Hilbert and the Foundations of Physics

Abstract

In his major work (1968, III), Kronecker referred to Kirchhoff’s mechanism as a model of a scientific theory for its simplicity and completeness, attributes he claimed for his own general arithmetic. The same Kirchhoff furnished to Hilbert a radiation theory for his early work on foundations of physics (Hilbert, 1965, III, 217–257). What we call now Kirchhoff’s law on the equality between rates of emission and absorbtion of energy in thermal equilibrium is indeed a good example of a physical domain that should be investigated in view of the consitency of its axioms. One is reminded here that Hilbert had made of this question already in 1900 the sixth problem of his list « The mathematical treatment of the axioms of physics ». Hilbert names probability theory and mechanics as the two privileged domains of such interpretations. The central problem in physical theories is still the consistency problem, because a fundamental physical theory proceeds like geometry from general axioms to more specific ones and the extension from the first principles to the secondary ones must preserve consistency. Consistency is not a matter of feeling or experimentation, but of logic, Hilbert insists, and the extension of the theory of thermal radiation to elementary optics is possible only on the grounds of consistency.