As you have probably guessed, the best measurement to exemplify wave-particle duality in matter is the good old double-slit experiment. If a beam of electrons is directed through a pair of narrow slits (where the spacing between the slits is comparable to the de Broglie wavelength of the electrons), peculiar things begin to happen.
When Thomas Young performed his double slit experiment with light, he needed a way to detect or observe the intensity of the light on some sort of screen positioned some distance from the slits. In a dark room, he could just observe the intensity pattern with his eyes, but even better would be to expose a photographic plate, for example, and thus make a record of the measurement. When he did so, as you’ll recall, a whole series of stripes appeared downstream, something we called a diffraction pattern. It wasn’t just two bright bars, one for each slit, as you would expect if the light only traveled in straight lines.
Young correctly interpreted the series of bright and dark lines as constructive and destructive interference of light waves. The two slits acted as two sources of light waves with the same wavelength. Different locations on the screen corresponded to different angles with respect to the original direction of the light. At different angles the different distances from the two slits led to either constructive (bright line) or destructive (dark line) interference.
Returning to our humble electrons, we’ll need a photographic plate or some other kind of electron detector located in the plane where Young’s screen was. Instead of the brightness of light, we detect the arrival of individual electrons at the “screen.”
We know that electrons are discrete particles, each with the same definite mass. We can think of the electron beam as being like a stream of identical bullets fired from a very fast machine gun. In fact, devices that produce such beams are often called “electron guns.” For two slits separated by a distance much larger than the de Broglie wavelength, the electrons that pass through the slits would pile up in two locations on the screen, directly in line with the two slits. But if those slits are brought close enough together, that is not what we observe. Instead, the electrons strike the screen in a different, more complicated pattern.
If we send a large number of electrons through the two slits and keep track of where they all hit the screen, we see they tend to hit more often at certain locations, and are never seen at others. When we graph the number of hits vs. location, the pattern of peaks and valleys looks exactly like the diffraction pattern that Young observed for light! The bright lines correspond to areas with a high probability for electrons to land, and the dark spaces in between correspond to areas where electrons never hit.
This is a schematic of the electron double-slit experiment. On the screen downstream, bright stripes will emerge where the waves interfere constructively, darkness will prevail where the waves interfere destructively.
The amazing thing is that the pattern of hits with two slits open simultaneously is nothing like the sum of the patterns from the two slits if only one is open at a time. If only one slit is open at a time, the electrons tend to strike the screen most often directly in line with the open slit, and there is practically no interference. The peak in the electron probability is spread somewhat wider than the slit, which can be explained by scattering from the edges, but is otherwise unremarkable.
This exact experiment was not actually performed with electrons until 1961, but even as a thought experiment, it was and is extremely helpful for understanding the nature of matter on a small scale. At the instant we detect an electron arriving at the screen, we can know its location very precisely (assuming a good detector) and it doesn’t look very wavelike. Yet interference is happening before its arrival, influencing the probability of where each electron will be detected.
As more and more electrons pass through the two slits, the revealing interference pattern slowly emerges.
The observed behavior doesn’t depend on the rate at which electrons are passing though the slits, either. Slow down the rate, and it takes longer for the pattern to develop, but it is the same pattern of peaks and dips in the likely places for electrons to hit. You can make it so slow that only one electron at a time is anywhere near the slits, and you still get interference and a diffraction pattern. It means that a single electron is actually interfering with itself, and must be somehow present at both slits on its way to the detector.
In some strange way, electrons must be both particles and waves at the same time. This is very difficult for us to imagine, but it’s the way that nature works. Since the scale of the subatomic world is so far removed from everyday objects, maybe it is not too surprising that electrons and protons don’t behave much like billiard balls.
The wavelike nature of electrons does provide the key to the existence of stable energy states of atoms, as de Broglie and others suspected. But we will have to explore the nature of these matter waves a bit further before we can see how that is manifest.
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