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Proceedings Paper

Extreme physical information and the nonlinear wave equation
Author(s): B. Roy Frieden
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Paper Abstract

The nonlinear wave equation an be derived from a principle of extreme physical information (EPI) K. This is for a scenario where a probe electron moves through a medium in a weak magnetic field. The field is caused by a probabilistic line current source. Assume that the probability current density S of the electron is approximately constant, and directed parallel to the current source. Both the source probability amplitudes (rho) and the electron probability amplitudes (phi) are unknowns (called 'modes') of the problem. The net physical information K here consists of two components: functional K1[(phi) ] due to modes (phi) and K2[(rho) ] due to modes (rho) , respectively. To form K1[(phi) ], the Fisher information functional I1[(phi) ] for the electron modes is first constructed. This is of a fixed mathematical form. Then, a unitary transformation on (phi) to a physical space is sought that leaves I1 invariant, as form J1. This is, of course, the Fourier transformation, where the transform coordinates are momenta and I1 is essentially the mean-square electron momentum. Information K1[(phi) ] is then defined as (I1 - J1). Information K2 is formed similarly. The total information K is formed as the sum of the two components K1[(phi) ] and K2[(rho) ], by the additivity of Fisher information, and is then extremized in both (phi) and (rho) . Extremizing first in (rho) gives a Taylor series in powers of (phi) n*(phi) n, which is cut off at the quadratic term. Back-substituting this into the total Lagrangian gives one that is quadratic in (phi) n*(phi) n. Now varying (phi) * gives the required cubic wave equation in (phi) .

Paper Details

Date Published: 15 September 1995
PDF: 10 pages
Proc. SPIE 2528, Optical and Photonic Applications of Electroactive and Conducting Polymers, (15 September 1995); doi: 10.1117/12.219553
Show Author Affiliations
B. Roy Frieden, Optical Sciences Ctr./Univ. of Arizona (United States)

Published in SPIE Proceedings Vol. 2528:
Optical and Photonic Applications of Electroactive and Conducting Polymers
Sze Chang Yang; Prasanna Chandrasekhar, Editor(s)

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