There is no doubt that the development of ideas in physics, as well as in many other sciences, has been enriched by the extraordinary elucidation that some familiar concepts in one area can be transferred to another one, and thereby gain new insights into either or both of them.
Analogies are a powerful cognitive tool that allow us to make inferences and learn new aspects from the comparison of two things by highlighting their similarities. In general, the reasoning behind this process involves the abstraction of details from a particular set of problems and the resolution of structural resemblance between previously distinct problems. In the book entitled “Quantum-Classical Analogies” by Dragoman and Dragoman we are presented with an extensive number of analogies drawn between the two seemingly dissimilar worlds of classical and quantum physics. Many of these links are more than mere curiosities as it is patently shown in the book with the discussion of a number of recent developments in different areas of physics. The book is divided in 10 different chapters ranging from analogies between ballistic electrons and electromagnetic waves to analogies in phase space, passing through acoustics and particle optics.
Writing a book like this one is an arduous and ambitious task and as such it is hardly surprising that the final product is somewhat unbalanced in the depth in which the different subjects are treated or in the way the subjects are introduced. In many cases, for instance, the authors jump without warning from discussing a classical system in the light of the quantum case to the opposite point of view, making it difficult for the reader to follow their arguments. It is important to mention that the book is intended to be a catalogue of phenomena shared between classical and quantum physics, rather than a textbook about them. Taking that into consideration, the reader must be aware that most sections contain mathematical statements about the subject under discussion, together with appropriate references. In some cases the mathematical formulation is of great help, specially if the reader has some experience in that particular area, however if the reader is new to the subject, it might be more difficult to grasp the full significance of the analogy. In such cases, the references given are an invaluable asset. Personally, I believe that the later chapters of the book accomplish much better the original aim of the authors.
Finally, as a warning for the interested reader, I would like to point out that the book does not discuss any philosophical or epistemological arguments about the quantum-classical correspondence principle. Similarly, the authors make it quite clear that they do not treat any classical-classical or quantum-quantum analogies and that they concentrate in analogies that imply formal similarities. This book is therefore a very good choice for those interested in bridging ideas from classical physics into the quantum world or visce versa, bearing in mind that only the shades are delineated here, the full picture will have to be sought elsewhere.