Foundations of quantum theory

M. A. B. Whitaker

David Geoffrey Holdsworth

In this paper I shall outline a possibility for incorporating category theory in an essential way into the foundations of quantum theory. The role for category theory which I shall sketch here is strictly foundational in the sense that it offers no new perspectives for a physicist working within the quantum formalism, but rather provides a way of interpreting the algebraic structure by giving an alternative axiomatization of the underlying logic of the theory. The axiomatization is given without recourse to any classical set theory by invoking methods closely connected with the work of F. W. Lawvere. More precisely, then, a possible approach to the foundations of physics which axiomatizes its algebraic structure in a way which is independent of set theory and hence points, as it were, to a structuralist foundation of physical theories, will be proposed.

Alfred Landé, E. Richard Cohen

Alexei Grinbaum

A paradigmatic shift in the foundations of quantum mechanics is recorded, from interpreting to reconstructing quantum theory. Examples of reconstruction are analyzed, and conceptual foundations of the information-theoretic reconstruction developed. A concept of intentionally incomplete reconstruction is introduced to mark the novel content of research in the foundation of quantum theory.

D. I. Blokhint︠s︡ev

Tina Bilban

Zeilinger-Brukner's informational foundations of quantum theory, a theory based on Zeilinger's foundational principle for quantum mechanics that an elementary system carried one bit of information, explains seemingly unintuitive quantum behavior with simple theoretical framework. It is based on the notion that distinction between reality and information cannot be made, therefore they are the same. As the critics of informational foundations of quantum theory show, this antirealistic move captures the theory in tautology, where information only refers to itself, while the relationships outside the information with the help of which the nature of information would be defined are lost and the questions "Whose information? Information about what?" cannot be answered. The critic's solution is a return to realism, where the observer's effects on the information are neglected. We show that radical antirealism of informational foundations of quantum theory is not necessary and that the return to realism is not the only way forward. A comprehensive approach that exceeds mere realism and antirealism is also possible: we can consider both sources of the constraints on the information, those coming from the observer and those coming from the observed system/nature/reality. The information is always the observer's information about the observed. Such a comprehensive philosophical approach can still support the theoretical framework of informational foundations of quantum theory: If we take that one bit is the smallest amount of information in the form of which the observed reality can be grasped by the observer, we can say that an elementary system (grasped and defined as such by the observer) correlates to one bit of information. Our approach thus explains all the features of the quantum behavior explained by informational foundations of quantum theory: the wave function and its collapse, entanglement, complementarity and quantum randomness. However, it does so in a more comprehensive and intuitive way. The presented approach is close to Husserl's explanation of the relationship between reality and the knowledge we have about it, and to Bohr's personal explanation of quantum mechanics, the complexity of which has often been missed and simplified to mere antirealism. Our approach thus reconnects phenomenology with contemporary philosophy of science and introduces the comprehensive approach that exceeds mere realism and antirealism to the field of quantum theories with informational foundations, where such an approach has not been taken before. Quanta 2014; 3: 32–42.