What principle states you cannot simultaneously know a particle's exact position and momentum?

The Heisenberg uncertainty principle states that a particle's exact position and exact momentum cannot be known simultaneously. It is a fundamental limit built into quantum mechanics, not merely a restriction caused by imperfect instruments.

Position and momentum are mathematically linked quantities called conjugate variables. Their uncertainties obey a relation commonly written as ΔxΔp ≥ ħ/2, where ħ is the reduced Planck constant. Making a particle's position more precisely defined produces a broader range of possible momenta, while a sharply defined momentum corresponds to a more spread-out position.

Werner Heisenberg introduced the principle in 1927 during the development of modern quantum mechanics. The familiar microscope explanation, in which measuring position disturbs momentum, is useful but incomplete: the deeper origin is that the quantum operators for position and momentum do not commute.

A common mistake is to treat the principle as saying that every measurement is simply inaccurate. Instead, it describes the structure of quantum states themselves. Similar uncertainty relationships apply to other pairs of observables, including certain components of angular momentum.