The mathematical basis for physical laws (Q816144)

The author proposes a unified mathematical treatment for physical laws of classical mechanics, quantum mechanics, classical electrodynamics, gravitation and relativity theory based solely on the existence of a joint probability distribution for the position and velocity of a particle moving on a Riemannian manifold. Within this framework the author is able to incorporate gravitation in special relativity theory, providing an alternative to general relativity theory. One of the weak points of such a proposal is its use in quantum theories. In the case of quantum mechanics, for example, such an approach is necessarily committed to Bohmian-like theories, which is a serious constraint. The case of quantum electrodynamics is even not discussed. The main ideas of the paper are really interesting, but many important questions should be answered. For example, what about thermodynamics? Can be this theory embodied within such a geometrical framework?