A short technical comment on Bub's There is No Quantum World (arXiv:2512.18400v2) and a brief remark on related Grangier's reply (arXiv:2512.22965v1)

TL;DR

This paper provides a technical review of Bub's work on quantum foundations, identifying a mathematical slip and suggesting clarifications on topics like infinite tensor products, without critiquing interpretive goals.

Contribution

It offers a detailed mathematical critique and clarifications of Bub's arguments, emphasizing the importance of precise mathematical language in quantum foundations.

Findings

Identified a mathematical slip related to the Continuum Hypothesis

Suggested clearer wording for discussions on infinite tensor products and measurement updates

Clarified the distinction between mathematical constraints and interpretive choices

Abstract

This note is a friendly technical check of Jeffrey Bub's There is No Quantum World (arXiv:2512.18400v2). I flag one unambiguous mathematical slip (a cardinality identity that implicitly assumes the Continuum Hypothesis) and then point out a few places where the discussion of infinite tensor products, ``sectorization,'' and measurement updates would benefit from sharper wording. Nothing here is meant as a critique of Bub's interpretive goals; the aim is simply to separate what is mathematically forced from what depends on choices of algebra, representation, or philosophical stance. I end with a short remark on Philippe Grangier's reply (arXiv:2512.22965v1).