In [[physics]], '''Canonical conjugate variables''' in [[physics]] are pairs of variables that share an [[uncertainty principle|uncertainty relation]]. The terminology comes from classical [[Hamiltonian mechanics]], but also appears in [[quantum mechanics]] and engineering.
Examples of canonically conjugate vairables include the following:
*time Time and frequency: the longer a musical note is sustained, the more precise we know its frequency (but it spans more time). Conversely, a very short musical note becomes just a click, and so weone can't know very accurately its frequency very accurately.
* Position and momentum: precise measurements of position lead to ambiguity of momentum, and v.v.
*position and momentum
* [[dopplerDoppler]] and range: the more we know about how far away a [[radar]] target is, the less we can know about the exact velocity of approach or retreat, and vice versa. In this case, the two dimensional function of doppler and range is known as a [[radar ambiguity function]] or '''radar ambiguity diagram'''.
In [[quantum mechanics]], the term denotes a pair of [[observable]]s whose [[operator]]s do not commute.
A more precise [[mathematical]] definition, in the context of [[Hamiltonian mechanics]], is given in the article [[canonical coordinates]].
