On 10/17/2019 4:34 PM, Bruce Kellett wrote:
On Fri, Oct 18, 2019 at 10:05 AM 'Brent Meeker' via Everything List
<[email protected]
<mailto:[email protected]>> wrote:
But I wonder what happens in Carroll's experiment if, after
measuring in the left/right basis and noting that two different
interference patterns can then be discerned by considering either
those due to left spin recording particles or considering right
spin particles, one measures the recording particles again in the
up/down basis. The overall pattern is the same, it's just that
you've relabeled spots on the screen according to whether the
second measurement of recording particles assigned them to UP or
to DOWN. Now you can consider the subset labeled UP (or DOWN).
This should be a superposition of ensembles randomly selected from
the left and right ensembles and in that case would not show an
interference pattern...but the information has certainly been
erased (twice)?
If I understand you, what you are suggesting is that either the left
polarized, or right polarized, are measured again in the up-down
direction. I think that if you do this second measurement, you will
simply reduce the intensity by a factor of two.
No. You just partitioning the spots on the screen in a different way,
so there are the same number of spots. After the first measurement of
the recording particles spins, in the left/right basis, you labeled the
spots on screen according to left or right. And when you looked only at
the left labeled spots they showed an interference pattern. And
necessarily the right labeled spots were the complement relative to the
no-interference pattern. So there are two implicit complementary
interference patterns hidden in the no-interference pattern. But on the
second measurement of the recording particles in the up/down basis each
one should be up or down with probability 1/2. So all those measuring
UP is just a random selection of the overall ensemble, the ensemble that
showed no interference. So yes it's intensity is reduce (only half the
spots end up labeled UP) but it's a no-interference pattern.
The welcher weg information was permanently erased by the first
left-right measurement.
Right. So why doesn't the interference pattern persist after the second
measurement of the recording particles? I suppose the answer is that it
does, we just don't have the information necessary to pick it out
anymore. Still it seems curious that we can erase the which-way once
and, by looking at the results, find the interference pattern. But if
we erase twice we can't find it.
Brent
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