Heisenberg, together with Max Born and Pascal Jordan, tried a totally different approach using mathematical matrices. As part of their work Heisenberg developed a principle that demonstrates that in the atomic world our knowledge is limited. The uncertainty principle is written as Δx Δp s=h/4π. In words, the uncertainty of a particle’s position times the uncertainty in its momentum is never less than Planck’s constant divided by 4π. If it has a precise location, then its momentum, and thus its speed (measured at the same time), must be imprecise. Planck’s constant is extremely small, and so the uncertainty principle is important only for objects the size of atoms or smaller. The position and momentum of a baseball, for example, can both be precisely known at the same time.

The uncertainty principle shows why Bohr’s electron orbits cannot exist. If you know the radius of the circle precisely, then it must have some velocity along the radius—smearing out its orbit. The uncertainty principle also exists in a form linking energy and time. In this form it says that if an electron is in a state that lasts for only a short time, then its energy is not precisely defined.