Physikalische Mathematik

Hilberts idea of a physical axiomatics: the analytical apparatus of quantum mechanics

Abstract

Yvon Gauthier

We discuss the Hilbert program for the axiomatization of physics in the context of what Hilbert and von Neumann came to call the analytical apparatus and its conditions of reality. We suggest that the idea of a physical logic is the basis for a physical mathematics and we use quantum mechanics as a paradigm case for axiomatics in the sense of Hilbert. Finite probability theory requires nite derivations in the measurement theory of QM and we give a polynomial formulation of local complementation for the metric induced on the topology of the Hilbert space. The conclusion hints at a constructivist physics.