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Springer eBooks

Mathematical structure of orthodox quantum theory and its relation to operationally definable physical principles

Rudolf Haag

Published Apr 6, 2008• 2 citations
Publisher
DOI
10.1007/3-540-11192-1_33

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In this paper we discuss the representational realist stance as a pluralist ontic approach to inter-theoretic relationships. Our stance stresses the fact that physical theories require the necessary consideration of a conceptual level of discourse which determines and configures the specific field of phenomena discussed by each particular theory. We will criticize the orthodox line of research which has grounded the analysis about QM in two (Bohrian) metaphysical presuppositions -accepted in the present as dogmas that all interpretations must follow. We will also examine how the orthodox project of "bridging the gap" between the quantum and the classical domains has constrained the possibilities of research, producing only a limited set of interpretational problems which only focus in the justification of "classical reality" and exclude the possibility of analyzing the possibilities of non-classical conceptual representations of QM. The representational realist stance introduces two new problems, namely, the superposition problem and the contextuality problem, which consider explicitly the conceptual representation of orthodox QM beyond the mere reference to mathematical structures and measurement outcomes. In the final part of the paper, we revisit, from a representational realist perspective, the quantum to classical limit and the orthodox claim that this inter-theoretic relation can be explained through the principle of decoherence.
We propose a preliminary mathematical framework for physical theories based on experimentally grounded constraints. A physical theory is represented as a structured object (S, O, D) consisting of a state space, a set of observables, and a dynamical law. We introduce constraint operators acting on the space of candidate theories, encoding symmetry, causality, quantum, and dynamical requirements. The space of physically admissible theories is defined as the intersection of constraint-defined subsets, leading to a constraint-based interpretation of physical laws as consistency conditions. This framework provides a unified mathematical perspective in which classical mechanics, relativity, and quantum theory can be understood as different realizations within a common structure. This work presents a preliminary but structured conceptual and mathematical framework.