On Friday, January 18, 2019 at 4:26:25 AM UTC, [email protected] wrote: > > > > On Friday, January 18, 2019 at 3:49:10 AM UTC, Brent wrote: >> >> >> >> On 1/17/2019 5:23 PM, [email protected] wrote: >> >> >> >> On Thursday, January 17, 2019 at 8:33:21 AM UTC, [email protected] >> wrote: >>> >>> >>> >>> On Thursday, January 17, 2019 at 3:58:48 AM UTC, Brent wrote: >>>> >>>> >>>> >>>> On 1/16/2019 7:25 PM, [email protected] wrote: >>>> >>>> >>>> >>>> On Monday, January 14, 2019 at 6:12:43 AM UTC, Brent wrote: >>>>> >>>>> >>>>> >>>>> On 1/13/2019 9:51 PM, [email protected] 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 * >
*I suppose you could start with a superposition of eigenstates and get, or not get interference depending on the type of mathematical operation is performed. So I am unclear what's going on here; why taking the inner product is tantamount to looking at which slit the particle is going through. 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.
