Mathematical Constraint on Realistic Theories

We consider realistic theories in which some physical property f(r,t) is assumed to exist regardless of whether or not we measure it. It is shown that the value of f(r,t) at position r and time t is completely determined by its value at all other locations r$'$ and earlier times t$' <$ t provided that f(r,t) has continuous second partial derivatives [1]. Mathematical functions of this kind are sufficiently general to describe many situations of physical interest. These results are based on a mathematical identity that is similar in some respects to Cauchy's integral theorem and it can be viewed as a generalization of Green's third identity. The physical implications of weak determinism of this kind will be discussed and it will be contrasted with the properties of quantum systems. \\[4pt] [1] J.D. Franson, arXiv: 1007.1941.