Fisher information as a measure of time |
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| Authors: | B R Frieden |
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| Institution: | (1) Optical Sciences Center, University of Arizona, 85721-0094 Tucson, Arizona |
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| Abstract: | Fisher informationI is a classical concept that originates in estimation theory. Through the Cramer-Rao inequality, it defines the smallest possible error in the estimation of a parameter in the presence of noise obeying a given probability law. More recently, Fisher information has been incorporated within a variational principle for forming the laws of physics (Schrödinger wave equation, Dirac equation, etc.). The premise is thatdI/dt 0, witht the time, so that, at equilibrium,I=min. The premise has recently been proven for any process obeying a Fokker-Planck differential equation. Hence, Fisher information provides a new measure of the passage of time. All errors of estimation increase, on average, with time. |
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