wrote a very short dissertation in which he put forth the novel idea that
matter could also have wavelike qualities. The core of his dissertation was
a single equation expressing a simple relation between the particle’s
wavelength (obviously a wave property) and its momentum (a particle
property). In 1927, this was experimentally confirmed, and de Broglie re-
ceived the Nobel Prize in 1929.
To get a feel for this remarkable idea, imagine that we adjust the paint
sprayer we described earlier so that the paint particles come out in a
straight line, and very slowly—maybe one lonely particle of paint every few
seconds. We aim this paint sprayer at the double-slit array, and after wait-
ing for an agonizingly long period of time, look behind the slits to see
what the rear piece of cardboard looks like. To no one’s great surprise,
it looks basically like it did when we turned the paint sprayer on full
blast—two blobs with diffuse edges centered behind each of the two slits.
Perform this exact same experiment using, instead of a paint sprayer, an
electron gun firing electrons instead of paint particles (and using a detec-
tor that records the impact of an electron by illuminating a pixel at the
point of impact), and something weird and totally unexpected (well, except
possibly by de Broglie) happens. Instead of seeing two blobs of light with
diffuse edges, we see alternating dark patches and light patches—the sig-
nature of wave interference. The conclusion is inescapable—under these
circumstances, the electron behaves like a wave. Matter, like light, some-
times behaves like a particle, sometimes like a wave.
Split Decisions—Experiments with Beam Splitters
A number of intriguing experiments in this area are conducted with
beam splitters. Imagine that a photon starts its journey at home plate of
a baseball diamond and hits a double, sliding into second base. In this
experiment, however, the photon can get to second base via the usual
route—going to first base and then to second—or by a path which in
baseball would get the batter declared out—by going to third base and
then to second. This is the modern version of the double-slit experiment.
There is a light detector behind second base that records the impact of the
photon, just as before; the paths that the photons can follow converge at
second base so that wave interference, if it exists, can be detected. The
beam splitter sends the photon by one of the two routes, via first or third
base, and does so randomly but with equal probability of going via either
route. In this variation, the light detector reveals interference patterns, as
did the double-slit experiment; the photons are acting as waves.
Now change the experiment a little. Place a photon detector in the first-
50 How Math Explains the World