Edward MacKinnon

An epistemological interpretation of quantum mechanics hinges on the claim that the distinctive features of quantum mechanics can be derived from some distinctive features of an observational basis. Old and new variations of this theme are listed. The program has a limited success in non-relativistic quantum mechanics. The crucial issue is how far it can be extended to quantum field theory without introducing significant ontological postulates. A C*-formulation covers algebraic quantum field theory, but not the standard model. Julian Schwinger’s anabatic methodology extended a strict measurement-based formulation of quantum mechanics through field theory. His extension also excluded the quark hypothesis and the standard model. Quarks and local gauge invariance are postulates that go beyond the limits of an epistemological interpretation of quantum mechanics. The ontological significance ascribed to these advances depends on the role accorded ontology.

Philosophical interpretations of theories generally presuppose that a theory can be presented as a consistent mathematical formulation that is interpreted through models. Algebraic quantum field theory (AQFT) can fit this interpretative model. However, standard Lagrangian quantum field theory (LQFT), as well as quantum electrodynamics and nuclear physics, resists recasting along such formal lines. The difference has a distinct bearing on ontological issues. AQFT does not treat particle interactions or the standard model. This paper develops a framework and methodology for interpreting such informal theories as LQFT and the standard model. We begin by summarizing two minimal epistemological interpretation of non-relativistic quantum mechanics (NRQM): Bohrian semantics, which focuses on communicables; and quantum information theory, which focuses on the algebra of local observables. Schwinger's development of quantum field theory supplies a unique path from NRQM to QFT, where each step is conceptually anchored in local measurements. LQFT and the standard model rely on postulates that go beyond the limits set by AQFT and Schwinger's anabatic methodology. The particle ontology of the standard model is clarified by regarding the standard model as an informal modular theory with a limited range of validity.

In the course of his long development, Kant's concept of matter changed somewhat, while his concept of scientific explanation changed considerably. Both developments achieved a coherent integration in Kant's Metaphysical Foundations of Natural Science. Using this developmental background, the present paper argues that the Foundations should be interpreted as an attempted rational reconstruction of the mechanics of Newton and Euler. Kant attempted to do this by constructing a concept of matter that would confer a Leibnizian intelligibility on Newtonian mechanics, and also accord with Kant's theories on the nature of concepts and their role in scientific explanation.

One of the key interpretative problems generated by the development of quantum theory was the conceptual consistency underlying scientific change, a problem not adequately treated by any of the leading theories of scientific development. In different but related ways Quine, Sellars, and Davidson have treated the problem of conceptual consistency by showing how one can begin with ordinary language and proceed to specialized extensions. Their techniques have not been applied to modern physics. However, one basis for applying them arises from the deep similarities between some of the work of these analysts and the Copenhagen interpretation rightly interpreted. To make this more concrete three concepts whose meanings have changed as a result of scientific progress are considered: 'atom', 'state of a system', and 'particle'. Each functions in a different way and requires a different type of analysis.