Review of Jeff Bub’s Bananaworld: Quantum mechanics for Primates

Jeffrey Bub is one of the most distinguished philosophers of quantum mechanics writing today. His first book on the subject, The Interpretation of Quantum Mechanics, was published more than forty years ago, and he has written many works on the subject since, including the Lakatos Prize winning Interpreting the Quantum World in 1997. His latest book presents a wealth of material that has emerged in the last fifteen years related to the explanation of the central aspect of quantum mechanics as we understand it today: entanglement. A novel pedagogic device in the book is provided by an analogy to two different ways of peeling a banana, with a consequent difference in how it tastes. On the basis of this analogy there are some wonderful illustrations of a Carrollian bent — Tenniel himself would have been proud! I’ll come back to the analogy in the course of the essay.

There are two properties that quantum mechanics (henceforth QM) satisfies: 1) there is no superluminal signalling (NS); and 2) the observables can be contextual (C). Combined with the well known fact — a result of Bell’s theorem — that the predictions of QM cannot be reproduced by a non-contextual hidden variable theory (NCHV) and it follows that QM is non-local. From non-locality and (NS) it follows that QM cannot be fully deterministic. But — and this is the first surprise — principles (NS) and (C) do not uniquely delimit the set of correlations to just those predicted by QM. There are supra-quantal non-local correlations that are non-physical (as far as we know) which satisfy (some neutrally formulated) version of (NS) and (C). Thus (NS) and (C) are necessary but not sufficient for QM. The task then, as it is now formulated, is to find the underlying principles that distinguish QM not just from classical physics, but also from supra-quantal ‘physics’.

The upper bound of QM has been known for a long time, since 1980: it is called the Tsirelson bound (from Cirel’son (1980)). In 1994 Sandu Popescu and Daniel Rohrlich devised a set of correlations that exceed the Tsirelson bound but that satisfy (NS) and non-locality (Popescu and Rohrlich  (1994)). This showed that what was above the Tsirelson bound was at least something that could be described consistently. But were there principles that would naturally rule out such supra-quantal correlations as unphysical, and does any of this shine a brighter light on QM itself? Why is our world not more non-local than it is? Or more indeterministic? These are the questions with which Bub’s book is concerned….

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