In a foreword to The Quantum Handshake, Carver Mead recalls Richard Feynman's verdict on Young's two-slit experiment and on quantum mechanics in general: “Nobody knows how it can be like that.” Mead himself is more optimistic. In fact, Feynman's quote came more than ten years after David Bohm had resurrected Louis de Broglie's pilot wave theory, providing at least a possible way of understanding the two-slit experiment. Bohm's theory gives an answer to the question “How can the world be for quantum mechanics to be true?” Answering this question is, I believe, precisely what is meant by interpreting quantum mechanics. The Copenhagen Interpretation, Everett's approach in its different guises and, more recently, Quantum Bayesianism, all propose their own answer to this fundamental question.

In a paper published 30 years ago in Reviews of Modern Physics [58, 647 (1986)], John G. Cramer suggested a different and original answer, which he called the Transactional Interpretation of quantum mechanics. The Quantum Handshake is an elaboration of this work, written for “the intelligent reader with some grasp of basic mathematics and a curiosity about quantum mechanics…” It enlarges upon the RMP paper with many topics that have developed in the past three decades, like quantum computing, interaction-free measurements, entanglement swapping, to name a few.

Inspired by the Wheeler-Feynman electrodynamic theory, the Transactional Interpretation (TI) postulates that the complex conjugate of a solution of the Schrödinger equation is just as important as the genuine solution. Both originate from a time-symmetric relativistic version of the Schrödinger equation (like the Klein-Gordon equation). In a quantum process like the emission and subsequent absorption of an alpha-particle, the solution of the Schrödinger equation is to be viewed as an “offer wave,” which propagates from the emitter to one or several potential absorbers. The absorbers respond by “confirmation waves,” i.e., the complex conjugate solutions, which propagate backward in time to the emitter. Cramer argues that the confirmation wave leaving an absorber at space-time point (r,t) reaches the emitter with a strength proportional to ψ(r,t)ψ*(r,t). A transaction is henceforth established between the emitter and one of the absorbers, which enforces relevant conservation laws. The probability of a transaction with a given absorber is proportional to the strength of that absorber's confirmation wave, from which Born's rule follows.

After motivating and developing TI, Cramer proceeds to apply his interpretation to more than 20 different real or thought experiments, every one of them presenting some paradoxical aspect. Cramer argues that TI does much better than the Copenhagen Interpretation in dissolving the paradoxes. Nonlocality, for instance, has a straightforward explanation in TI. In experiments about Bell's inequalities, correlations between Alice's and Bob's results are not enforced through superluminal influence, but through backward causation effected by confirmation waves. That is, correlations are explained if the world is such that waves do indeed propagate in the negative time direction.

Cramer claims that TI “solves all of the interpretational problems and paradoxes of quantum mechanics…” Moreover, he believes that TI does this much better than the Copenhagen or other interpretations, although his explicit comparisons mainly focus on the former. Why then has TI received comparatively little attention? There is Ruth Kastner's 2013 book (The Transactional Interpretation of Quantum Mechanics: The Reality of Possibility), but a quick search of arXiv yields only about 17 titles on TI, compared with about 45 on Everett's approach and 200 on Bohm's.

I believe there are essentially two reasons for this. The first one has to do with advanced causation. Even if carefully balanced so as not to result in pathological causal loops, advanced causation is for most people hard to swallow. This may or may not be an intellectual prejudice, just like the view against splitting into many worlds or against a quantum potential acting on particles without being acted upon in return.

The second reason, however, has little to do with prejudice. In an important sense, TI is not better defined than the Copenhagen Interpretation or von Neumann's theory of measurement. In Bohr's view, classical mechanics is logically prior to quantum mechanics, but we are not given the precise conditions under which an aggregate of particles behaves classically. Similarly, von Neumann does not specify conditions under which Process 1 (collapse) takes over Process 2 (unitary evolution). In Cramer's view, transactions play the part of collapse. True, they are somewhat immune to questions like “When does the collapse occur?,” but they require emitters and absorbers. These should be macroscopic (classical) objects if transactions are truly irreversible. The classical-quantum distinction or apparatus definition therefore plagues Cramer's view just as it does Bohr's or von Neumann's.

All interpretations of quantum mechanics are subject to strong criticism. This is what makes the field fascinating. My criticism of TI should therefore not deter anyone from reading The Quantum Handshake. In fact, Cramer has written a very good book, living up largely to its objective of reaching the intelligent general reader. His overview of the conceptual development of quantum mechanics is clear and concise, just as his discussion of entanglement and nonlocality. Chapter 6 on Quantum Paradoxes and Applications of the TI is especially interesting, his description of experiments being informed by decades of experience. An appendix provides Cramer's own answers to general questions on quantum mechanics or specific ones on TI. Careful editing and proofreading has caught most typos. All in all, this is a book everyone will learn from. It is as good a take as any other on the difficult problem of interpreting quantum mechanics.

Louis Marchildon is Professor of Physics (Emeritus) at Université du Québec à Trois-Rivières. In the past 15 years, his research has focused on the interpretation of quantum mechanics. He is the author of Quantum Mechanics: From Basic Principles to Numerical Methods and Applications (Springer, 2002).