On Friday, January 18, 2019 at 3:49:10 AM UTC, Brent wrote: > > > > On 1/17/2019 5:23 PM, agrays...@gmail.com <javascript:> wrote: > > > > On Thursday, January 17, 2019 at 8:33:21 AM UTC, agrays...@gmail.com > wrote: >> >> >> >> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote: >>> >>> >>> >>> On 1/16/2019 7:25 PM, agrays...@gmail.com wrote: >>> >>> >>> >>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: >>>> >>>> >>>> >>>> On 1/13/2019 9:51 PM, agrays...@gmail.com wrote: >>>> >>>> This means, to me, that the arbitrary phase angles have absolutely no >>>> effect on the resultant interference pattern which is observed. But isn't >>>> this what the phase angles are supposed to effect? AG >>>> >>>> >>>> The screen pattern is determined by *relative phase angles for the >>>> different paths that reach the same point on the screen*. The >>>> relative angles only depend on different path lengths, so the overall >>>> phase >>>> angle is irrelevant. >>>> >>>> Brent >>>> >>> >>> >>> *Sure, except there areTWO forms of phase interference in Wave >>> Mechanics; the one you refer to above, and another discussed in the >>> Stackexchange links I previously posted. In the latter case, the wf is >>> expressed as a superposition, say of two states, where we consider two >>> cases; a multiplicative complex phase shift is included prior to the sum, >>> and different complex phase shifts multiplying each component, all of the >>> form e^i (theta). Easy to show that interference exists in the latter case, >>> but not the former. Now suppose we take the inner product of the wf with >>> the ith eigenstate of the superposition, in order to calculate the >>> probability of measuring the eigenvalue of the ith eigenstate, applying one >>> of the postulates of QM, keeping in mind that each eigenstate is multiplied >>> by a DIFFERENT complex phase shift. If we further assume the eigenstates >>> are mutually orthogonal, the probability of measuring each eigenvalue does >>> NOT depend on the different phase shifts. What happened to the interference >>> demonstrated by the Stackexchange links? TIA, AG * >>> >>> Your measurement projected it out. It's like measuring which slit the >>> photon goes through...it eliminates the interference. >>> >>> Brent >>> >> >> *That's what I suspected; that going to an orthogonal basis, I departed >> from the examples in Stackexchange where an arbitrary superposition is used >> in the analysis of interference. Nevertheless, isn't it possible to >> transform from an arbitrary superposition to one using an orthogonal basis? >> And aren't all bases equivalent from a linear algebra pov? If all bases are >> equivalent, why would transforming to an orthogonal basis lose >> interference, whereas a general superposition does not? TIA, AG* >> > > *I don't get it. If it's easy to show the existence of interference for a > general superposition where the components have different phase shifts, why > would the interference disappear for a special case using orthonormal basis > components? TIA, AG * > > > But taking the inner product with the *ith* eigenstate is not > transforming to a different basis. > > Brent >
*I know. I meant that from a general superposition used in the Stackexchange articles, I wrote that general form as a superposition of eigenstates, and this is where there was an implicit transformation to a different, specific basis. 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
