Those eureka moments

From Aristotle to Galileo, Descartes to Newton, Faraday to Maxwell, Bohr to Dirac, Fermat to Feynman and Einstein to Hawking, all of modern physics is in this book. This is a bold and courageous text that presents an authoritative coverage of physics from the ancients to the present. The theme of the book is "hidden unity" in physics. One paradigm is, of course, the unification of electricity and magnetism in Maxwell's theory of electromagnetism and the explanation of light as electromagnetic waves. The other paradigm is the importance of the "vacuum" or lowest energy state.

For example, the alignment of individual atomic magnets in a piece of magnetised material causes the magnet "to choose" a particular direction of space. The lowest energy state of the magnet therefore breaks the symmetry between all directions of space. This idea has modern incarnations in quantum chromodynamics - the theory of strong interactions - and in the unification of weak and electromagnetic forces via the notorious Higgs.

Progress in physics by resolution of contradiction is a sub-theme of Taylor's book. Newton's theories of motion and gravity were in conflict with Maxwell's electromagnetic theory. Einstein resolved these contradictions by creating his two theories of relativity.

John Taylor's book is no run-of-the-mill popularisation of science. He himself is one of the early pioneers of modern gauge theories, and brings genuinely new insights to seemingly well-explored areas of science. This is evident throughout the book but probably the most striking example is his treatment of Fermat's principle of least time and its modern descendants - Hamilton's principle of least action and Feynman's "all histories" version of quantum mechanics. In his discussion of magnetic forces, Taylor introduces the reader to the concept of the magnetic flux for an open curve, for which he uses the acronym FFOC - "memorable but not offensive". Using this device Taylor is able to give the reader real insight into the important but difficult ideas of gauge ambiguities and gauge invariance. Taylor is also meticulous in his respect for physical and historical accuracy, and for his honest appraisal of problems. When the physics is still unclear he is not afraid to say so. For example, the chapter on cosmology concludes with the following memorable summary: "We are not certain about the nature or amount of much of the matter in the universe, and whether it is sufficient eventually to halt the expansion. We do not know when, if ever, vacuum energy plays an important role. We are not certain why the universe appears to be so flat and so uniform, why there is any matter remaining and why that matter is now organised in a structured way." Taylor also follows the example of Newton's famous "Optiks" by including an explicitly speculative chapter called "Queries".

Inclusion in this section makes it quite clear that the fascinating topics discussed - hidden dimensions, supersymmetry, quantum gravity, string theory and magnetic monopoles - are at a different level of speculation than the rest of the book. It is refreshing to see this distinction made explicit; this is not the case with most popular accounts.

The book also contains many interesting historical asides, again researched with much care and presented with caveats where appropriate. I learnt, for example, that it was apparently Queen Elizabeth's physician, William Gilbert, who invented the term electric and was first to realise that a magnetic needle points to a specific region of the earth. I was also surprised to learn that the superintendent of gardens to the king of France, Charles-Francois du Fay, first identified positive and negative electric charges. The text is enlivened with the inclusion of memorable quotations by the great and the good. There is Einstein's "happiest thought" about gravity that occurred to him while he should have been working at the patent office in Bern - "If a person falls freely he will not experience his own weight" - and his reaction when he realised that his new theory predicted the anomaly in the orbit of Mercury: "For a few days, I was beside myself with joyous excitement." I also enjoyed Feynman's greeting to Bruno Zumino, one of the discoverers of supersymmetry: "So you're the guy who thinks that fermions are the same as bosons."

This book covers a vast expanse of physics and is a genuine tour de force for its insights and intellectual honesty. Taylor has tried to avoid writing equations in mathematical symbols, but no one could pretend that this book is an "easy read". Understanding does not come without effort, and for those willing to make the effort this book will repay them handsomely. This is an exceptional book by an exceptional physicist.

Tony Hey is professor of computation, University of Southampton, and director, UK e-Science Core Programme.