> >> >> >> On Monday, January 7, 2019 at 11:37:13 PM UTC, [email protected] >> <http://gmail.com/> wrote: >> >> >> 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 >> <http://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 >> >> Puzzling, isn't it? We have waves in Wave Mechanics. Waves interfere with >> each other, even if they're probability waves, and this is one of the core >> features of Wave Mechanics. So phase angles must relate to degrees of >> interference. But if the phase angles are arbitrary; ERGO, so is the >> interference; arbitrary and thus NOT well defined. What am I missing? TIA, AG > > > The *global* phase angle is arbitrary: Psi = e^phi Psi. > > The relative phase angle is not arbitrary: you can distinguish all states up > + e^phi down, when phi varies. > > All this follows from the Born rule. > > Bruno > > Born's rule calculates a complex conjugate, in which case any phase angle > cancels out in the calculation. I don't see how it could be used to > *calculate* a phase angle. Moreover, Bruce is most knowledgeable here about > QM (along with Brent) and he indicates otherwise; that phase angles cannot be > calculated. AG
The global phase cannot be calculated. The relative phase is what we calculate all the time when doing quantum mechanics. Psi is not experimentally distinguishable from e^phi Psi. But (up + down) can be distinguished from (up + e^phi down). Have you got the book by David Albert? Bruno >> <javascript:> <javascript:> >> <https://groups.google.com/group/everything-list> >> <https://groups.google.com/d/optout> > > -- > 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] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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.
