Abstract

We introduce the mathematical structure PES (preparation-effect structure), which is capable of a physical interpretation thus making the five axioms of PES physically plausible. In this way, PES can be considered a general mathematical structure that underlies many physical theories. We then introduce four more axioms to obtain a more specific structure [the pure states (PS) complete orthogonality (OG) PES satisfying the covering law]. This more specific structure can be considered as the basic mathematical structure for quantum physics (QP). We show that some definitions and results pertaining to different axiomatic approaches to QP can be interpreted into a PES. (This allows a better comparison of the approaches.) In particular, we consider the Jauch-Piron (JP) approach to QP, reformulate it to make it completely axiomatical thus distinguishing between a basic underlying mathematical structure [i.e., the question-preparation structure (QPS)] and its specific mathematical structure (i.e., the JP QPS), and show that it can be completely interpreted into a PS complete OG PES satisfying the covering law.