In 1927 the German physicist Werner Heisenberg (1901–1976) showed that quantum mechanics leads to the conclusion that certain pairs of quantities can never be measured simultaneously with arbitrarily high precision, even with perfect measuring instruments. For example, it is not possible to measure the position and the momentum of a particle with unlimited precision. If one denotes the uncertainty in the measurement of its position by Δ x and the uncertainty in its momentum by Δ p then Heisenberg's Uncertainty Principle states that the axioms of quantum mechanics require that


where h is Planck's constant
(h = 6.626 068 76 × 10^-34 Js).

The Uncertainty Principle is often presented as a manifestation of the fact that the act of measurement...