Conjugate pairs are pairs of properties to which the Heisenberg Uncertainty Principle applies. Conjugate pairs are also called “conjugate variables” or “incompatible observables.” The Heisenberg Uncertainty Principle says that some of the properties of atoms and the components of atoms have an inherent fuzziness. For example, it is not possible to discover with precision both the momentum and the position of a quantum particle simultaneously. Indeed, the particles do not have precisely defined momentum and position at the same time. To the degree that the position of a particle is precise, to that degree the momentum is imprecise. And vice versa. Position and momentum form a conjugate pair.

Further, if the momentum is measured and then, the position is measured, the original measurement of momentum is no longer accurate. This is because the particle will now have a new momentum. And vice versa: If the position is measured and then, momentum is measured, the position measurement will have been invalidated and rendered inaccurate due to the position having changed. In summary, we will get different measurements if we measure the momentum first than if we measure the position first.

The HUP applies to each individual particle.

Conjugate pairs may also be called “incompatible observables.” For more information, see the Heisenberg Uncertainty Principle.

Etymology: “Conjugate” means “joined together, especially in a pair…, coupled.” From the Latin con- (together) and jug (yoked).