Canonical conjugate variables in physics are pairs of variables that share an uncertainty relation. The terminology comes from Hamiltonian mechanics.
Examples include the following:
- 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, so we can't know very accurately its frequency.
- position and momentum
- doppler 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.
A more precise mathematical definition, in the context of Hamiltonian mechanics, is given in the article canonical coordinates.