On Tue, Aug 13, 2019 at 10:43 AM smitra <[email protected]> wrote: > On 13-08-2019 01:41, Bruce Kellett wrote: > > On Tue, Aug 13, 2019 at 9:09 AM smitra <[email protected]> wrote: > > > >> On 12-08-2019 08:29, Bruce Kellett wrote: > >>> > >>> Look at this another way. It is just an illustration of > >>> complementarity. Measuring which slit the photon went through is > >> a > >>> position measurement at the slits. Measuring the interference > >> pattern > >>> at the screen is equivalent to a momentum measurement at the > >> slits. > >>> Such measurement operators do not commute -- the measurements are > >>> complementary and cannot be performed simultaneously. > >>> > >> > >> It doesn't matter for orthogonality of the states whether or not > >> they > >> are measured. > > > > Of course it does. The slits are not orthogonal states unless they are > > measured position eigenstates. If they are not measured, they are > > individually superpositions of many position eigenstates (including > > eigenstates that overlap both slits), so the slits themselves are no > > longer orthogonal. Orthogonal states cannot interfere, that is why a > > position measurement at the slits makes the interference pattern on > > the screen disappear. > > > > The fact remains, that orthogonal states cannot interfere: > > > > (<A| + <B|)(|A> + |B>) = <A|A> + <B|B> + 2 <A|B> > > > > and the interference term <A|B> vanishes if |A> and |B> are > > orthogonal. You can't get away from this basic fact about quantum > > mechanics. > > > > <A|B> is zero in the two slit experiment, if you integrate the > interference term over the screen you get zero. > > Thing is that the interference we can observe at some position x on the > screen is Re[<A|x><x|B>], which for general x is nonzero despite the > fact that <A|B> = 0. >
So you agree that if the overlap vanishes you do not get interference. You go to some lengths to try and avoid this fact. Saying that the integral over the screen vanishes is beside the point. 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/CAFxXSLST6TbXhcBPmNOw4pV%2BA6EGnhVHdYkBGAKonAT8_RbW7Q%40mail.gmail.com.
