Interpreting the quantum world, by Jeffrey Bub

Asher Peres

This is an "Essay-Review" of a book with the same title, by Jeffrey Bub (Cambridge University Press, 1997).

Kaj Börge Hansen

Krzysztof Sienicki

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).

Jeffrey Bub

Philippe Grangier

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.