Wizards, mermaids, dragons and aliens. Walking, running, flying and space travel. A hi-tech elevator, a computer, a propulsion engine and a black hole. What do all of these things have in common? This might seem like a really hard brainteaser but the answer is simple: they all obey the fundamental laws of our universe. Accordingly, there are certain dos and don'ts, maybes and no ways that should guide our imaginations when we think about them.

That, at least, is the argument that physicist and science-fiction aficionado Charles Adler makes in Wizards, Aliens and Starships: Physics and Math in Fantasy and Science Fiction. In the book, Adler, a professor at St Mary's College of Maryland, US, offers a grand tour of almost all of the main themes encountered in the -sci-fi literature and attempts to evaluate their plausibility using first principles from physics. From the mythical world of J K Rowling's Harry Potter series to the many stories that deal with the possibility of space travel, the future of our civilization or the existence of civilizations elsewhere in the universe, he considers a wide variety of topics and scenarios.

Written in a relaxed style, the book is full of enjoyable discussions, and readers who are already familiar with the sci-fi literature will appreciate the numerous references to other works. Those who are less familiar will, most probably, feel tempted to read some of the works referenced and commented on.

Adler's main tools in exploring the possibility or impossibility of an idea are the "back-of-the-envelope calculations" popularized by Enrico Fermi. As the last great generalist in physics, Fermi combined an exceptional training in theoretical physics with tremendous skill in experimental physics. Equipped with this unique combination of abilities, he was able to ask seemingly impossible questions and, with a few simple arguments, produce fast, approximate answers to them with an accuracy that only detailed and time-consuming computations could surpass.

One topic that Adler examines in the book using this "Fermi problems" approach concerns how size affects various aspects of any living creature, whether real or fantastic. For example, size considerations can explain why humans walk at about 2 m/s, how this speed might change on another planet and how it compares with the speed of species with longer legs. Similarly, in the same chapter, the reader learns why there are no biological flying species beyond a certain mass (roughly that of the California condor). Later, Adler uses the same approach to evaluate the feasibility and cost efficiency of the space elevator – a breathtaking engineering project that has been proposed by some as a way to transport material and people to space. Using conservative estimations, he argues that a space elevator would be risky and its benefits not as great as proponents have insisted.

Having taught a course on physics in Hollywood movies many times using some of the same source material, I must confess that this is the book I have always meant to write if I ever had the time to do so. Reading it, I felt like my notes and my course slides had been magically transformed from their raw form into an engaging book. Although not a textbook in itself, Wizards, Aliens and Starships could serve as a great companion book for courses offered to non-science students, as a means of taking away the students' boredom and animosity towards science.

The book contains a few typos but, fortunately, they do not create any serious problems for the reader. In some places, however, I found myself questioning a few of the assumptions and/or statements. On occasion, additional research might also have been beneficial. For example, in chapter 11, where Adler discusses speculative propulsion systems, he places a lot of emphasis on the cost, time and efficiency required to produce antimatter. I found his assumptions and calculations unpersuasive because they are based on superficial limitations of the current time. Humans' engineering efforts have never been focused on the mass production of antimatter, and it is easy to imagine that, with dedication and will, we could create a high--efficiency production factory that would make antiparticles at a much lower cost. The more important issue, I believe, is the separation and storage of antimatter for an extremely long period of time – periods that must be fantastically longer than the lifetimes of the antimatter particles themselves. This issue is not touched on at all.

Similarly, when discussing the possibility of fire-breathing dragons, the author calls the suggestion that dragons might generate large amounts of methane in their digestive systems "ingenious", but also states that "there may be some reason that this mechanism is fundamentally impossible". Here, I feel that his intuition might be wrong. Exobiologists study how creatures could have evolved on other planets, and one possibility that has drawn their attention is a "methane world" – that is, one where methane plays a role similar to that of water on Earth. Using scientific principles and imagination, exobiologists have envisioned a very complex, biodiverse environment on such a planet. One could also imagine a milder version where methane is not the dominant compound but nevertheless plays an important role. As Murray Gell-Mann has stated: "anything that is not forbidden [by fundamental laws] is compulsory". However, in the author's defence, introducing reasonable assumptions is part of the nature of back-of-the-envelope problems, and hence I cannot be extremely negative on this point. Also, for a book that covers so many topics, adding more details would have made it too bulky.

My other criticism is more important. The book uses a vast number of facts from science and a long list of formulae from physics. As a result, and based on my experience with the general public, the book is not really accessible to people who prefer to read plain text with no calculations, just the facts and the results spelled out explicitly. That is not a problem for readers like myself, who are trained in science and will find much to appreciate here, but the publisher's declaration that the book "will speak to anyone wanting to know about the correct – and incorrect – science of science fiction and fantasy" is not necessarily valid.

Overall, though, this is an exciting book. To paraphrase John Wheeler, it is about our universe as it really is; a museum of wonder and beauty that often contrasts with the fictional universes of imagination encountered in the sci-fi literature. I would not hesitate to recommend it to anyone who is interested in understanding the relationship between physics and science fiction. Instructors of introductory physics courses, especially, will find it a valuable supplement to dry physics textbooks, and its use may even boost students' evaluations of the course. I will certainly use it in my classes.