3.4 Heisenberg’s uncertainty principle
One of the fundamental consequences of the wave nature of matter is known as Heisenberg’s uncertainty principle. There are limits to what can be definitively known about certain pairs of physical properties of a particle. The most commonly used example is the position and the momentum of a particle: the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. You can know either one of them reasonably precisely while having very little information on the other, or you can know both approximately. This is linked to the final complication discussed about the double-slit experiment earlier – if you try to determine the position of the electron by detecting which slit it passes through, you affect its momentum and destroy the interference pattern.
Heisenberg’s uncertainty principle, then, puts a fundamental limit on what we can know. And there are other strange consequences. One of these is known as the ‘zero-point energy’ or ‘zero-point motion’. If you put an electron into a very small box, then its position is determined up to the size of the box. Its momentum has an uncertainty that directly relates to the size of the box: the smaller the box, the larger the uncertainty in momentum, and the quicker the electron will move around in the box.
A similar consequence is that in the ground state (lowest energy state) of a hydrogen atom (the simplest atom consisting of a single proton as its nucleus and an electron), the electron is not sitting on the atomic nucleus, but is moving in a region close to the nucleus. You can estimate the lowest energy from the uncertainty principle alone. More precisely, quantum theory will determine the energy as well as the probability to find an electron at a given distance from the nucleus at any one time. Unlike the planets in our solar system orbiting the sun, the electron does not stay on a circular or elliptical orbit, but can, with a certain probability, be found over a range of distances.