On Wed, Aug 14, 2019 at 8:28 AM smitra <[email protected]> wrote: > On 13-08-2019 13:33, Bruce Kellett wrote: > > > > Of course A(x) and B(x) refer to the same point on the screen. That is > > not a collapse, that is just what the notation means. > > A(x) and B(x) considered as the representations of |A> and |B> in the > position basis, i.e. A(x) = <x|A> and B(x) = <x|B> are still orthogonal > states, as they represent the orthogonal states |A> and |B>: > > 0 = <A|B> = Integral over x of <A|x><x|B>d^3x = Integral over x of > A*(x)B(x) d^3x > > But you interpret this as the total counts of particles on the entire > screen not changing which you call an absence of interference. However > interference is what we detect locally on each point on the screen. You > can't say that for each point x0 on the screen, A(x0) and B(x0) are > particle states. These values are not the quantum states of the particle > before it hits the screen, unless you would have done a measurement > localizing the particle near x0. >
The spot on the screen may well be such an experiment. > So, your argument only makes sense if you invoke collapse via a position > measurement. > You over-elaborate a simple schematic. My A(x) and B(x) are simply the amplitudes of the wave function at point x on the screen from the two slits. To get the intensity at x, you add the amplitudes and take the modulus squared -- you do not add the intensities from each slit separately. Perhaps the problem stems from my using the ket vector representation for single complex numbers. But complex numbers are never orthogonal, so using the ket generalises this interference result to general state vectors. Integrating over the screen is not relevant to the intensity at each 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/CAFxXSLRi2uEG%2B9HdzHQ_RdO4sCL4pLcrXiJmUvDaaYzAr8thBA%40mail.gmail.com.
