On Sat, Aug 10, 2019 at 5:51 PM smitra <[email protected]> wrote: > On 09-08-2019 13:49, Bruce Kellett wrote: > > From: SMITRA <[email protected]> > > > >> On 09-08-2019 07:54, Bruce Kellett wrote: > >>> > >>> What is nonsense? The fact that separate states for the two slits > >> does > >>> not aid comprehension? Or the fact that orthogonal states do not > >>> interfere? > >>> > >> > >> Your statement that orthogonal states don't interfere is plain > >> nonsense. > > > > Huh?? Did you not understand my example above of the state (|A> + > > |B>)? There is interference in the norm only if |A> and |B> are not > > orthogonal. This is elementary text book stuff. > > What you call "interference of the norm" here has nothing to do with > interference as discussed in this thread. >
It is just the difference between classical and quantum physics. Classical states are orthogonal. Quantum states show interference if they are not orthogonal. > >>>> What we observe at a point x on the screen is the expectation > >>>> value of the projection operator |x><x|. > >>> > >>> No, we don't observe an expectation value, which is a weighted > >> average > >>> over possible outcomes. We measure a particular outcome at each > >> point > >>> on the screen. > >>> > >> > >> And that's precisely given by the expectation value of the > >> projection > >> operator |x><x|, which is > >> > >> <psi|x><x|psi> = psi*(x) psi(x) = |psi(x)|^2 > > > > That is the expectation value over all possible results. We only > > observe one spot on the screen for each photon through the slits -- we > > do not directly observe expectation values. The states <x|0> and <x|1> > > are not orthogonal. > > The expectation value of |x><x| depends on the position x, it gives the > probability that the particle will be detected at position x on the > screen. And <x|0> and <x|1> are complex numbers not states, but if you > consider them as wavefunctions in the position representation, then they > represent the states |0> and |1> which are orthogonal states. > > > I don't understand why you keep on claiming that in the two slit > experiment the coherent superposition of the two orthogonal states won't > show interference. If you measure the which way information and the > measurement result is stored coherently in a physical variable that can > take the value 0 or 1, then we may represent the superposition as: > > 1/sqrt(2) [|0,0> + |1,1>] > > where the second component of the ket denotes the state of the system > that measures the which way information. In this case there is no > interference. In general, if the two states of that system are not > orthogonal, and we denote them as |u> and |v>, then the interference > term becomes: > > Re[<0|x><x|1><u|v>] > > So, if |u> and |v> are orthogonal then we have perfect which way > information, and the interference term vanishes. However, it doesn't > matter whether or not |0> and |1> are orthogonal. > I think the point is that we observe interference of the photon waves at the screen, not at the slits. The slits do not interfere. Bruce -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLTkuBL5%2BUrQRdq9p8ty_8FpPP8LtRB-2esKUwdZ6kb3%2BQ%40mail.gmail.com.
