Quantum Mechanics: The Theoretical Minimum: What You Need to Know to Start Doing Physics Leonard Susskind and Art Friedman. Basic Books/Allen Lane: 2014. 9780241003442

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It is all too easy to compound the perplexities of quantum mechanics. Monographs are often weighed down by abstruse mathematics; other treatments struggle to separate physics from formalism. The problem is to communicate the subject's intrinsic strangeness without burdensome mathematical demands — but also without resorting to gee-whiz platitudes that assert, but do not explain, the incongruities between the quantum world and everyday experience.

Leonard Susskind and Art Friedman's Quantum Mechanics is the second entry in Susskind's Theoretical Minimum series, based on an Internet course of the same name and designed to satisfy a mathematically literate audience looking for more detail than can be found in a popular-science offering. The authors set their aims at the outset: “the goal”, they say, “is not to hide the utter strangeness of quantum logic but to bring it out into the light of day”.

To achieve this, Susskind, a physicist, and Friedman, a data engineer, eschew the analogies and qualitative descriptions typically used to explain quantum mechanics to a lay audience. Instead, readers are expected to invest time in getting to grips with mathematical concepts such as complex numbers, vector spaces, linear operators and tensor products, all of which are deftly explained in a series of interludes. In return, the authors offer self-contained chapters that vividly articulate aspects of the theory: the space of states, time evolution, uncertainty, entanglement, particle dynamics and so on, leading eventually to the harmonic oscillator, a quantized mechanical spring. This is the most important of all simple quantum systems because quantum field theory, the discipline's description of the forces in nature, interprets particles as harmonic oscillators.

The selection of concepts is close to what would be found in a typical undergraduate course. It steers clear of the philosophical morass surrounding interpretation and focuses on how quantum mechanics is used and understood today, rather than its development or the human stories behind it. This is a book about physics, not history.

The writing is fresh and immediate, with plenty of detail packaged into the smooth narrative. It will not teach anyone to carry out complex calculations, and it may leave the reader with questions that can be resolved only by digging into more conventional textbooks. But on their own terms, I found Susskind and Friedman's explanations crisp and satisfying. The chapters on entanglement — in which particles interact in such a way that they cannot be described independently — are especially clear, taking pains to draw out the distinction between quantum entanglement and correlation. In either case, we can predict something about the relationship between measurements in different parts of a composite system. The puzzling feature of entanglement is that, although we may know everything about the state, it might be impossible to predict anything about the outcome of these measurements individually.

Susskind and Friedman's choices will suit their intended readership, but might make the book less attractive to others. Those with the determination to navigate the complexities of Hermitian operators, normalizable wavefunctions or creation–annihilation operators will struggle to find a book that serves them better. Secondary-school pupils, however, may find the more detailed passages too demanding; university students might find that the early chapters proceed slowly, and that overall the book is too light on detail to serve as a principal text.

Still, I maintain a clear recollection of the bewilderment with which I struggled through my own university quantum-mechanics courses. For students in a similar position, trying to draw together the fragments of formalism into a clear conceptual whole, Susskind and Friedman's persuasive overview — and their insistence on explaining, with sharp mathematical detail, exactly what it is that is strange about quantum mechanics — may be just what is needed.