On 10/12/2017 10:02 am, [email protected] wrote:
On Friday, December 8, 2017 at 6:19:20 PM UTC, Brent wrote:On 12/8/2017 12:01 AM, [email protected] <javascript:> 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. BrentThis 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.
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