LAGRANGIANS OF PHYSICS AND THE GAME OF FISHER-INFORMATION TRANSFER

The Lagrangians of physics arise out of a mathematical game between a ''smart'' measurer and nature (personified by a demon). Each contestan t wants to maximize his level of Fisher information I. The game is zer o sum, by conservation of information in the closed system. The payoff of the game introduces a variational principle - extreme physical inf ormation (EPI)- which fixes both the Lagrangian and the physical const ant of each scenario. The EPI approach provides an understanding of th e relationship between measurement and physical law. EPI also defines a prescription for constructing Lagrangians. The prior knowledge requi red for this purpose is a rule of symmetry or conservation that implie s a unitary transformation for which I remains invariant. As an exampl e, when applied to the smart measurement of the space-time coordinate of a particle, the symmetry used is that between position-time space a nd momentum-energy space. Then the unitary transformation is the Fouri er one, and EPI derives the following: the equivalence of energy, mome ntum, and mass; the constancy of Planck's parameter h; and the Lagrang ian that implies both the Klein-Gordon equation and the Dirac equation of quantum mechanics.