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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Frieden, B. R.: 1992,Phys. Lett. A,169, 123
Risken, H.: 1984,The Fokker-Planck Equation, (Springer-Verlag, New York), p. 133
Frieden, B. R.: 1989,Am. J. Phys.,57, 1004
Frieden, B. R.: 1990,Phys. Rev. A,41, 4265
Frieden, B. R.: 1993,Phys. Rev. A,198, 262
Frieden, B. R.: 1994,Phys. Rev. E,49, 2644
Frieden, B. R. and Cocke, W. J.: 1996,Phys. Rev. E,54, 257
Frieden, B. R.: 1995,Adv. in Imaging and Electron Phys.,90, (Acad. Press, Orlando), p. 123
Frieden, B. R. and Soffer, B. H.: 1995,Phys. Rev. E,52, 2274
Cocke, W. J. and Frieden, B. R.: 1996, inClassical and Quantum Gravity, under review
Frieden, B. R. and Soffer, B. H.: 1996,Phys. Rev. E, under review
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Frieden, B.R. Fisher information as a measure of time. Astrophys Space Sci 244, 387–391 (1996). https://doi.org/10.1007/BF00642309
Issue Date:
DOI: https://doi.org/10.1007/BF00642309