An Information Based Theory of Stationary Action and the Origin of Quantum Phenomena

The quantization of energy proposed by Planck to account for the observed spectrum of black body radiation has associated with it a quantization of entropy. This in turn implies a quantization of observable information, directly implying observational uncertainty on the order of Planck’s constant. The effect of that uncertainty is analyzed. In order to adhere strictly to the use of observable quantities, a probability measure is employed based on the distinguishability of statistical samples. This leads directly to the description of probability in terms of the absolute square of a complex amplitude. The Feynman rules may then be applied naturally for indistinguishable events without contradiction to the conventional rules for distinguishable events. This enables the straightforward calculation of the probability that a particle moves from one arbitrary point to another. The Feynman formulation of non-relativistic quantum mechanics and the principle of stationary action results when it is assumed that the classical action represents the measure of distinguishability. Parallel analysis on a Lorentz manifold yields the geodesic principle. The entropic nature of uncertainty allows for the existence of hidden underlying physical processes analogous to the way statistical physics underlies the continuum gas model. These processes may be deterministic but unobservable or they may simply not contain the necessary information to fully describe classical particle behavior. In either case the observer experiences them as random. Since we show the probabilistic nature of the problem to be a consequence of deficient information, we treat the amplitude as a representation of the state of available information about the physical state of the system rather than the physical state proper. In the Dirac von Neumann quantum model this constitutes the psi-epistemic viewpoint.