On 09-08-2019 13:49, Bruce Kellett wrote:
From: SMITRA <[email protected]>
On 09-08-2019 07:54, Bruce Kellett wrote:
On Fri, Aug 9, 2019 at 3:16 PM smitra <[email protected]> wrote:
On 09-08-2019 05:35, Bruce Kellett wrote:
It is really quite simple. If a state is a sum of two
components,
|psi> = (|A> + |B>), then we measure <psi|psi> = (<A| +
<B|)(|A>
+
|B>) = <A|A> + <B|B> + 2<A|B>. If <A|B> does not vanish (the
components are not orthogonal), then there is interference. For
orthogonal components <A|B> = 0, and there is no interference.
Introducing separate states for the two slits does not aid
comprehension here.
Nonsense.
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.
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.
Saibal
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