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

TL;DR

This paper defends the use of mathematical infinities in quantum theory and clarifies misunderstandings about the transition between classical and quantum physics, supporting neo-Bohrian interpretations.

Contribution

It argues that incorporating infinities in physical theories is valid and clarifies misconceptions about the classical-quantum relationship in neo-Bohrian views.

Findings

Mathematical infinities can be properly integrated into physical theories.

Misunderstandings about the transition from classical to quantum physics are clarified.

Supports the validity of neo-Bohrian interpretations in quantum mechanics.

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.