Pedagogy of QM Double Slit Experiment

Dear Experts,

I believe that the standard textbook presentations of the quantum mechanical
double slit experiment are often poor. They throw in complicating elements
that tend to confuse beginning students and obscure, at least in the
student's mind, the essential phenomenon. I would be interested in your
comments to make certain that I haven't missed the essential points myself.

1) Why 'double slit' instead of 'double pinhole'?
2) Doesn't a single pinhole, or single slit, experiment already show that
there is an essential quantum mechanical randomness that is introduced, and
that this randomness has a wavelike behavior?
3) What exactly does a double slit experiment add to our knowledge that is
not already contained in the single slit experiment? (Is it just that it is
experimentally easier?)

In the following, I will be thinking of a presentation such as Figure 21.4
(§21.4, page 504) in Penrose's 'Road to Reality' that shows, in 3D
perspective, an electron gun aimed at a screen with two vertical slits, and
a detection screen behind. I believe his is a pretty standard picture and
discussion. And in all of this we can assume the one particle at a time
case, since the experiment has actually been done.

Penrose first discusses the case when one slit is covered. We get a smeared
out distribution. Penrose writes: "No puzzle here." But I think that to the
beginning student there are a lot of puzzles! Classically, if the electron
gun was perfectly fixed and aimed at the center of the slit, then wouldn't
we get simply a single spot on the screen where all the electrons hit?
Instead there is a distribution of hits that is spread out both horizontally
AND vertically. Why does the distribution get spread out vertically? Perhaps
the gun is a long way away, the electron is approximated by a plane wave
function that would more than encompass the length of the slits, so it would
behave just like an optical slit case. But the student doesn't know anything
about that yet and this vertical spreading becomes a source of confusion.

So wouldn't it be better to begin with a pinhole, in which classically the
electrons were aimed right through the center of the pinhole? Classically,
they would all hit at one spot on the screen. But actually we obtain a
circular distribution of hits. Doesn't this already show that QM introduces
an essential randomness that has wavelike behavior? We can see some of this
wavelike behavior by how the amount of spreading depends on the momentum of
the electrons.

(In the Feynman Lectures on Physics, Volume III, Feynman introduces the
analogy of a machine gun spraying bullets in all directions and supposedly
the single slit horizontal spreading is due to the random jerking around of
the gun, and maybe the ricocheting of bullets off the edge of the slit. So
we might also think of the electron gun having random classical motions that
spread the electrons around and shoots them in different directions. But
isn't this just introducing a confusing and complicated classical effect
that hides a true quantum mechanical effect?)

So I think it is misleading to suggest that there is nothing unusual about
the single slit, or single pinhole, experiment. I think it would be better
to give a careful discussion of the single pinhole case before going to the
double slit experiment. But the discussions should definitely be coupled
together.

If we do a double pinhole experiment, then we would obtain a complicated
2-dimensional interference pattern so perhaps going to the double slit
experiment where the phenomenon is essentially one dimensional is better.
But this switch should be justified to the student. (Or could we have a
vertical array of electron guns to match the vertical slits?)

What is it that the double slit case actually adds? Here I am not completely
certain and so am looking for clarification. With the single pinhole
experiment we might not be certain that the electrons do not have unique
trajectories. Couldn't all the electrons that hit a given spot have followed
a definite trajectory? So we might try to describe it by random but definite
trajectories. (On the other hand, wouldn't the diffraction itself imply
that the electron had sampled all parts of the pinhole and therefore could
not have a definite trajectory?) The double slit case, with the clear
physical separation, and the clear change when the second slit is opened
shows that the electron must know about both slits and therefore can't be
given a definite trajectory. Also the interference pattern with its null
points is a more dramatic demonstration of wavelike character. But is this
just a clearer indication or is there something essential about the double
slit case that is not contained in the single pinhole case?

Thanks in advance for any comments.

David Park
djmp@xxxxxxxxxxxxx
http://home.earthlink.net/~djmp/

.

Relevant Pages

  • Re: Is a fact something that has been proven?
    ... There's nothing there at all about a double slit experiment ... A single electron is not entangled with another, ... 1.TURN OFF THE ELECTRON DETECTORS AT THE SLITS. ... An individual photon passing ...
    (talk.origins)
  • Re: Double Slit Puzzle Explained (?)
    ... Normally, when only one slit is open, the pattern on the plate is a ... let's look at where that radiation might come from. ... I believe the way an electron experiment is done is ... An electron is also a wave. ...
    (sci.physics.electromag)
  • Many-Worlds again
    ... The observer seems like he must be ... each electron goes through ... itself after it goes past the rock: ... through only either the monitored slit or the ...
    (soc.retirement)
  • Re: Double Slit Puzzle Explained (?)
    ... shone at a solid thin plate that has two slits cut into it. ... Normally, when only one slit is open, the pattern on the plate is a ... where that radiation might come from. ... I believe the way an electron experiment is done is ...
    (sci.physics.electromag)
  • Re: Double Slit Puzzle Explained (?)
    ... Normally, when only one slit is open, the pattern on the plate is a diffraction pattern, a fairly narrow central band with dimmer bands parallel to it on each side. ... Since the mechanism for recording these "baffling" events is photographic plates, and since the plates are sensitive to radiation, let's look at where that radiation might come from. ... I believe the way an electron experiment is done is that it is actually an electron hitting the detection "plate" that is recorded. ... So it will morph -- on impact -- into a wave that just happens to have the exact pattern of peaks and valleys as would have formed if another electron had simultaneously gone through the other slit. ...
    (sci.physics.electromag)