Inquiries into foundations of quantum physics

Alexandru Baltag, Sonja Smets

In this paper we show how ideas coming from two areas of research in logic can reinforce each other. The first such line of inquiry concerns the “dynamic turn” in logic and especially the formalisms inspired by Propositional Dynamic Logic (PDL); while the second line concerns research into the logical foundations of Quantum Physics, and in particular the area known as Operational Quantum Logic, as developed by Jauch and Piron (Helve Phys Acta 42:842–848, 1969 ), Piron (Foundations of Quantum Physics, 1976 ). By bringing these areas together we explain the basic ingredients of Dynamic Quantum Logic, a new direction of research in the logical foundations of physics.

Toyoki Koga

Charles E. Burkhardt, Jacob J. Leventhal

Richard Dawid

Abstract Physics and mentality are most often understood to be paradigmatically separate fields of inquiry. The foundational debate has a long history of attempts, however, to introduce aspects of mentality into physical analysis. In the context of Everettian quantum mechanics considerations of this kind play out in a different way than in collapse theories. This paper reviews some of those thoughts.

C. Piron

John Skilling, Kevin H. Knuth

As physicists, we wish to make mental models of the world around us. For this to be useful, we need to be able to classify features of the world into symbols and develop a rational calculus for their manipulation. In seeking maximal generality, we aim for minimal restrictive assumptions. That inquiry starts by developing basic arithmetic and proceeds to develop the formalism of quantum theory and relativity.