scerir quotes Basil Hiley saying:
>Sure there is an interference effect simply because Afshar's
>experiments do not 'follow' anything and they do not 'look at' each
>photon as it passes through a pinhole. He is simply collecting and
>counting the distribution of photon arrivals at his two detectors.
>Then he makes inferences about what could possibly be going on and
>concludes, incorrectly that a photon detected in the 'photon detector
>for pinhole 1' came from pinhole 1. However that conclusion is based
>on the assumption that the rays emanating from pinhole 1 arrive at
>the 'photon detector for pinhole 1'. But the ray picture breaks
>down as soon as you enter the region of overlap of the two beams and
>you cannot conclude that the photon entering pinhole 1 arrives at the
>'photon detector for pinhole 1'. You haven't measured which pinhole
>each photon passed through so you have not contradicted Bohr.
>
>Unfortunately Afshar's conclusion, "According to my experiment one of
>the key assumptions about quantum theory is wrong" is incorrect. His
>conclusion is wrong simply because he doesn't understand the physical
>optics that lies behind the experiment he is doing.
I think Basil Hiley's analysis here may be incorrect. In the normal
double-slit experiment, the interference pattern in probabilities you get
from quantum physics when you don't know which slit the photon went through
is the same as the interference pattern in light intensities you get from
classical optics when you shine a light through two slits. So, if classical
optics predicts that light from two pinholes shining on a lens will be
focused onto two distinct spots, with no interference between the spots and
with all the light from one pinhole focused on one spot, then it seems
likely that quantum mechanics would predict the same thing.
Also notice that in the analysis of Afshar's experiment by W. Unruh at
http://axion.physics.ubc.ca/rebel.html which scerir linked to, Unruh does
not dispute Afshar's claim that all the photons from the each pinhole end up
in a single detector. In fact, he offers a "simpler version of the
experiment" involving a multiple pass interferometer, depicted in figure 2,
and says that in this experiment you do know which path a photon took by
looking at which detector it hits: "By measuring which detector they
triggered, 5 or 6, one measures which of the beams, 1 or 2, the photon
traveled along". Since the experiment in figure 2 is just supposed to be a
"simpler version" of Afshar's experiment, it's pretty clear that Unruh would
not disagree that the lens insures that knowing which detector absorbed a
photon is enough to tell you which path the photon must have taken through
the pinholes. Unruh is a fairly big-name physicist and his explanation of
what's wrong with Afshar's conclusions about complementarity are pretty
detailed, while I don't know anything about Basil Hiley and his criticisms
are more vague.
Anyway, after thinking more about this experiment it's clear to me that even
if the lens is enough to insure that all photons from the left pinhole end
up in the right detector and vice versa, complementarity should still
predict that wires placed at the interference minima will not register any
hits. Consider modifying Afshar's experiment by adding extra wires at
positions other than the interference minima, and sending the photons
through the pinholes one-by-one. In some cases the photon will be registered
at one of the wires in front of the lens, in others it will be registered at
one of the detectors behind the lens. Now, if you consider *only* the subset
of cases where the photon was absorbed by a wire, in these cases the photon
never passed through the lens, so you have absolutely no information on
which pinhole these photons went through. So if you compare the frequency
that the photons hit different wires, complementarity must predict that
you'll get an interference pattern--wires closer to the interference maxima
will register more hits, wires closer to the interference minima will
register fewer hits, and wires placed exactly at the minima will register
zero. So why should an advocate of complementarity be surprised that, after
removing all the wires *except* those placed exactly at the minima, these
wires continue to register zero hits?
You could also turn this into a "proof-by-contradiction" that
complementarity actually demands that wires exactly at the minima will not
register any photons. Suppose in Afshar's experiment you sent photons
through one-by-one, and found that there was some nonzero number of cases
where the photons hit one of the wires at the minima. Since these photons
did not make it to the lens, you have no information about which slit they
went through, and so complemantarity says that the probability of finding
these photons in any given location is determined by an interference
pattern. But the interference pattern predicts *zero* probability of finding
a photon whose path you don't know at an interference minima, in
contradiction with the initial assumption that you saw a nonzero number of
cases where the photon was detected at one of the wires at these minima.
Thus, the only outcome consistent with complementarity is to have zero cases
where the photons hit one of these wires, just as Afshar found.
Jesse Mazer
Received on Thu Aug 12 2004 - 01:11:00 PDT