BOOK REVIEW

# Dirac's Due

*Paul Dirac: The Man and His Work.* Peter Goddard, ed. 124 pp. Cambridge University Press, 1998. $19.95.

Paul Dirac, one of quantum mechanics' founders, is among the greatest physicists ever. This small volume of four lectures delivered in Westminster Abbey during the dedication of a plaque in Dirac's honor captures the relation between his personality and his science via a mosaic of historical recollections and scientific reviews.

As Abraham Pais explains in the first lecture, there were already two seemingly unrelated formulations of quantum mechanics when Dirac started working on the subject in the 1920s. In line with his philosophy that the job of a mathematical physicist is "to remove inconsistencies" and to "unite theories that are previously disjoint," Dirac proposed a formulation that reconciled both approaches and raised the field to new heights.

He then moved on to address new challenges since "as it frequently happens in research, the solving of a difficulty leads to the other ... brought to prominence by the removal of the first."

The new hurdle was to conciliate quantum mechanics with special relativity and formulate a relativistic theory of the electron. This pursuit led Dirac to his major discovery, the Dirac equation, a harmless-looking equation that, in Dirac's own words, "governs most of physics and the whole of chemistry."

Sixty years later, one cannot help marvel at the impact that it has also had on modern mathematics, as illustrated in Sir Michael Atiyah's lecture. The Dirac equation is perhaps the most powerful example yet of the deep and mysterious connection between mathematics and physics. But Dirac did not content himself with writing this equation, as he believed that a theoretical physicist "must be prepared to follow up the consequences of a theory."

The consequence of the Dirac equation was the prediction of anti-matter, the subject of Maurice Jacob's lecture. In his introductory address Stephen Hawking laments that Dirac "was never well known to the public" despite the enormous implications of his discoveries for science and technology. True enough, today quantum mechanics is not part of the layman's consciousness, but one wonders whether this situation might change if quantum computers, hypothetical machines that would exploit the superposition principle of quantum mechanics, really become practical. Then the quantum-mechanical concepts so elegantly presented in Dirac's classic book *Principles of Quantum Mechanics* might become part of everyone's vocabulary.

The progress in quantum computers recently reported in the press is not the only reason why this book is timely. Theoretical physics is now at a junction very similar to the one that Dirac faced 60 years ago, since it is attempting to reconcile quantum mechanics with general relativity. Hurdles in physics never end, as Dirac well knew. While solving this new puzzle, physicists have resurrected Dirac's old idea of electric-magnetic symmetry. Starting from Dirac's daring suggestion of magnetic monopoles, particles that carry an isolated magnetic charge, David Olive describes in his lecture the progress that electric-magnetic duality has undergone since Dirac's formulation in 1931 and its implications on the current thinking at the forefront of theoretical physics. Interestingly enough, in 1960 Dirac also suggested that elementary particles might correspond to modes of a vibrating membrane. Today we believe that string and membrane theories might hold the key to the unification of all forces and symmetries. It is precisely in the context of the modern reincarnation of these theories that electric-magnetic duality plays such an exciting role.

Probably the reason behind the long-lasting effects of Dirac's contributions to physics is his belief that "if one is working from the point of view of getting beauty in one's equation, and if one has really sound insights, one is on a sure line of progress." It is this same quest for beauty, unity and consistency that fuels theoretical physics today.—*Chiara R. Nappi, School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey
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