Department of Physics and AstronomySwarthmore College, Swarthmore, Pennsylvania 19081AbstractA model for the interpretation of spacetime as a Weyl geometry is proposed, based on thehypothesis that a system moves on any given path with a probability which is inversely proportionalto the resulting change in length of the system. The results of physical measurements are calculatedas the product of Weyl-conjugate gauge dependent probabilities for the detection of conjugateobjects. Each probability, expressed as a Wiener integral, is the Green function for a diffusionequation. If the line integral of the Weyl field equals the action functional divided by +h , thisequation provides the stochastic equivalent of the Schrodinger equation, with expanding andcontracting states replacing the oscillating states of standard quantum theory. These dilatations arenot directly measurable within the theory, but the rates of expansion and contraction are. Weestablish the classical limit of the theory by proving that the most general form of the Weyl fieldwhich gives an extremum of the action is restricted to be of a special form. Particles obeying theequations of motion for these extremal Weyl fields experience no measurable dilatation. However,the Weyl field itself is classically detectable, and gives a correct description of the electromagneticinteraction of a point particle.Current address: Department of Physics, Utah State University, Logan, Utah 84322.