On 12-08-2019 08:29, Bruce Kellett wrote:
On Mon, Aug 12, 2019 at 4:09 PM Bruce Kellett <bhkellet...@gmail.com>
wrote:
On Mon, Aug 12, 2019 at 3:56 PM smitra <smi...@zonnet.nl> wrote:
On 12-08-2019 04:06, Bruce Kellett wrote:
On Mon, Aug 12, 2019 at 3:48 AM Bruno Marchal
<marc...@ulb.ac.be>
wrote:
In the sense you mention I am OK, but we have a slight
vocabulary
problem. Not important, if you agree that measurement are
self-entanglement, so that the superposition of the orthogonal
state
SlitA and SlitB, say some oblique (with sqrt(2) = 1) SlitA +
SlitB is
inherited by the observer “looking” which is which.
If you do not measure which slit the photon went through, then
the
superposition of slits is not broken by decoherence. But the
interference at the screen depends only on things like the
wavelength
of the light, the separation of the slits, and the distance
between
the slits and the screen. If you refine this calculation by
taking the
finite width of the slits into account, you convolute the
interference
pattern with the diffraction pattern due to finite slit width.
This is
an elementary calculation in physical optics, not even
requiring
quantum mechanics. But the waves at the screen cannot be
orthogonal,
or else they would not interfere.
The states at the screen are orthogonal because they were at the
start
and inner product is conserved under the unitary time evolution.
The sits are orthogonal if you measure which slit the photon went
through, in which case the interference pattern disappears, as
required by orthogonality. But they are not orthogonal if they are
not measured, else there would be no interference. Orthogonal states
cannot interfere.
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. It's of course true that if we measure the position at the
screen we're measuring something else than the which way information and
the position eigenstates are not the original superposition. But it
remain a fact that the state of which we're measuring the position
operator on the screen is a superposition of two orthogonal states and
we're then seeing an interference effect defined as the difference in
the number of dots in the screen of the actual counts and the sum of
what would be seen if slit 1 were cloes and slit 2 open and vice versa.
Saibal
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