Going Further 11.1: Testing the Uncertainty Principle
The Heisenberg uncertainty principle is one of the more bizarre aspects of quantum mechanics, a fairly non-intuitive description of the world to begin with. Why should anyone believe any of the strange predictions of the theory? Well, nobody should believe them; scientists are forced to accept the strangeness of the theory because its predictions are borne out by experiment. The uncertainty principle is basic to quantum mechanics and affects all aspects of the theory, but it has two consequences that are particularly useful in demonstrating that the theory has merit.
One consequence of the uncertainty principle is the Lamb shift, a tiny shift in the energy level of the electron in a hydrogen atom. The shift is caused by the sort of quantum vacuum fluctuations associated with the production of virtual particle–antiparticle pairs as discussed for electrons and positrons. Even though any particle–antiparticle pair exists for a time that is too short to measure, new pairs are popping up (and then disappearing) all the time. These fluctuations of the vacuum perturb the electrons in an atom, gently shifting its energy—in effect, the hydrogen atom constantly absorbs and then re-emits virtual photons. Because the effect is averaged over many virtual particle pairs constantly appearing and disappearing, the energy shift looks like a slight broadening of the energy of an atomic orbital. Using the quantum theory of the electromagnetic interaction, called quantum electrodynamics (QED), it is possible to calculate the size of this broadening. In a hydrogen atom, the shift slightly separates the orbitals known as 2S1/2 and 2P1/2, which would otherwise have the same energy. The splitting was actually measured in 1947 before the theory of QED was fully developed. However, once the theory was available, its prediction for the splitting matched the observed amount to one part in a trillion. Or in other words, the theory matched the measurement to the eleventh decimal place, which is the limit of experimental precision. Such spectacular agreement between theory and experiment suggests that the notion of virtual particles is a valid description of nature, no matter the philosophical discomfort it might cause.
An additional verification of the quantum view of nature is the Casimir effect. In this experiment, two grounded conducting plates are placed very close together, in effect creating a region of space where only certain energy states of particles, including virtual particles, can exist. The reason is that quantum mechanics predicts that particles should have a wave-like nature in addition to their particle nature. The wavelength of a particle depends on its energy. Within an enclosed space, an even number of half-wavelengths must be able to fit. This is a bit like the vibrating string on a violin or guitar, which is fixed at both ends, as shown in Figure B.11.1. The restriction on wavelengths is a restriction on energy states of any particles within the space between the plates. Since any particle energies are possible outside the two plates, the exclusion of certain states between them causes a pressure difference between the inside and outside of the plates. As a result they are pushed together. This happens in accord with the predictions of quantum electrodynamics, just as the Lamb shift does.
