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Forms of Time: Unity in Plurality Jirˇ´I Wackermann Dept

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Forms of Time: Unity in Plurality Jirˇ´I Wackermann Dept SR21 Working Document Conference paper 1 Forms of Time: Unity in Plurality Jirˇ´ı Wackermann Dept. of Empirical and Analytical Psychophysics Institute for Frontier Areas of Psychology and Mental Health Freiburg i. Br., Germany 1 Time, the measure and the measurable Time is not a thing among other things; time is rather a form of the process of universal change, given in a succession of distinct world’s states. The world is a theatre of appearances arising from and receding to an undifferentiated background. Things of the world are in a continuous flux, in permanent alternation and succession, according to the order of time.1 — In this archaic view, time is a synonym for the ordering principle ruling the Universe, o¹o&. Time is primarily cosmic time, manifesting itself in the regularity of the world’s process. In Plato’s philosophical myth, time was a “moving image of eternity,”2 constructed on mathematical principles (fixed arithmetic ratios). Therefore, time can be conceived as a quantitative measure of change, or, in Aristotle’s classical definition, the “number of motion in respect of ‘before and after’.”3 This notion of arithmetised time was a precursor of the notion of ‘mathematical time,’ required by the rise of new, dynamical physics (Galilei, Huygens, Newton et al.). Conceptually, time in physics is a parameter of dynamic equations, increasing monotonically with the succession of world states. Operationally, time is measured by a clock, a system implementing a locally bound inertial motion, and thus believed to provide a uniform measure of time (Huygens). Newton postulated “absolute, true, mathematical time [which] flows equably without relation to anything external,”4 that is, an objective reality independent from clocks and observers. Later criticism of Newton’s concepts (Mach, Poincare;´ see Section 2) emphasised the relational notion of time and enforced operational analysis of two key notions, namely, simultaneity of events, and uniformity of time- scales: a ‘prelude’ to Einstein’s special relativity and subsequent theoretical developments. There is a peculiar dialectic in the historical movement of the concept of time: first implanting the cosmic ideal of uniform time in local clocks, and then aiming at a reconstruction of the unitary concept of time out of scattered clocks’ readings.5 As a residue of this development, there is a certain ambiguity permeating our language: time is thought as the measure of all things, and also as some-thing measurable. 1Anaximander: “·®¿® ¿´º ¿o ½oºo ¿®»¶º”; see G. S. Kirk, J. E. Raven, M. Schofield, The Presocratic Philoso- phers (2nd ed.), Cambridge: University Press, 1983. The ‘undifferentiated background’ of phenomena can be identified with Anaximander’s ‘unlimited,’ ®¼"¶½oº. 2Plato, Timaeus 37d: “"¶·!º ·¶º´¿oº ®¶!ºo&”; see The Collected Dialogues of Plato (ed. by E. Hamilton & H. Cairns), Princeton: University Press, 1963. 3Aristotle, Physics 219b: “®½¶#¹o& ·¶º´"!& ·®¿® ¿o ¼½o¿"½oº ·®¶ ¿"½oº”; see The Complete Works of Aristotle, Vol. I (ed. by J. Barnes) Princeton: University Press, 1984. 4I. Newton, Philosophiae Naturalis Principia Mathematica, Book I (transl. by A. Motte, rev. by F. Cajori), Berkeley: University of California Press, 1934. (Original work dated 1689.) 5P. Galison (Empires of Time. Einstein’s Clock and Poincare’´ s Maps, New York: Norton, 2003) links the late 19th century’s development of transportation, communication and clock synchronisation technologies with the conceptual development of Einstein’s relativity. SR21 Working Document Conference paper 2 2 Reality of time: observational approach The common language maintains a highly pictorial metaphor of time as something stuff-like, something that ‘flows’; clocks, then, are seen as clever instruments capable to detect, measure, and indicate the amount of ‘the flown’ (elapsed duration). In this na¨ıve view, clocks are like spinning windmills driven by the ‘wind of time’: maybe a nice poetical image, but certainly a wrong concept.6 The misleading metaphor is further supported by some authors’ claims that ‘passage of time’ is an immediate, introspectively accessible datum of consciousness.7 This common intuition fits well with the image provided by Newton’s concept of ‘absolute time’ unrelated to any empirical reality or observable process. However, this concept was rejected by Ernst Mach “as an idle metaphysical conception,” since “time independent of change [...] absolute time can be measured by comparison with no motion [...] has therefore neither a practical nor a scientific value.”8 In Mach’s view, it is incorrect to say that we “measure the changes of things by time. Quite the contrary, time is an abstraction, at which we arrive by means of the changes of things; made because we are not restricted to any one definite measure, all being interconnected.”9 In a similar vein, Henri Poincare´ emphasised the multiplicity of possible operational definitions of a measure of time, and concluded: “Time should be so defined that the equations of mechanics may be as simple as possible. [...] [T]here is not one way of measuring time more true than another; that which is generally adopted is only more convenient.”10 Poincare´ thought primarily of simple expression of laws of mechanics (in Newtonian tradition);11 but Mach properly observed that actu- ally any physical process may serve as the basis of time measure as, for example, “the excess of the temperature of a cooling body over that of its surroundings.”12 There is no ground for preference of mechanical motions as a standard of time-keeping; and there is no a priori necessity that time-scales conveniently applicable within different domains of phenomena be identical.13 In a brief summary: Mach’ and Poincare’´ s critiques amounted to a complete revision of the concept of time; in the famous brief phrasing, ‘time is what the clock indicates.’ — Clocks are not passive devices ‘driven by time,’ but rather artifacts superimposed on the observation field, and actively generating a measure of time; that is, providing indications w. r. t. which any particular process can be compared. In observational terms, there is nothing like ‘true time,’ approximated by clocks, but only classes of clocks defining the same time-scale (see Section 6). Physical theories, or individual chapters of physics (mechanics, thermodynamics, etc.) are self-consistent (as far as 6An amusing simile between a clock and a gas-meter is found in the classical work of Victorian physics, Elements of Natural Philosophy by W. Thomson and P. G. Tait, x367. 7A. S. Eddington, The Nature of the Physical World, Cambridge: University Press, 1928, p. 51. 8E. Mach, The Science of Mechanics. A Critical and Historical Account of Its Development, LaSalle (IL): Open Court, 1960, p. 272. (Original work dated 1883.) 9Mach, ref. 8, p. 273. 10 H. Poincare,´ The Value of Science, pp. 227–228; in The Foundations of Science (transl. by G. B. Halsted), New York: Science Press, 1929. (Original work dated 1898.) 11Cf. P. Mittelstaedt, Der Zeitbegriff in der Physik, Mannheim: BI-Wissenchaftsverlag, 1989, esp. Chapter 2. 12E. Mach, Analysis of Sensations (transl. by C. M. Williams), New York: Dover, 1959, p. 349. (Original work dated 1886.) — Mach’s proposal to measure durations as function of the test body’s temperature requires that a temperature scale is already defined; Mach himself was dealing with the latter problem in Principles of the Theory of Heat. Later we shall see a construction of a time-keeping mechanism on a pre-metric basis. 13J. Bergquist, S. Jefferts, and D. Wineland, Physics Today 54.3: 37, 2001. SR21 Working Document Conference paper 3 possible) descriptions of observational relations between phenomena under study, out of which the time dimension is “obtained by abstraction,” said with Mach. This radically observational stance may be confusing for adherents of na¨ıve realism, but also frustrating for philosophers who misinterpret it as a philosophical doctrine. Indeed, the operational (instrumentalist, conventionalist) position is often presented and criticised (or ridiculised) as an opposite of ‘scientifically informed realism.’ We wish to emphasise that questions such as ‘does time really exist?’ and arguments in favour of a positive or negative answer, are perfectly irrelevant for our investigations. As said in the introduction, “time is not a thing among other things”; in other words, time is ‘no-thing’—which is not the same as saying ‘time is nothing,’ therefore not real, therefore inexistent. Time is as real as other ‘abstractions’ are real: not things, not substances, but rather co-ordinates in a given descriptive system. 3 Plurality of times? For centuries, the Earth’s rotation served as the standard for synchronisation and correction of terrestrial, mechanical clocks. At present, measure of time is defined via a frequency standard based on atomic spectrometry, which is in good empirical agreement with the earlier definition.14 This standard is also at the basis of the ‘universal time’ (UT) implemented in a planet-wide system of synchronised clocks.15 The notion of time derived from fundamental laws of physics, thus perme- ates all domains of empirical reality, in sciences and technology as well as in practical, social and economical life. Due to this unitary concept, all temporal data—e. g. life-times of elementary parti- cles, firing rates of neural cells, dating of historical events and geological epochs—can be projected onto one axis of numeric coordinates. Yet, it is often felt that this notion of uniform time is alien to the proper dynamics of biological, psychological, or social processes. It is claimed that time of physics is not intrinsically or naturally related to the ‘proper time’ (eigentime) of biological or social systems. So, for example, the notion of ‘physiological’ time has been coined in biological sciences: the proper time-scale of an individual organism’s life-span, non-linearly related to physical time, and operationalised by the growth rate of cellular tissues,16 or via dynamic parameters of the organismic metabolism.17 In the same vein, the eigentime of biological evolution would be defined by the evolutionary process itself, for ex- ample, by the production rate of genomic combinations.
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