Comment on "There is No Quantum World" by Jeffrey Bub

TL;DR

The paper defends the legitimacy of mathematical infinities in physics and advocates a Contexts, Systems and Modalities (CSM) ontology in which quantum systems siempre reside within classical contexts. By leveraging von Neumann's infinite tensor product and the associated tail algebra, it shows how sectorization encodes macroscopic definiteness and stabilizes classical records, while still recovering standard quantum mechanics via Gleason-Uhlhorn. This framework unifies quantum and classical descriptions within an operator-algebraic setting, offering a robust realist interpretation based on contextual objectivity rather than classical reductionism. The approach clarifies the measurement problem by tying definite outcomes to macroscopic contexts and suggests fruitful directions for foundational research into quantum-classical structure and interpretation.

Abstract

In a recent preprint [1] Jeffrey Bub presents a discussion of neo-Bohrian interpretations of quantum mechanics, and also of von Neumann's work on infinite tensor products [2]. He rightfully writes that this work provides a theoretical framework that deflates the measurement problem and justifies Bohr's insistence on the primacy of classical concepts. But then he rejects these ideas, on the basis that the infinity limit is "never reached for any real system composed of a finite number of elementary systems". In this note we present opposite views on two major points: first, admitting mathematical infinities in a physical theory is not a problem, if properly done; second, the critics of [3,4,5] comes with a major misunderstanding of these papers: they don't ask about "the significance of the transition from classical to quantum mechanics", but they start from a physical ontology where classical and quantum physics need each other from the beginning. This is because they postulate that a microscopic physical object (or degree of freedom) always appears as a quantum system, within a classical context. Here we argue why this (neo-Bohrian) position makes sense.