What principle of quantum mechanics says you cannot know both position and momentum exactly?

The uncertainty principle states that position and momentum cannot both be known with unlimited precision at the same time. In quantum mechanics, the uncertainties obey ΔxΔp ≥ ħ/2, so sharpening the knowledge of one quantity necessarily limits the precision of the other.

Werner Heisenberg introduced the principle in 1927 while developing quantum mechanics. It is not simply a flaw in measuring equipment or a consequence of clumsy observation. Position and momentum are represented by noncommuting operators, meaning quantum states cannot generally assign both properties exact, simultaneous values.

One useful picture comes from wave behavior. A particle localized into a narrow wave packet requires combining many wavelengths, and those wavelengths correspond to a range of momenta. A wave with one precisely defined momentum, by contrast, is spread out in position. This relationship is mathematically connected to Fourier transforms.

The principle is easy to confuse with the observer effect, in which a measurement physically disturbs a system. Disturbance can occur, but the uncertainty principle is more fundamental: even an ideal preparation of a quantum state has limits on the joint precision of position and momentum. Similar uncertainty relations apply to other pairs of quantum observables.