2. The Mathematical Formalism and the Standard Way of Thinking about It

Sisir Roy

Arkady Plotnitsky, Andrei Yu. Khrennikov, Gregg S. Jaeger +2 more

Beginning with its introduction by W. Heisenberg, quantum mechanics was often seen as an overly abstract theory, mathematically and physically, vis‐à‐vis classical physics or relativity. This perception was amplified by the fact that, while the quantum‐mechanical formalism provided effective predictive algorithms for the probabilistic predictions concerning quantum experiments, it appeared unable to describe, even by way idealization, quantum processes themselves in space and time, in the way classical mechanics or relativity did. The aim of the present paper is to reconsider the nature of mathematical and physical abstraction in modern physics by offering an analysis of the concept of “physical fact” and of the concept of “physical concept,” in part by following G. W. F. Hegel’s and G. Deleuze’s arguments concerning the nature of conceptual thinking. In classical physics, relativity, and quantum physics alike, I argue, physical concepts are defined by the following main features—1) their multi‐component multiplicity; 2) their essential relations to problems; 3) and the interactions between physical, mathematical, and philosophical components within each concept. It is the particular character of these interactions in quantum mechanics, as defined by its essentially predictive (rather than descriptive) nature, that distinguishes it from classical physics and relativity.

André Mercier, R. Bruce Lindsay

Arkady Plotnitsky

Beginning with its introduction by W. Heisenberg, quantum mechanics was often seen as an overly abstract theory, mathematically and physically, vis‐à‐vis classical physics or relativity. This perception was amplified by the fact that, while the quantum‐mechanical formalism provided effective predictive algorithms for the probabilistic predictions concerning quantum experiments, it appeared unable to describe, even by way idealization, quantum processes themselves in space and time, in the way classical mechanics or relativity did. The aim of the present paper is to reconsider the nature of mathematical and physical abstraction in modern physics by offering an analysis of the concept of “physical fact” and of the concept of “physical concept,” in part by following G. W. F. Hegel’s and G. Deleuze’s arguments concerning the nature of conceptual thinking. In classical physics, relativity, and quantum physics alike, I argue, physical concepts are defined by the following main features—1) their multi‐component multiplicity; 2) their essential relations to problems; 3) and the interactions between physical, mathematical, and philosophical components within each concept. It is the particular character of these interactions in quantum mechanics, as defined by its essentially predictive (rather than descriptive) nature, that distinguishes it from classical physics and relativity.

Edward Nelson