Are the physical theories we use to understand our world necessarily true? When applying the philosophical concept of ‘necessity’ to physics, what is meant is that the theories we know, which have been deduced from empirical observations, might also have been rationally derived: by reasoning alone, one may logically prove that the laws of physics must be A, and cannot be B. More often known from the opposition between rationalism and empiricism, the rationalist approach has often been dismissed by practising physicists, as necessity always seems to be derived in hindsight. Could it really have been possible to derive the most fundamental laws of physics entirely through rational thought alone, without having had recourse to experimental methods? In his monograph Physics and Necessity, physicist and historian of physics Olivier Darrigol presents a historical survey of such rationalist attempts to derive the theories of physics. Through teasing out those instances where empiricism and rationalism have combined in modern science, and opposing the two, he argues in favour of a moderate amount of rationalism in physics. He thus shows that a rationalist approach in itself can get impressively far in deriving the foundations of theoretical physics.

In nine chapters, Darrigol gives a roughly chronological overview of the history of necessity in physics. The arguments Darrigol has selected for this book are sampled based on ‘historical impact or … intrinsic merit’ (p. viii). He therefore begins each chapter with a historical contextualization of the arguments, before deciding to what extent these are still valid in the twenty-first century, starting, as the title indicates, with René Descartes's geometric reduction of physics and Isaac Newton's opposition to this reduction. From here onwards, he covers necessity in a large part of classical physics: classical mechanics, thermodynamics, geometry, space–time and classical field theories are all covered before he arrives at his most impressive, hundred-page chapter on quantum mechanics. He additionally devotes a chapter to mathematics in physics, and finishes his work with a chapter discussing both the preconditions of necessity, and the necessity of modularity, in which he argues that the best necessity arguments are based on Hermann von Helmholtz's interpretation of comprehensibility. Perhaps surprisingly, no attention is given to astrophysics, one field of physics in which the possibilities for empirical investigation are limited.

Darrigol writes for a specialist audience trained in physics up to at least the undergraduate level in this equation-heavy work. Although the monograph engagingly covers some of the most important episodes from the history of physics, for the general reader interested in this history the scope of this book is likely out of their league. Even so, as Darrigol writes in his introduction, his mathematical approach is much less rigorous than that used in the original rational deductions he collects in his work, especially in the chapter on quantum mechanics.

The field of quantum mechanics in particular poses a challenge to Darrigol's objective of arguing the rational necessity of physics, given the manner in which the new laws of quantum physics undermine the causality and rationality of classical physics. Darrigol therefore presents two arguments based on historical necessity, both of them by means of analogy, one argument based on mathematical necessity, which claims that mathematically speaking ‘classical mechanics already contains quantum mechanics’ (p. 237), and one based on operational necessity, the latter of which he considers the most rational approach. It is in this chapter, which contains no fewer than three hundred equations, that the most is demanded from the scientific training of the reader: this chapter would be challenging even for a physics undergraduate.

Darrigol's derivations are often impressive, yet it is still the case that physicists can sceptically point out that these are all aided by hindsight, and therefore not of any interest to their work. Once a general framework has been established from which to look back, it is much easier indeed to derive the laws through a purely theoretical approach. Darrigol argues that rationalism can also help in looking forward. He moderates this claim carefully: he proposes that some rationalism is healthy and helpful in physics, but his work also confronts readers with the unavoidable truth that pure rationalism is unlikely to advance physics. Darrigol's most important contribution, then, is to present a compelling argument that empiricism need not be entirely void of rationalism, and especially that a rationalist approach does not undermine empiricism. In light of this claim, it would have been interesting to see Darrigol applying his approach to fields that are as yet empirically unresolved, such as string theory, rather than only staying with a historical overview.