Malcolm Longair believes that undergraduate students in physics can be stimulated by examining the arguments and models used by great physicists to make their discoveries. Whether or not one joins him in this belief - I do to some extent - the existence of an unconventional book such as this highlights an important issue for the teaching of physics. Where does such a course fit into an already crowded syllabus?

It seems undeniable that part of the pleasure of being a teacher lies in trying out new approaches to stimulating students. But freedom to try new approaches carries with it the possibility of failure. It seems to me that this freedom of expression is in danger of being eroded by the increasing rigidity of the processes we have put in place to document the quality of our teaching. The advertising material for this book makes reference to * The Feynman Lectures on Physics * as a "competing title". In fact, Longair's book is very different, but the analogy made me wonder whether Richard Feynman would nowadays be allowed to attempt his great experiment with the teaching of undergraduate physics.

Longair's book was originally based on a course of lectures at Cambridge University in the late 1970s that were "entirely optional and strictly non-examinable". The present volume is a revised edition based on revisiting this course 20 years on. The book represents an attempt to capture aspects of the practice of physics by research professionals that are often missed in standard undergraduate physics courses. These include the value of approaching problems from several different viewpoints; an appreciation of what it feels like to be involved in research; the excitement of the processes of discovery; and the value of hard work and experience, but also the key role of intuition in any great discovery.

Longair illustrates these issues by examining seven case studies that cover much of modern physics. They are: Newton's laws and gravity; Maxwell's equations; mechanics and dynamics; thermodynamics and statistical physics; quanta; special relativity; and general relativity and cosmology.

Needless to say, the studies reflect Longair's personal research interests - but that is precisely the point. He believes that no two professional physicists think in exactly the same way about a problem because their experiences of using the tools of theoretical physics are coloured by their particular research area. These case studies contain detailed accounts of the struggles of some of the greatest scientists in solving the great physics problems of their time. In this way, their extraordinary powers of concentration and intellectual commitment to the problem at hand are revealed.

I particularly liked Longair's opening study on the challenge to the geocentric Ptolemaic model of the universe given by Copernicus and Kepler.

His account of the observations of Tycho Brahe - the first modern astronomer despite having no telescopes - is fascinating and a magnificent illustration of the essential features of experimental science. Then we come to Kepler, one of my personal heroes. It was he who first understood that the much greater accuracy of Brahe's astronomical data meant that it was not possible to fit the orbit of Mars to a circle. Instead, Kepler showed that the orbit of Mars was an ellipse with the Sun at one of the foci. This was a truly revolutionary step because it demolished the Aristotelian edict that all motion was either linear or circular.

Observational science finally triumphed over ill-informed prejudice, but it is interesting that even Galileo was troubled by Kepler's result. It was Kepler who first put the laws of planetary motion in mathematical form, and it was his third law, buried deep in his book * The Harmony of the World * , that was crucial in leading Newton to his law of gravity. Of course, Kepler was a curious mixture of the rational and non-rational but so was Newton, with his studies of alchemy and interpretations of the Bible.

Longair's erudition and scholarship are evident throughout the case studies. This is typified by his careful analysis of Galileo's experiments, accompanied by a strikingly modern-looking photograph of Galileo's notes on the laws of the pendulum. However, I am less convinced by some of the other case studies. I am doubtful of the value of analysing in detail Maxwell's rotating vortex model of the magnetic field or of understanding Planck's models for black-body radiation. By contrast, the section on "Dimensional analysis, chaos and self-organised criticality" is fascinating. I learnt about Buckingham's theorem for dimensional analysis and also how the famous Cambridge physicist G.I. Taylor annoyed the US Government by using this technique to estimate the explosive power of the Trinity atomic bomb test purely by looking at the movie of the explosion.

Longair's book is, as he says, for "students who love physics and theoretical physics", not for amateurs. However, it gives great insight into the equations of modern physics, and I enjoyed it very much. Although I doubt that many undergraduate physics curricula can afford the luxury of a whole course based on this book, I would hope that parts could be used to enliven the standard course fodder.

Tony Hey is professor of computation, Southampton University, and director of e-science, Engineering and Physical Sciences Research Council.

## Theoretical Concepts in Physics: An Alternative View of Theoretical Reasoning in Physics

Author - Malcolm Longair

Publisher - Cambridge University Press

Pages - 569

Price - £80.00 and £30.00

ISBN - 0 521 82126 6 and 52878 X

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