On Friday, January 11, 2019 at 10:11:10 AM UTC, Bruno Marchal wrote: > > > On 11 Jan 2019, at 10:54, [email protected] <javascript:> wrote: > > > > On Friday, January 11, 2019 at 9:07:50 AM UTC, Bruno Marchal wrote: >> >> >> On 10 Jan 2019, at 22:08, [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] wrote: >>> >>> >>> >>> On Monday, January 7, 2019 at 11:37:13 PM UTC, [email protected] >>> 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 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 >>> >> >> What about the case where the superposition is a sum of many eigenstates? >> >> >> That is always the case. >> > > * ???* > >> How do you *calculate* the phase angle of each eigenstate? I don't see >> how Born's rule helps. AG >> >> By looking at the interference obtained when preparing many particles in >> that superposition states. >> > > *How can you prepare a system in any superposition state if you don't know > the phase angles beforehand? * > > > ? > > That is the point of the preparation. It is enough to rotate the polariser > (say) in some special direction. > I can prepare particles in some “up” state, and then I make them passing a > polariser with a relative angle alpha, so that I can get the state > sin(alpha) up + cos(alpha) down. I can verify this by measuring the density > corresponding to the probabilities sin^2(alpha) of being up, and > cos^2(alpha) of being down, + some other direction to make the difference > with a mixture (as already explained once). > > > > > *You fail to distinguish measuring or assuming the phase angles from > calculating them. One doesn't need Born's rule to calculate them. Maybe > what Bruce meant is that you can never calculate them, but you can prepare > a system with any relative phase angles. AG * > > > I have no clue what you mean by calculating. >
*It means you can use theory to predict the phase differences. This isn't what Bruce claimed AFAICT. For a superposition with many eigenstates, what is the math that produces the phase differences? I don't understand your rotation example. AG* I postulate QM, and talk about experience done with state which have been > prepared, as we can only do that in QM. I think that all what Bruce said > about this is correct. We cannot distinguish Psi from e^phi Psi, but there > is no problem distinguishing up + e^phi down from up + down. > > Bruno > > > > > You will find more explanation on all this in David Albert’s book, which >> minimises well the use of mathematics. >> >> Bruno >> > > > >> >> >> >> -- >> 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. >> >> >> > -- > 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] <javascript:>. > To post to this group, send email to [email protected] > <javascript:>. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit 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.
