Statistical Basis of Physical Laws

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Abstract
The premise that physical variables must be viewed as random variables, with observed values, assigned as averages over distributions, is shown to yield the formalisms of thermodynamics, Hamiltonian mechanics, and quantum theory. A general mathematical argument first establishes the validity of an embedding of th space of physical variables in a larger manifold of "hidden" variables and a general structure for the distribution of these variables. Then, by consideration of various ways of specifying the preparation of a system for measurement, the formalisms of physics cited above are deduced. It is also shown that the generalized Langevin equation follows from these premises and is applicable to a wide class of phenomena. This formulation yields a new definition for compatible observables as used in quantum theory and demonstrates, in a natural way, that physical laws should be invariant under orthogonal transformations of certain variables, which in one circumstance include the complex orthogonal transformations of the Lorentz form, as in special relativity. In summary, it appears that most of the formal structure of physical theory is a consequence of the statistical nature of physical variables.