Warped Passages - Lisa Randall [66]
Figure 43. An example of a probability function for an electron.
Even though you map out the wave with many electrons, what makes quantum mechanics special is that an individual electron is nonetheless described by a wave. That means you can never predict everything about that electron with certainty. If you measure its location, you will find it in a definite spot. But until you make that measurement, you can predict only that the electron has a particular probability of winding up there. You can’t say definitively where it will end up.
This particle-wave dichotomy is revealed in the famous double-slit experiment that Electra’s unknown origin in the opening story referred to.11 Until 1961, when the German physicist Claus Jonsson actually performed it in the lab, the electron double-slit experiment was merely a thought experiment that physicists used to elucidate the meaning and consequences of the electron wavefunction. The experiment consists of an electron-emitter that sends electrons through a barrier pierced by two parallel slits (see Figure 44). The electrons pass through the slits and hit a screen behind the barrier, where they are recorded.
Figure 44. Schematic arrangement of the double-slit electron interference experiment. Electrons can go through either of two slits before they hit a screen. The wave pattern that is recorded on the screen is a result of the interference of the two paths.
This experiment was meant to mimic a similar experiment that demonstrated the wavelike nature of light in the early nineteenth century. At that time, Thomas Young, a British physician, physicist, and Egyptologist,* sent monochromatic light through two slits and observed the wavelike pattern that light made on a screen behind the slits. The experiment demonstrated that light behaved like a wave. The point of imagining the same experiment with electrons is to see how you might observe the electron’s wavelike nature.
And indeed, if you were to perform the double-slit experiment with electrons, you would see what Young saw for light: a wavelike pattern on the screen behind the slits (see Figure 45). In the case of light, we understand that the wave is caused by interference. Some of the light goes through one slit and some of it goes though the other, and the wave pattern that is then recorded reflects the interference between the two. But what does a wavelike pattern mean for electrons?
The wavelike pattern on the screen tells us the very unintuitive fact that we should think of each electron as passing through both slits. You can’t know everything about an individual electron. Any electron can pass through either slit. Even though each electron’s location gets recorded when it reaches the screen, no one knows which of the two slits any individual electron passed through.
Quantum mechanics tells us that a particle can take any possible path from its starting point to its endpoint, and the wavefunction for that particle reflects this fact. This is one of the many remarkable features of quantum mechanics. Unlike classical physics, quantum mechanics does not assign a particle a definite trajectory.
Figure 45. The interference pattern that is recorded in the double slit experiment. The four panels on the left show, clockwise from the top left, the pattern seen after 50, 500, 5, 000, and 50, 000 electrons have been shot through. The curves on the right compare the distribution of the number of electrons (upper curve) to the pattern you would get for a wave that passes through the two slits. They are nearly identical, which shows that the electron wavefunction does in fact act like a wave.
But how can the double-slit experiment indicate that an individual electron acts like a wave, when we already