Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by a probability distribution. The corresponding configuration space is a statistical manifold the geometry of which is defined by the information metric. The trajectory follows from a principle of inference, the method of Maximum Entropy No additional “physical” postulates such as an equation of motion, or an action principle, nor the concepts of momentum and of phase space, not even the notion of time, need to be postulated. The resulting entropic dynamics reproduces the Newtonian dynamics of any number of particles interacting among themselves and with external fields. Both the mass of the particles and their interactions are explained as a consequence of the underlying statistical manifold.
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13 November 2007
BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: 27th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering
8–13 July 2007
Saratoga Springs (NY)
Research Article|
November 13 2007
From Information Geometry to Newtonian Dynamics
Ariel Caticha;
Ariel Caticha
Department of Physics, University at Albany‐SUNY, Albany, NY 12222, USA
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Carlo Cafaro
Carlo Cafaro
Department of Physics, University at Albany‐SUNY, Albany, NY 12222, USA
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AIP Conf. Proc. 954, 165–174 (2007)
Citation
Ariel Caticha, Carlo Cafaro; From Information Geometry to Newtonian Dynamics. AIP Conf. Proc. 13 November 2007; 954 (1): 165–174. https://doi.org/10.1063/1.2821259
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