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Conjugate variables are pairs of variables mathematically defined in such a way that they become Fourier transform duals of one another,〔(Heisenberg – Quantum Mechanics, 1925–1927: The Uncertainty Relations )〕〔(Some remarks on time and energy as conjugate variables )〕 or more generally are related through Pontryagin duality. The duality relations lead naturally to an uncertainty in physics called the Heisenberg uncertainty principle relation between them. In mathematical terms, conjugate variables are part of a symplectic basis, and the uncertainty principle corresponds to the symplectic form. ==Examples== There are many types of conjugate variables, depending on the type of work a certain system is doing (or is being subjected to). Examples of canonically conjugate variables include the following: * Lifetime 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 determine its frequency very accurately. * 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. * Surface energy: γdA (''γ'' = surface tension ; ''A'' = surface area). * Elastic stretching: FdL (''F'' = elastic force; ''L'' length stretched). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Conjugate variables」の詳細全文を読む スポンサード リンク
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