Attempt of an axiomatic foundation of quantum mechanics and more general theories, II

Abstract

The consequences of an axiomatic formulation of physical probability fields established in a first paper [1] are investigated in case of a finite dimensional ensemble-space.

It will be shown that the stated number of axioms can be diminuished essentially. Further the structure of an ortho-complemented orthomodular lattice for the decision effects (also often called “properties” or still more misunderstandingly “propositions”) and the orthoadditivity of the probability measures upon this lattice, both, can be essentially inferred from the axioms 3 and 4,only. This seems to give a better comprehension of the lattice structure defined by the decision effects.

Particularly, it is pointed out that no assumption (axiom) concerning the commensurability of two decision effectsE ₁ E ₂ withE ₁≦E ₂ must be made but that this commensurability is a theorem of the theory.