Fisher information as the basis for Maxwell's equations

B.Roy Frieden

Physica A: Statistical Mechanics and its Applications, 1992, vol. 180, issue 3, 359-385

Abstract: Maxwell's equations of classical electrodynamics may be derived on the following statistical basis. Consider a gedanken experiment whereby the mean space-time coordinate for photons in an electromagnetic field is to be determined by observation of one photon's space-time coordinate. An efficient (i.e. optimum) estimate obeys a condition of minimum Fisher information, or minimum precision, according to the second law of thermodynamics. The Fisher information I is a simple functional of the probability law governing space-time coordinates of the “particles” of the field. This probability law is modeled as the source-free Poynting energy flow density, i.e., the ordinary local intensity in the optical sense, or, the square of the four-vector potential. When the Fisher information is extremized subject to an additive constraint term in the total interaction energy, Maxwell's equations result.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:180:y:1992:i:3:p:359-385

DOI: 10.1016/0378-4371(92)90395-7

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