Conjugate variables: Difference between revisions

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==Physics==

AIn [[physics]], '''conjugate variables''' are pair of variables mathematically defined in such a way that they become [[Fourier transform]] [[dual (mathematics)|duals]] of one-another, or more generally are related through [[Pontryagin duality]]. The duality relations lead naturally to an uncertainty ([[Heisenberg uncertainty principle]]) relation between them. A more precise [[mathematical]] definition, in the context of [[Hamiltonian mechanics]], is given in the article [[canonical coordinates]]. Examples of canonically conjugate variables include the following:

A more precise [[mathematical]] definition, in the context of [[Hamiltonian mechanics]], is given in the article [[canonical coordinates]].

===Examples===

Examples of canonically conjugate variables include the following:

* [[Time]] and [[frequency]]: the longer a musical note is sustained, the more precisely we know its frequency (but it spans more time). Conversely, a very short musical note becomes just a click, and so one can't know its frequency very accurately.

* [[Time]] and [[energy]] - as energy and frequency in [[Quantum Mechanics]] are directly proportional to each other.