Re: Pedagogy of QM Double Slit Experiment

> For example, Akira Tonomura, at Hitachi, has a page[1] describing
> the electron double slit experimentin with modern equipment.
> It even has a movie[2] of the detector monitor showing the
> detection of individual electrons and the gradual formation
> of an interference pattern.

The Tonomura experiments do not show how is the effect quantiatively
distingushable from a perfectly classical matter field i.e. whether a
spread out Dirac matter field triggers a detector _independently_ of
what other detectors did. A classical, even a macroscopic, system can
easily replicate what you see on his video. Just consider a water in
bucket with small holes -- the water above the holes forms a continuum
(analog of field) while the droplets come out well spaced in time and
space, one by one. To exclude the classical field case combined with
quantized detection in this type of experiment one needs to show that
the probability of a double drop p2 is smaller than p1*p1 i.e. that
occurence of a drop on one hole makes occurence of drop on another
remote hole significantly smaller than p1*p1 (cf.
http://marcus.whitman.edu/~beckmk/QM/grangier/Thorn_ajp.pdf ).

Additional problem with this experiment (as a proof of anything that
could surprise, say, Maxwell or Faraday) is that the "biprism" is made
of conductors, so that even a moving point charge will have EM fields
interacting with distributed geometry of the setup, so that one can't
argue that covering one path (or one hole) cannot have any effect on a
point particle going via the other path. To suprise, say, Maxwell, the
experimenters would need to show indepndence of the effect on the
materials of the "biprism" e.g. by replacing a metal filament with a
glass fiber and metal plates by glass (unfortunately the experiment
wouldn't show 'interference' then). Furthermore, to fully eliminate
plain EM field effects on point particles, one would need to show that
the effects propagate faster than c (fast random change of "slit"
configuration, a la the 2nd Aspect's Bell inequality experiment with
"random" [these were actually periodic] switching of polarizer
orientation).

You can find more detailed calculations on the kinds of interestig, but
perfectly classical, effects between the Maxwell and Dirac fields that
would have to be eliminated (to surprise Maxwell) in the Jaynes' paper:

E.T. Jaynes "Scattering of Light by Free Electrons"
in The Electron, D. Hestenes and A. Weingartshofer (eds.),
Kluwer, Dordrecht 1991 p. 1

http://bayes.wustl.edu/etj/articles/scattering.by.free.pdf


As a qualitative demonstration of "wave-particle duality" for high
school physics students, these experiments are fine, though. For
college students one needs the QO type of experiments (e.g. see Beck's
undergraduate lab demonstrations at
http://marcus.whitman.edu/~beckmk/QM/grangier/grangier.html ). Still,
none of these, or any other experiment in existence, would make Maxwell
or Faraday (or even a critical minded graduate student) raise eyebrows
(provided you give them a brief course on detector & counting
electronics).

.

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