# Histories of kinematics and Einstein’s relativity theory: A collage of historiographies

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DOI: 10.1007/s11016-011-9532-6

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- Hon, G. Metascience (2012) 21: 131. doi:10.1007/s11016-011-9532-6

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Einstein was 26 years old in 1905 when he put forward a new physical theory in a paper entitled, “On the electrodynamics of moving bodies”. This is the theory of special relativity that effected a revolution in the annals of physics. In choosing this title, “Zur Elektrodynamik bewegter Körper”, Einstein followed a tradition that can be traced back to Hertz’s paper of 1890, “Ueber die Grundgleichungen der Elektrodynamik für bewegte Körper”. Given this title, it seems *prima facie* that Einstein included his theory in this tradition. However, as is well known, this is not the case. To be sure, Einstein was deeply engaged with Hertz’s theory, but he was dissatisfied with this account. Indeed, as early as 1899, Einstein was convinced that the electrodynamics of moving bodies is not correct. He realized this conviction in his celebrated relativity paper of 1905: he adhered to the title of Hertz’s original paper but revolutionized the analysis, both in form and in content. He did not adopt the traditional approach of commencing with the dynamical equations based on a hypothesis regarding the constitution of matter or the intermolecular forces, rather he divided the paper into two parts, namely, kinematical and electrodynamical, and proceeded to develop a theory of principle. The “Kinematical Part” famously begins with a new definition of simultaneity based on an analysis of the transformation between stationary and moving coordinate systems.

As the title and the subtitle of the book under review indicate, the author, Alberto A. Martínez, set out to explore the physical domain called *Kinematics* and the role it played in the development of Einstein’s relativity theory. The subtitle implies that the author was engaged in some archeological excavation in search for a lost treasure trove. In my opinion, Martínez overstated the case, but the reader will benefit from the book.

The author begins the discussion with the “big picture: rise of a rejected science”: the “big picture” is the classificatory schemes of knowledge, and the “rejected science” is kinematics. The goal is to bring out the relations of the discipline of kinematics to other disciplines. Kinematics, a term of Greek origin that means to move, is the study of motion of bodies and systems irrespective of its causes. The author reaches back to antiquity and offers a trajectory of classifications from Aristotle via (among others) Aquinas, Bacon, Newton, d’Alembert and Diderot to Ampère. This is a wide view of history of ideas, the result of what the author calls “*teleological approach*”; it is “mainly chronological narrative that gropes toward a preestablished destination.” (p. xi)

In the second chapter, “Where to begin? Invisible causes or visible motions”, the author examines contemporaneous influences on Ampère whom Martínez regards as the key figure in the story. The motivating question is, “What were the origins of Ampère’s notion of kinematics?” (p. 38) According to the author, engineers such as Lanz and Betancourt and scientists such as Carnot and Monge influenced Ampère. In contrast to the first chapter, here Martínez adopts an “*archeological approach*”, namely, moving backward in time from Ampère’s new conception of kinematics (pp. xi, 38). The author remarks that the case of kinematics is paradoxical: up to the 1830s, most physicists believed that the science of motion had been very well developed, yet many thought that this scientific domain was grossly neglected and therefore set out to develop it. Ampère is the prime example (p. 63). At that time, force was still a central concept, but questioning its physical reality became legitimate (pp. 64–65).

The stage is now set for the third chapter, “Ambiguous truths: The allegedly pure science of motion”. Here, the author traces the “sporadic growth [of kinematics] from the 1830s until the early 1900s, as engineers, scientists, mathematicians, and philosophers pulled it in different directions.” (p. xii) Originally, kinematics was conceived as the study of motion as it appears in observation, yet it soon was misconstrued, so the author claims, “as the pure geometry of motion, independent of experience.” (pp. xii, 76) The influential work of Kirchhoff is singled out, leading to Hertz’s *Principles of Mechanics* (1894) in which the causal relation between force and motion is thoroughly questioned. “Instead of a physics of force, Hertz structured mechanics in terms of only three ‘independent fundamental conceptions,’ namely, space, time, and mass.” (p. 79) Martínez remarks that, like Thomson and Tait, Hertz considered his principles of mechanics a physical domain completely independent of experience (p. 80). Kantian philosophy offered a consistent and coherent framework for this development. Parallel to this approach, and in tension with it, there evolved the critical history of mechanics, culminating in the work of Mach (1883). His “antimetaphysical” approach stipulated that the origin of the principles of mechanics is to be found in the experience of relative positions and motions of bodies (p. 113). Kinematics changed. “Belief in the abstract mathematical truth of kinematics was replaced by belief in the necessity of grounding concepts on perceptions or on feasible or idealized procedures of measurement.” (p. 121) In this section, history is pursued by subject matter, that is, a sort of “*genealogy*”, as the author calls it, which traces the family relations among fields and ideas (p. xii).

In the fourth chapter, “Debates over language: Coordinates versus vectors”, Martínez inquires into the role of mathematics in contributing to the remaking of kinematics. This chapter focuses on the evolution during the 1800s of basic mathematical methods for representing motion. In particular, how did vector theory arise in the 1890s as an alternative to the traditional coordinate algebra? Martínez refers to this account as “*history of dissent*”, complete with objections, and controversies (pp. xii–xiii). The author begins the discussion with the legacy of Descartes and continues with an extensive study of Hamilton’s quaternions and the work of Grassmann. This is then followed up by an account of Gibbs and Heaviside who developed vector theory (p. 151).

The subsequent chapter, “Scientific definitions: The concepts of space and time”, concludes the discussion of kinematics before turning to Einstein’s relativity paper. The fifth chapter traces the way mathematics (algebra, calculus, coordinates, and vectors) was applied by physicists in the years leading to the end of the nineteenth century to define concepts such as speed, velocity, distance, and displacements. According to Martínez, here the narrative proceeds by topic and, he adds, “like many histories, it is *impressionistic*, it brings together various facets of related and converging developments.” (p. xii)

In chapter 6, “Discovery and invention: Conceptual origins of Einstein’s relativity”, the author reaches the centerpiece of his historical study. This is “a *biographical account* of how Albert Einstein came to formulate his relativistic kinematics.” The author considers his effort to present this biography “comprehensive” (p. xiii). The narrative proceeds chronologically “to a degree that has not been attempted previously in historical accounts of Einstein’s relativity”, so the author claims (pp. xiii–xiv). This case study of creativity culminates in the moment of revelation, when in the spring of 1905, Einstein realized the arbitrariness of the fundamental kinematic concepts (p. 273). He then sought to render them meaningful only when they convey definite empirical relations (p. 275).

Chapter 7, “Text and equations: Elements of Einstein’s kinematics”, leaves behind the biographical account and the creative act, and focuses on the text. This is “a line-by-line *textual analysis*” of the kinematical part. This close reading uncovers, according to the author, Einstein’s peculiar mathematical moves that engendered confusion that the author sets out to clarify (p. 353). The kinematical part of the relativity paper consists of five sections: Martínez focuses on the first three, namely, the definition of simultaneity, the relativity of lengths and times, and the theory of transformation. The author places these sections, as it were, under the microscope. He considers the remaining two sections, the physical meaning of the equations and the composition of velocities, consequences that he discusses briefly. Martínez concludes that “by rejecting the traditional rule of velocities, Einstein created a new kinematics.” (p. 359) However, this act of creativity was accomplished without resorting to vector algebra, the latest innovation in kinematics. How did Einstein’s “preference to old-fashioned coordinates affected his kinematics”? (p. xiv) This is the question that leads to the last chapter.

In the final chapter, “Critical history: The algebra of motion”, the author seeks to bring together several threads from the preceding chapters that “did not converge”. The chapter “elucidates issues that remained unresolved despite the emergence of relativistic kinematics.” (p. xiv) The author adopts here “the style of *critical history*” in the spirit of Mach (p. xiv). This last chapter is designed to open up a new vista of analysis. Martínez formulates the historical difficulty: “In contrast to vector theorists,… [Einstein] did not operate with the distinction between scalars and vectors. In particular, while he focused his analysis on the exact significance of the concept of time, he did not distinguish between the concept of speed and velocity and between the concepts of position, distance, and displacement.” (p. 392) In the author’s view, the revolution was executed with inappropriate tools: “old algebraic methods that were not originally designed for the analysis of motion.” (p. xv; see also pp. 378, 381, 392) This “is not a good story”, the author remarks (p. 210).

The historical account that Martínez developed is disjointed—teleological, archeological, genealogical, of dissent, impressionistic, biographical, textual, and critical. The scheme is disparate by (historiographical) design; the author made it so intentionally. Even the central piece, the relativity paper, is not treated as a whole: the “Electrodynamical Part” is left unexamined. As the author indicates, the intention was to abstain from framing general conclusions and to encourage the reader to pursue further open issues (p. x). Martínez’s wish is that the “book be read as a reliable sourcebook rather than as the apparently definitive last word on anything.” (p. xvi) In this sense, the author has indeed succeeded in offering the reader a wealth of material, presented in an accessible way.