In quantum physics, what principle states that position and momentum cannot both be known exactly?

In quantum physics, the Heisenberg uncertainty principle states that position and momentum cannot both be known exactly.

Werner Heisenberg introduced the principle in 1927. In its familiar form, the uncertainties in a particle’s position and momentum obey a mathematical lower bound, written as ΔxΔp ≥ ħ/2. This is not merely a limitation caused by imperfect instruments; it is a fundamental feature of quantum states.

A particle prepared with a very sharply defined position must have a wider range of possible momenta. Conversely, a state with a narrowly defined momentum is spread across position. The principle is especially important for microscopic particles such as electrons, whose wave-like behavior is significant.

A common mix-up is treating uncertainty as ordinary measurement error. Better instruments can reduce experimental error, but they cannot remove the quantum trade-off itself. Related uncertainty relations also apply to other pairs of observables, including certain components of angular momentum.