Concepts of Simultaneity: From Antiquity to Einstein and Beyond

6 The Transition to the Relativistic Conception of Simultaneity

Modern science and, in particular, modern physics—and with it the modern conceptions of simultaneity—are deeply indebted to several intellectual developments of the nineteenth century. Foremost among these was the discovery of non-Euclidean geometry. By abolishing the monopoly of Euclidean geometry this discovery stimulated an intense interest in critically re-examining not only the accepted ideas of space and time but also the general principles of scientific methodology. Two of these principles had a decisive impact on the development of the modern concept of simultaneity: (1) the positivistic tendency of demetaphysicizing the Newtonian concepts of absolute space and time, with Ernst Mach as its main representative, and (2) the doctrine, now generally called conventionalism, associated primarily with the name of Henri Poincaré. Much has been written about Mach’s rejection of Newton’s concept of absolute or substantival space and absolute motion. In contrast, rather little1 C H A P T E R S I X The Transition to the Relativistic Conception of Simultaneity 1 For example, M. Čapek, in The Concepts of Space and Time (Dordrecht: Reidel, 1976), quotes a lengthy excerpt from Mach’s Science of Mechanics concerning his rejection of absolute space but not a single word about his rejection of absolute time. 96 Concepts of Simultaneity has been written about Mach’s rejection of Newton’s absolute time, which he called a “superfluous metaphysical concept,”2 and still less about how Mach conceived what are generally regarded as temporal concepts such as the concept of simultaneity. As a matter of fact, as his writings testify,3 the notion of time occupied Mach’s attention much more than the notion of space. Although the notion of simultaneity was not dealt with explicitly in any of his books or essays, it implicitly underlay his very conception of time. According to Mach, time as an independent reality, like Newton’s absolute time, does not exist. It is nevertheless used so frequently in physics or in ordinary experience because it serves as a coordinator among different processes. Psychological time, that is, time as sensation, is obtained “by the connection of that which is contained in the province of our memory with that which is contained in the province of our sense-perception. When we say that time flows on in a definite direction or sense, we mean that physical events generally (and therefore also physiological events) take place only in a definite sense. . . . In all this there is simply expressed a peculiar and profound connection of things.”4 Mach’s favorite example to illustrate the role of time as a linking mediator between different events was the thermodynamic cooling-down process of a hot body and the mechanical process of free fall. Because these two processes are described by equations that contain the time variable, “the time can be eliminated from them and the temperature can be determined by the distance of fall. The elements [processes] then reveal themselves simply as interdependent .”5 “If we once made clear to ourselves that we are concerned only with the ascertainment of the interdependence of phenomena . . . all metaphysical obscurities disappear.”6 2 “ein müssiger metaphysischer Begriff.” E. Mach, Die Mechanik in ihrer Entwicklung (Leipzig: Brockhaus, 1883, 1921), p. 217; The Science of Mechanics (Chicago: Open Court, 1893, 1960), p. 273. 3 See E. Mach, “Untersuchungen über den Zeitsinn des Ohres,” Sitzungsberichte der Kaiserlichen Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Classe, Wien, 51, 133–150 (1865); Die Mechanik in ihrer Entwicklung (note 2) chapter 2, section 6; Die Analyse der Empfindungen (Jena: Fischer, 1885, 1922), chapter XII (“Die Zeitempfindung”); The Analysis of Sensations (Chicago: Open Court, 1914); Die Principien der Wärmelehre (Leipzig: Barth, 1896, 1919); Erkenntnis und Irrtum (Leipzig: Barth, 1905, 1920); Knowledge and Error (Dordrecht: Reidel, 1976), chapter XXIII, “Physiological Time in Contrast to Metrical Time,” and chapter XXIV, “Space and Time Physically Considered.” 4 E. Mach, Die Mechanik in ihrer Entwicklung, note 2 (1921), pp. 218–219; (1960), pp. 274–275. 5 E. Mach, Die Analyse der Empfindungen, note 3 (1922), p. 286. 6 Note 2 (1921), p. 219; (1960), pp. 275–276. It is not surprising that Mach never used the notion of distant simultaneity , for his rejection of time necessarily implied the rejection of simultaneity as a temporal concept. The nearest substitute can be found in his essay Space and Time Physically Considered in which he wrote...