What it shows:
In the Heisenberg uncertainty relation, the momentum of a particle cannot be known with any greater accuracy than h/∆x where h is Planck's constant and ∆x is the uncertainty in spatial position. The more you localize its spatial position, the less certain you become about its momentum. An optical illustration for this is the diffraction of light though a slit.
How it works:
For a laser beam, the transverse momentum is pretty well known (i.e. it's zero) but you have no localization of its spatial x coordinate. You can localize it spatially, by passing the beam through a slit, but by doing this you become uncertain about your x momentum. The more you localize spatially by closing down the slit, the more uncertain becomes the momentum. This manifests itself in a broadening of the diffraction pattern in the x direction which means that you've given the photons some momentum ∆px that wasn't there before (see figure 1).
figure 1. Schematic illustration of single slit diffraction
Setting it up:
Mount a HeNe laser on an optics bench, with an adjustable slit about 20cm in front of it. The resulting pattern can be projected onto a screen. With the lights down it should be visible to the audience.
Interesting slant on a diffraction demonstration primarily used to show the wave nature of light.