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 quantum phenomena 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.