Bananaworld: Quantum Mechanics for Primates by Jeffrey Bub (PDF)

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What on earth do bananas have to do with quantum mechanics? From a modern perspective, quantum mechanics is about strangely counterintuitive correlations between separated systems, which can be exploited in feats like quantum teleportation, unbreakable cryptographic schemes, and computers with enormously enhanced computing power. Schrodinger coined the term “entanglement” to describe these bizarre correlations. Bananaworld — an imaginary island with “entangled”bananas — brings to life the fascinating discoveries of the new field of quantum information without the mathematical machinery of quantum mechanics. The connection with quantum correlations is fully explained in sections written for the non-physicist reader with a serious interest in understanding themysteries of the quantum world. The result is a subversive but entertaining book that is accessible and interesting to a wide range of readers, with the novel thesis that quantum mechanics is about the structure of information. What we have discovered is that the possibilities for representing, manipulating, and communicating information are very different than we thought.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Great topic well presented.What I didn’t like was I thought I was ordering for my regular Kindle. I discovered too late it was not compatible with the Kindle Paperwhite so I am having to read on on the Kindle for PC.

⭐Let me start off with the main point. This book has the clearest explanation of entanglement and a variety of related topics from research in quantum foundations (e.g. contextuality) that I have ever read.The central strength of the book is that it approaches these topics looking at a fictitious world (the bananaworld of the title) where statistical correlations stronger than those in quantum mechanics are present, superquantum correlations as they are known.These correlations have all the same qualitative consequences as those found in quantum mechanics, but are mathematically much simpler, to the point where little formal mathematics is required.It begins with a brief motivation for the book and a review of the physics behind qubits in the first two chapters.Chapter 3 is where it properly begins with an account of the EPR and PR (Popescu-Rohrlich) correlations. The latter are the superquantum correlations mentioned above.The wonderful thing about the PR correlations is that they have a very simple form that can be summarized in a 2×2 array. The book then gives a discussion of Bell’s theorem. The incredible thing is that by using the PR correlations it becomes obvious as you read that for these types of correlations something like Bell’s theorem should be true. Many other accounts of the theorem, at least for me, often took the form of “Oh here’s a bound on local realist theories, oh look this quantum state violates it”. However with the PR correlations it’s obvious, you just can’t assign properties in a way that satisfies the 2×2 array.Chapter 4 then provides a version of the Colbeck-Renner theorem, or in the style of the book the “Really Random” nature of quantum theory. One sees that if the PR correlations were real then probability 0 or 1 assignments (i.e. determinism) are impossible, even when conditioned on any event in your past light cone! Once again via PR correlations this is obvious, avoiding the intricacies of the true quantum proof.Chapter 5 deals with classifying correlations (classical, quantum, superquantum). Setting up a question dealt with in chapter 9, why does our world specifically have quantum correlations and not more general ones? This is a strong anecdote to the often encountered claim that there are no generalizations of quantum theory that are non-pathological, which I don’t think is well enough known outside of Foundations research.Chapter 6 discusses contextuality. The use of the Aravind-Mermin correlations is well chosen here I think to show the tension with locality and provides a clear enough way to see that contextual theories would need to be nonlocal.Chapters 7 and 8 deal with topics in Quantum Information. Gems here are:(a) A cleaner explanation of the power of quantum computers, lying in their ability to deduce OR statements without evaluating the arguments, not “doing all parts of the computation at once”(b) By this point I think many will be searching for some reason for these correlations, some mechanism. Essentially it’s very hard not to imagine some nonlocal influence going on. A nice way of thinking about them is provided via Bub’s colleague Allen Stairs. It uses the lack of time ordering for spacelike events to argue that, for now, they are simply patterns in the world’s structure of events we have no explanation for and that typical ‘common cause’ or ‘causal influences’ are ruled out. This is sort of a culmination of a thread through the book: That Quantum theory is a revolution in the information structure of the universe, not directly a pictorial/representational account of phenomena.Chapter 9 deals with how we can characterize the quantum correlations. I especially recommend 9.2 and the discussion of the work of Cabello and Specker.(On a personal note, this chapter really reinforced the information theoretic picture for me. Cabello’s work aims to show quantum mechanics is simply what one gets when you allow all correlations consistent with a certain weak principle about measurements/macroevents. It really does seem the laws of nature don’t determine events, they simply guarantee certain relations/correlations between events, but anything consistent with those correlations may happen, i.e. they are about the information theoretic structure of the even tapestry of the world)Chapter 10 then presents Bub’s interpretation of quantum theory in light of all this. I’m not qualified to judge interpretations and think too many will focus on this section. It provides excellent food for thought and takes you up to recent work with the PBR and Frauchiger-Renner theorem.To sum up:(i) Uses superquantum correlations to make several fundamental aspects of QM more obvious, avoiding the intricacies of QM(ii) Via this it then covers a broad swath of Foundations researchIt left me in the position to actual comprehend what was going on in foundations research. I really can’t recommend it enough, it’s one of my new favorites up there with Gravitation and Weinberg’s QFT texts.

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