On Sunday, December 10, 2017 at 3:26:52 AM UTC, Bruce wrote: > > On 10/12/2017 10:02 am, [email protected] <javascript:> wrote: > > On Friday, December 8, 2017 at 6:19:20 PM UTC, Brent wrote: >> >> >> On 12/8/2017 12:01 AM, [email protected] wrote: >> >> >> On Thursday, December 7, 2017 at 11:54:39 PM UTC, Bruce wrote: >>> >>> On 8/12/2017 10:40 am, [email protected] wrote: >>> >>> On Thursday, December 7, 2017 at 4:44:01 PM UTC, Bruno Marchal wrote: >>>> >>>> >>>> >>>> Yes, but only if the phase are indeed different at each slits, I would >>>> say. The interference pattern would shift. >>>> >>> >>> >>> >>> >>> >>> >>> >>> *I had a confusing and testy response from Bruce on this issue. To >>> recapitulate: AG> Are the phase angles of components of a superposition >>> identical? If so, is this the definition of coherence? TIA, AG BK> No, why >>> should they be equal. You really do have to learn some basic quantum >>> mechanics, Alan, and stop bothering the list with such questions. I might >>> be mistaken, but In the double slit I think the phase angles must be equal >>> to get the interference pattern observed, and if they're different at each >>> slit, we won't get what's observed. And if each component of a >>> superposition with many components has an arbitrary phase angle, I don't >>> see how we get coherent waves. I know this is not an interesting issue for >>> Bruce, but maybe he will clarify the situation. IIRC, on another message >>> list, Roahn, a Ph'D physicist known to Bruce, claimed the phase angles of >>> components of a superposition are equal. It would seem so, for if one has a >>> solution of the SWE and assigns a phase angle arbitrarily, and then expands >>> the solution in some basis, I think the basis vectors would inherit the >>> same phase angles. Still studying Bruce's link! * >>> >>> >>> Bruno is right on this -- the only effect of changing the phase in one >>> arm of the superposition would be to shift the interference pattern to the >>> side, it would still be the same pattern. >>> >> >> *That's what I was trying to say above; shifting the pattern would be a >> new result IMO, same form but shifted in one direction. What I was puzzled >> about was the relation of the phase factors to coherence. If the >> superposition consists of three components with each pair of phases being >> multiples of each other, but not all three. Would the resultant >> superposition still be considered to be coherent? (not discussed in any >> links I can find). AG* >> >> >> The superposition is considered to be not coherent in the FAPP limit >> where there are many components with different varying phases (different >> frequencies) so the cross-terms of the density matrix tend to average to >> zero. This is the situation when the system includes the instrument and >> the environment. In theory the system+instrument+environment is in a >> superposition but almost all of its components are unobservable so we >> regard it as decohered. >> >> Brent >> >> >>> This is explained in the Wikipedia page I referenced. Linearity of the >>> SWE means that the sum of any two solutions is also a solution, but the >>> individual solutions can be added with arbitrary complex weights (phases). >>> The overall phase has no physical consequences, but the relative phase is >>> all-important. There is no reason for the relative phases to be equal, they >>> can be anything at all. >>> >> > *Bruce; bear with me on this one. IIRC, Roahn claimed the phases are > equal. I think he was referring to the case of a solution of the SWE which > has an arbitrary phase assigned, and is then expanded into a superposition > in some basis. In this *particular* case, I believe the components would > inherit the phase of the original wf. If the phases of the components are > different from the original assigned phase of the original wf, I don't > think the sum would represent the original wf. Is this correct? AG* > > > I don't know what Roahn was referring to, and I don't remember the > comment. But in general it is wrong. If you have a wave function, it can be > expanded in terms of some basis vectors for the relevant Hilbert space. The > complex coefficient (phases) will depend on the original wave function so > expanded. But the basis is arbitrary, so if you expand as a superposition > of some other set of basis vectors, the coefficients and phases will > generally be different. This is just fairly basic linear algebra. > > Bruce >
> > *FWIW, Roahn's comment was not on Avoid2 but in private email. Any event, > you're obviously correct. As I now recall, there are specific > transformation equations for coefficients in linear algebra when going from > one basis to another. 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.
