Making Time: A Study in the Epistemology of Measurement Eran Tal

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1 Brit. J. Phil. Sci. 67 (2016), Making Time: A Study in the Epistemology of Measurement ABSTRACT This article develops a model-based account of the standardization of physical measurement, taking the contemporary standardization of time as its central case study. To standardize the measurement of a quantity, I argue, is to legislate the mode of application of a quantity concept to a collection of exemplary artefacts. Legislation involves an iterative exchange between top-down adjustments to theoretical and statistical models regulating the application of a concept, and bottom-up adjustments to material artefacts in light of remaining gaps. The model-based account clarifies the cognitive role of ad hoc corrections, arbitrary rules, and seemingly circular inferences involved in contemporary timekeeping, and explains the stability of networks of standards better than its conventionalist and constructivist counterparts. 1 Introduction 2 Making Time Universal 2.1 Stability and accuracy 2.2 Multiple realizability 2.3 The challenges of synchronicity 2.4 Divergent standards 2.5 The leap second 3 The Two Faces of Stability 3.1 An explanatory challenge 3.2 Conventionalist explanations 3.3 Constructivist explanations 4 Models and Standardization 4.1 A third alternative 4.2 Stability reconceived 4.3 Legislative freedom ß The Author Published by Oxford University Press on behalf of British Society for the Philosophy of Science. All rights reserved. doi: /bjps/axu037 For Permissions, please journals.permissions@oup.com Advance Access published on December 5, 2014

2 Discovering gaps 4.5 Nature and society entangled 4.6 Remark on scope 5 Conclusions 1 Introduction The reproducibility of quantitative results in the physical sciences depends on the availability of stable measurement standards. The maintenance, dissemination and improvement of standards are central tasks in metrology, the science of measurement, and its application (Joint Committee for Guides in Metrology [2012], Definition 2.2). Under the guidance of the Bureau International des Poids et Mesures (International Bureau of Weights and Measures, or BIPM) near Paris, a worldwide network of metrological institutions is responsible for the ongoing comparison and adjustment of standards. Among the various standardization projects in which metrologists are engaged, contemporary timekeeping is often considered the most successful, with the vast majority of national time signals agreeing well within a microsecond and stable to within a few nanoseconds a month. 1 The standard measure of time currently used in almost every context of civil and scientific life is known as coordinated universal time or UTC. 2 UTC is the product of an international cooperative effort by time centres that rely on state-of-the-art atomic clocks spread throughout the globe. These clocks are designed to measure the frequencies associated with specific atomic transitions, including the caesium transition, which has defined the second since The success of time standardization makes it an instructive case study for the epistemology of measurement, that is, for the study of the relationships between measurement and knowledge. Central topics that fall under the purview of the epistemology of measurement include the conditions under which measurement produces knowledge; the content, scope, justification, and limits of such knowledge; the reasons why particular methodologies of measurement and standardization succeed or fail in supporting particular knowledge claims; and the relationships between measurement and other knowledge-producing activities such as observation, theorizing, experimentation, modelling, and calculation. While these topics are certainly not new to philosophy, in Barring time zone and daylight saving differences. See (BIPM [2013]) for a sample comparison of national approximations to UTC. An excerpt from the latter document appears in Figure 1. UTC replaced Greenwich Mean Time as the global timekeeping reference in The acronym UTC was chosen as a compromise to avoid favouring the order of initials in either English (CUT) of French (TUC). The definition of the atomic second will be discussed in the next section.

3 Making Time 299 recent years they have been receiving focused and systematic attention from a growing number of scholars. 4 Intended as a contribution to the burgeoning body of literature on the epistemology of measurement, this article will attempt to clarify how successful standardization projects produce knowledge, what kind of knowledge they produce, and why such knowledge should be deemed reliable. I will develop my account of standardization by examining the methods currently used to standardize time and by tracing the sources of those methods reliability. A central desideratum for the reliability of measurement procedures is stability, conceived as a double-aspect notion: the stability of a single measuring instrument is its tendency to produce the same measurement outcome over repeated runs, whereas the stability of a collection of instruments is their tendency to reproduce each other s outcomes. In the case of clocks, the stability of a single clock is its tendency to tick at the same frequency over time, whereas the stability of an ensemble of clocks is their tendency to tick at the same frequency as each other. 5 What accounts for the overwhelming stability of contemporary timekeeping standards? Or, to phrase the question somewhat differently, what factors enable a variety of standardization laboratories around the world to closely reproduce coordinated universal time on an ongoing basis? I will use this question as a test for the epistemology of standardization. A satisfactory account of standardization would explain how the various methods currently employed to standardize time succeed in maintaining a stable global system of timekeeping and why these methods are justified from an epistemic perspective. The various explanans one could offer for stability may be divided into two broad kinds. First, one could appeal to the discovery of empirical regularities in the behaviour of the atomic clocks that keep world time. Second, one could appeal to agreement among the metrological institutions that interpret and correct these atomic clocks. The adequate combination of these two sorts of explanans and the limits of their respective contribution to stability are 4 5 See especially (Boumans [2005], [2007]; Chang [1995], [2001], [2004]; Klein and Morgan [2001]; Leplège [2003]; Mari [2003]; McClimans [2010]; Morrison [2009]; Riordan [2015]; Soler et al. [2013]; Tal [2011], [2012]; Teller [2013]; van Fraassen [2008], [2012]). For a discussion of the relationships between traditional and contemporary philosophy of measurement, see (Tal [2013]). In official metrological terminology, these aspects of stability are called measurement repeatability and measurement reproducibility, respectively (Joint Committee for Guides in Metrology [2012], 2.21 and 2.25). Though conceptually distinct, these two aspects of stability cannot be evaluated separately. In the case of time measurement, for example, the only way to evaluate the stability of a clock s frequency is to compare it with the frequencies of other clocks. Similarly, the only way to determine whether fluctuations in the outcomes of a mass measurement are due to changes in the mass of the object being measured or in the imperfections of the balance is to compare these outcomes to those obtained from other balances (or other mass-measuring instruments) under similar circumstances. From an epistemological point of view, then, these two aspects of stability are deeply entangled. My claims about stability throughout this article are intended to apply to both aspects unless otherwise specified.

4 300 contested issues among philosophers and sociologists of science. Following a discussion of the central methods and challenges involved in contemporary timekeeping (Section 2), I will explore the strengths and limits of two existing approaches to the study of standardization, namely, conventionalism and constructivism (Section 3). While both approaches offer valuable insights into the practice and semantics of standardization, I will show that they focus too narrowly on either natural or social explanations for the stability of standards. The fourth and final section will present a novel, model-based account of standardization. As I will argue, facts about the stability of measuring instruments are model-based, that is, sensitive to the theoretical and statistical assumptions under which those instruments are modelled. By making occasional modifications to the way measurement standards are modelled, standardization bureaus are able to regulate the mode of application of a quantity concept even when the concept s definition remains unchanged. The model-based account will explain how both natural and social elements are mobilized through metrological practice, and will provide an epistemic justification for the ad hoc and seemingly circular aspects of time standardization. In so doing, the modelbased account will shed light on the content and quality of knowledge produced by successful standardization projects. 2 Making Time Universal 2.1 Stability and accuracy The measurement of time relies predominantly on counting the periods of cyclical processes, namely, clocks. 6 Until the late 1960s, time was standardized by recurrent astronomical phenomena such as the apparent solar noon, and artificial clocks served only as secondary standards. Contemporary time standardization relies on atomic clocks, that is, instruments that produce an electromagnetic signal that tracks the frequency of a particular atomic resonance. The two central desiderata for a reliable clock are known in the metrological jargon as frequency stability and frequency accuracy. The frequency of a clock is said to be stable if it ticks at a uniform rate, that is, if its cycles mark equal time intervals. The frequency of a clock is said to be accurate if it ticks at the desired rate, that is, a specified number of cycles per second The term clock is used here in a broad sense to include both artificial and natural systems for measuring time. This is in line with the common definition of a clock in physics: a system consisting of an oscillator and a counter (Jones [2000], p. 26), where the oscillator may be a naturally occurring process such as the Earth s rotation around its axis. Frequency stability is, in principle, sufficient for reproducible timekeeping. A collection of clocks with perfectly stable frequencies would tick at constant rates relative to each other, and so the readings of any such clock would be sufficient to reproduce the readings of any of the others by simple linear conversion, barring relativistic effects. A collection of individually

5 Making Time 301 In practice, no clock has a perfectly stable frequency. The very notion of a stable frequency is an idealized one, derived from the theoretical definition of the standard second. Since 1967, the second has been defined as the duration of exactly 9,192,631,770 periods of the radiation corresponding to a hyperfine transition of caesium-133 in the ground state (BIPM [2006], p. 113). This definition plays a double role: it both defines the duration of the standard second and stipulates that a particular frequency associated with the caesium atom is uniform, that is, that its periods are equal to one another. However, the frequency in question is a highly idealized construct. As far as the definition is concerned, the caesium atom in question is at rest at zero degrees Kelvin with no background fields influencing the energy associated with the transition. It is only under these ideal conditions that a caesium atom would constitute a perfectly stable clock. 8 There are several different ways to construct clocks that would approximately satisfy or in metrological jargon, realize the conditions specified by the definition. Different clock designs result in different trade-offs between frequency accuracy, frequency stability, and other desiderata, such as ease of maintenance, ease of comparison, and low financial cost. Primary realizations of the second are designed for optimal accuracy, that is, minimal uncertainty with respect to the rate in which they tick. As of 2011, twelve primary realizations are maintained by leading national metrological laboratories worldwide. 9 These clocks are special by virtue of the fact that every known influence on their output frequency is controlled and rigorously modelled, resulting in detailed uncertainty budgets. The clock design implemented in most primary standards is the caesium fountain, so called because caesium atoms are tossed up in a vacuum and fall down due to gravity. 10 The complexity of caesium fountains, however, and the need to routinely monitor their performance and environment prevents them from running continuously. Instead, each caesium fountain clock usually operates only for a few weeks at a time, about five times a year. The intermittent operation of caesium fountain clocks means that they cannot be used directly for timekeeping. Instead, they are used to calibrate secondary standards, that is, atomic clocks that are less accurate but run continuously for years. About four hundred such secondary stable clocks is thus also stable in the global sense of the term, that is, they support the reproducibility of measurement outcomes (see also Footnote 5). 8 Paradoxically, under these ideal conditions it would be impossible to probe the caesium atom so as to induce the relevant transition. Hence the duration of the second is defined in a doubly counterfactual manner. 9 In 2011, active primary frequency standards were maintained by laboratories in France, Germany, Italy, Japan, the UK, and the US (BIPM [2011], p. 32) 10 This design allows for a higher signal-to-noise ratio through the use of Ramsey resonance. For a summary of the design principles of caesium fountains see (Audoin and Guinot [2001], pp ).

6 302 standards are currently employed to keep world time (Panfilo [2012], p. 242). These clocks are highly stable in the short run, meaning that the ratios between the frequencies of their ticks remain very nearly constant over weeks and months. But over longer periods the frequencies of secondary standards exhibit drifts, both relative to each other and in relation to the frequencies of primary standards. 2.2 Multiple realizability As neither primary nor secondary standards tick at exactly the same rate, metrologists are faced with a variety of real durations that can all be said to fit the definition of the second with some degree of uncertainty. Metrologists are thus faced with the task of realizing the second based on indications from multiple, and often divergent, clocks. Elsewhere I have called this the problem of multiple realizability of unit definitions and discussed the way this problem is solved in the case of primary frequency standards (Tal [2011]). By contrast, this article focuses on the ways metrologists solve the problem of multiple realizability in the context of international timekeeping, where the goal is not merely to produce good local approximations of the standard second but also to maintain a unified measure of time and synchronize clocks worldwide in accordance with this measure. To tackle this challenge, metrologists construct idealized theoretical representations of their clock ensemble. From a theoretical point of view, the unified timescale chosen as the basis for international timekeeping is called terrestrial time. Corresponding to coordinate time on the earth s surface, this timescale is chosen so that differences in proper time among local clocks could be accounted for. Ideally, one can imagine all of the atomic clocks that participate in global timekeeping as located on a rotating surface of equal gravitational potential that approximates the earth s sea level. Such a surface is called a geoid, and terrestrial time is the time a perfectly stable clock on that surface would tell when viewed by a distant observer. However, much like the definition of the second, the definition of terrestrial time is highly idealized and cannot be used directly to evaluate the accuracy of any concrete clock. Moreover, unlike primary standards, there is no practical way to evaluate the individual uncertainties of secondary standards from first theoretical principles. The solution is to introduce an operational measure of time that would approximate terrestrial time, while also maintaining a known relation to the indications of concrete clocks. This intermediary measure of time is coordinated universal time More exactly, Terrestrial Time is approximated by international atomic time (TAI), identical to UTC except for leap seconds. This point will be clarified below.

7 Making Time 303 Figure 1. Excerpt from Circular-T (BIPM [2013]), a monthly report with which the International Bureau of Weights and Measures disseminates coordinated universal time (UTC) to national standardization institutes. The numbers in the first seven columns indicate differences in nanoseconds between UTC and each of its local approximations at five-day intervals. The last three columns indicate type-a, type-b, and total uncertainties. Only data associated with the first twenty laboratories are shown (ß BIPM. Reproduced with permission). Coordinated universal time is a measure of time whose scale interval its basic unit is intended to remain as close as is practically possible to a standard second on the rotating geoid. Yet UTC is not a clock; it does not actually tick, and cannot be continuously read off the display of any instrument. Instead, UTC is an abstract measure of time: a set of numbers calculated monthly in retrospect, based on the readings of participating clocks. 12 At the BIPM near Paris, the indications of secondary standards from over sixty national laboratories are recorded at five-day intervals, and used to calculate UTC. The end result of the calculation is a table of numbers that indicate how late or early each nation s master time its local approximation of UTC has been running in the past month. Typically ranging from a few nanoseconds to a few microseconds, these numbers allow national metrological institutes to tune their clocks to internationally accepted time. Figure 1 is an excerpt from the monthly publication issued by the BIPM in which deviations from UTC are reported for each national laboratory. 12 There are many clocks that approximate UTC, of course. As will be mentioned below, the BIPM and national laboratories produce continuous time signals that are considered realizations of UTC. However, UTC itself is an abstract measure and should not be confused with its many realizations.

8 The challenges of synchronicity UTC is calculated in three major steps, each involving its own set of conceptual and methodological difficulties. The first step involves processing data from hundreds of continually operating atomic clocks and calculating the free-running time scale, EAL (Échelle Atomique Libre). EAL is an average of clock indications weighted by frequency stability. Finding out which clocks are more stable than others requires some higher standard of stability against which clocks would be compared, but arriving at such a standard is the very goal of the calculation. For this reason EAL itself is used as the standard of stability for the clocks contributing to it. Every month, the BIPM rates the weight of each clock depending on how well it predicted the weighted average of the EAL clock ensemble in the past twelve months. The updated weight is then used to average clock data in the next cycle of calculation. This method promotes clocks that are stable relative to each other, while clocks whose stability relative to the overall average falls below a fixed threshold are given a weight of zero and removed from that month s calculation. The average is then recalculated based on the remaining clocks. The process of removing offending clocks and recalculating is repeated exactly four times in each monthly cycle of calculation (Audoin and Guinot [2001], p. 249). Though effective in weeding out noisy clocks, the weight updating algorithm introduces new perils to the stability of world time. First, there is the danger of a positive feedback effect, in which a few clocks become increasingly influential in the calculation simply because they have been dominant in the past. In this scenario, EAL would become tied to the idiosyncrasies of a handful of clocks, thereby increasing the likelihood that the remaining clocks would drift farther away from EAL. For this reason, the BIPM limits the weight allowed to any clock to a maximum of about 0.7%. 13 Other than positive feedback, a second source of potential instability is the abruptness with which new clock weights are modified every month. Because different clocks tick at slightly different rates, a sudden change in weights results in a sudden change of frequency of the weighted average. To avoid frequency jumps, the BIPM adds cushion terms to the weighted average based on a prediction of that month s jump (Audoin and Guinot [2001], pp ). As a third precautionary measure, the BIPM assigns a zero weight to new clocks for a four month test interval before authorizing them to exert influence on international time. While the weighting algorithm stabilizes the average to some extent, further stabilization requires modifications to the composition of the clock ensemble. 13 The method of fixing this maximum weight has itself been modified four times in the past two decades to optimize stability, and as of 2012 a new method of calculating weights is being considered in order to increase stability further (Petit [2004], p. 308; Panfilo [2012], p. 246).

9 Making Time 305 As mentioned above, EAL is maintained by a free-running ensemble of secondary standards. Today the majority of these clocks are commercially manufactured by Hewlett Packard or one of its offshoot companies, Agilent or Symmetricom. These clocks have proven to be exceptionally stable relative to each other, and the number of Hewlett Packard clocks that participate in UTC has been steadily increasing since their introduction into world timekeeping in the early 1990s (Petit [2004], p. 208). 14 The results of averaging depend not only on the choice of weighting algorithm and clock manufacturer, but also on the selection of participating laboratories. Only laboratories in nations among the eighty members and associates of BIPM are eligible for participation in the determination of EAL. Funded by membership fees, the BIPM aims to balance the threshold requirements of metrological quality with the financial benefits of inclusiveness. Membership requires national diplomatic relations with France, the depositary of the intergovernmental treaty known as the Metre Convention (Convention du Mètre). This treaty authorizes BIPM to standardize industrial and scientific measurement. The BIPM encourages participation in the Metre Convention by highlighting the advantages of recognized metrological competence in the domain of global trade, and by offering reduced fees to smaller states and developing countries (Quinn [2003]). Economic trends and political considerations thus influence which countries contribute to world time and, indirectly, which atomic clocks are included in the calculation of UTC. Comparing clocks in different locations around the globe requires a reliable method of fixing the interval of comparison. This is another major challenge to globalizing time. Were the clocks located in the same room, they could be connected by optical fibres to a counter that would indicate the difference, in nanoseconds, among their readings every five days. Over large distances, time signals are transmitted via satellite. In most cases global positioning system (GPS) satellites are used, thereby linking the readings of participating clocks to GPS time. But satellite transmissions are subject to delays, which fluctuate depending on atmospheric conditions. Moreover, GPS time is itself a relatively unstable derivative of UTC. These factors introduce uncertainties to clock comparison data known as time transfer noise. Increasing with its distance from Paris, transfer noise is often much larger than the local instabilities of contributing clocks. This means that the stability of UTC is in effect limited by satellite transmission quality. 14 As of 2010, Hewlett Packard clocks constituted more than two-thirds of contributing clocks (BIPM [2011], p. 79). A smaller portion of continuously running clocks are hydrogen masers, an atomic clock that probes a transition in hydrogen rather than in caesium.

10 Divergent standards Despite the multiple means employed to stabilize the weighted average of clock readings, additional steps are necessary to guarantee stability, due to the fact that the frequencies of continuously operating clocks tend to drift away from those of primary standards. In the late 1950s, when atomic time scales were first calculated, they were based solely on free-running clocks. Over the course of the following two decades, technological advances revealed that universal time was running too fast: the primary standards that realized the second were beating slightly slower than the clocks that kept time. To align the two frequencies, in 1977 the second of UTC was artificially lengthened by one part in At this time it was decided that the BIPM would make regular small corrections that would steer the atomic second toward its officially realized duration, in an attempt to avoid future shocks (Audoin and Guinot [2001], p. 250; BIPM [1977], p. 54; BIPM [1978], p. 90). This decision effectively split atomic time into two separate scales, each ticking with a slightly different second: on the one hand, the weighted average of free-running clocks (EAL) and, on the other, the continually corrected (or steered ) international atomic time, TAI (Temps Atomique International). The monthly calculation of steering corrections is a remarkable algorithmic feat, relying upon intermittent calibrations against the world s twelve primary standards. These calibrations differ significantly from one another in quality and duration. 15 For this reason the BIPM assigns weights, or filters, to each calibration episode depending on its quality. But filtering is not sufficient: primary standards do not have exactly the same frequency, giving rise to the concern that the duration of the UTC second could fluctuate depending on which primary standard contributed the latest calibration. To circumvent this, the steering algorithm is endowed with memory, extrapolating data from past calibration episodes into times in which primary standards are offline. This extrapolation must itself be time-dependent, as noise limits the capacity of free-running clocks to remember the frequency to which they were last calibrated. The BIPM thus constructs statistical models for the relevant noise factors and uses them to derive a temporal coefficient, which is then incorporated into the calculation of filters (Arias and Petit [2005]; Azoubib et al. [1977]). This steering algorithm allows metrologists to track the difference in frequency between free-running clocks and primary standards. Ideally, the difference in frequency would remain stable, that is, there would be a constant 15 Some primary standards are active for longer periods than others, resulting in a better signal; some calibrations suffer from higher transfer noise; and some of the primary standards are more accurate than others. See (Tal [2011]) for a detailed discussion of how the accuracy of primary frequency standards is evaluated.

11 Making Time 307 ratio between the seconds of the two measures. In this ideal case, a simple linear transformation of EAL would provide us with a continuous timescale as accurate as a caesium fountain. In practice, EAL continues to drift. During the decade prior to 2009, its second has lengthened by a yearly average of about 4 parts in relative to primary standards (Panfilo and Arias [2009], p. 112). This presents metrologists with a twofold problem: First, they have to decide how fast they want to steer world time away from the drifting average. Overly aggressive steering would destabilize UTC, while too small a correction would cause clocks the world over to slowly diverge from the official (primary) second. Indeed, the BIPM has made several modifications to its steering policy in the past three decades in an attempt to optimize both smoothness and accuracy (Audoin and Guinot [2001], p. 251). The other aspect of the problem is the need to stabilize the frequency of EAL itself. One solution to this aspect of the problem is to replace clocks in the ensemble with others that drift to a lesser extent. This task has largely been accomplished in the past two decades by the proliferation of Hewlett Packard clocks, but some instability remained. Since 2011, the calculation of EAL has incorporated a nonlinear prediction algorithm that compensates for clock instabilities in advance, a method which appears to have significantly reduced its overall frequency drift (Panfilo [2012]). Disagreement among standards is not the sole reason for frequency steering. Abrupt changes in the official duration of the second as realized by primary standards may also trigger steering corrections. These abrupt changes can occur when metrologists modify the ways in which they model primary standards. For example, in 1996 the metrological community achieved consensus around the effects of thermal background radiation on caesium fountains, previously a much debated topic. A new systematic correction was subsequently applied to primary standards that shortened the second by approximately 2 parts in While this difference may seem minute, it took more than a year of monthly steering corrections for UTC to catch up with the suddenly shortened second (Audoin and Guinot [2001], p. 251). 2.5 The leap second With the calculation of TAI, the task of realizing a unified timescale based on the definition of the standard second is complete. TAI is considered to be a realization of terrestrial time: an approximation of general-relativistic coordinate time on the earth s sea level. However, a third and last step is required to keep UTC in step with traditional time as measured by the duration of the solar day. The mean solar day is slowly increasing in duration relative to atomic time due to gravitational interaction between the earth and the moon. To keep noon UTC closely aligned with the apparent passage of the sun over the Greenwich meridian, a leap second is occasionally added to

12 308 UTC based on astronomical observations. By contrast, TAI remains free of the constraint to match astronomical phenomena, and runs ahead of UTC by an integer number of seconds The Two Faces of Stability 3.1 An explanatory challenge The global synchronization of clocks in accordance with atomic time is a considerable technological achievement. Coordinated universal time is disseminated to all corners of civil life, from commerce and aviation to telecommunication, in a manner that is seamless to the vast majority of its users. 17 The task of the remainder of this article is to explain how metrologists succeed in synchronizing clocks worldwide to coordinated universal time. What are the sources of this measure s efficacy in maintaining agreement among time centres? An adequate answer must account for the way in which the various ingredients that make up the calculation of UTC contribute to its success. In particular, the function of ad hoc corrections, rules of thumb, and seemingly circular inferences prevalent in the production of UTC requires explanation. What role do these mechanisms play in stabilizing UTC, and is their use justified from an epistemic point of view? In tackling these questions, I will consider two kinds of explanans that have been traditionally proposed for the stability of networks of physical measurement standards: (1) The empirical regularities exhibited by the behaviour of measurement standards; (2) The social coordination of policies for regulating and interpreting the behaviour of measurement standards. When the first explanans is emphasized, standardization is viewed as the discovery of regularities in the behaviour of some physical phenomena and the exploitation of these regularities for constructing stable measurement standards. The efficacy of standardization methods is accordingly explained by appealing to their cognitive function, namely, their suitability for discovering 16 In May 2013 the difference between TAI and UTC was thirty-five seconds (BIPM [2013]). 17 This achievement is better appreciated when one contrasts it to the state of time coordination less than a century-and-a-half ago, when the transmission of time signals by telegraphic cables first became available. Peter Galison ([2003]) provides a detailed history of the efforts involved in extending a unified geography of simultaneity across the globe during the 1870s and 1880s, when railroad companies, national observatories, and municipalities kept separate and conflicting timescales. Today, the magnitude of discrepancies among timekeeping standards is far smaller than is required by almost all practical applications, with the exception of a few highly precise astronomical measurements such as the study of millisecond pulsars (Guinot and Petit [1991]).

13 Making Time 309 regularities in empirical data. When the second explanans is emphasized, standardization is viewed as the social coordination of policies for manipulating and interpreting physical phenomena. The efficacy of standardization methods is then explained by their consensus-building function, generating universal agreement about the proper ways to conduct such manipulation and interpretation. What is the correct combination of these two explanans, and what sort of account of standardization results from their combination? Answering these questions will shed light on the purpose and epistemic status of the algorithmic manoeuvres involved in the calculation of UTC. But the scope of these questions extends beyond the measurement of time. Answering them will involve an inquiry into the goals of standardization projects, the sort of knowledge such projects produce, and the reasons such projects succeed or fail. This inquiry itself falls under the wider field known as the epistemology of measurement, which has attracted increasing attention in recent years. 18 Below I will propose a model-based account of standardization. This account will offer a novel analysis of the interplay between cognitive and social aspects of standardization by appealing to the dual descriptive and normative roles of metrological models. I will frame the model-based account by comparison to two earlier strands of scholarship on measurement. The first strand is commonly labelled conventionalism and includes a variety of views expounded by figures such as Ernst Mach ([1883/1919], pp ), Henri Poincaré ([1898/1958]), Hans Reichenbach ([1928/1958], pp ) and Rudolf Carnap ([1966/1995], pp ), among others. The second strand, which I will label constructivism, belongs to the social studies of science, and will be represented here by Bruno Latour ([1987], pp ) and Simon Schaffer ([1992]). With the exception of Schaffer, none of the abovementioned authors were primarily concerned with standardization, but rather with questions concerning, for example, the relationship between theory and observation, the structure of space and time, and the processes governing the social acceptance of scientific claims. My goal here is not to offer a comprehensive commentary on their writings; instead I will use some of their insights concerning standardization as a starting point for the development of an epistemology of standardization. Before proceeding to the analysis, it is worth clarifying which problems this article will not attempt to resolve. I will not be concerned with realism about measurement in its many forms. Questions such as are there mind-independent facts about temporal uniformity?, does the success of time standardization provide grounds for believing in the existence of such facts?, and should statements about clock accuracy be understood literally as statements about 18 See Footnote 4 for references.

14 310 closeness to truth? are outside the scope of the current discussion. This is noteworthy for two reasons: First, conventionalism and constructivism are traditionally labelled as anti-realist positions, and their adoption as starting points for the discussion may give the mistaken impression that the modelbased account embraces a similar metaphysical standpoint. However, the lessons I will draw from conventionalist and constructivist literature concern the structure and dynamics of standardization rather than any claims about truth or reality. Second, debates concerning realism commonly invoke truth or reality as potential explanans of scientific success. By contrast, the epistemological approach to measurement adopted in this article aims to explain success and failure by appealing only to resources that are practically available to scientists when measuring and standardizing. Such resources include, for example, theories, models, definitions, statistical tools, materials, instruments, data, observations, calculations, methodological and linguistic conventions, and institutional policies and regulations. Mind-independent truths about measurable quantities for example, the exact true value of a quantity or the true equality of two magnitudes are not cognitively accessible to metrologists and thus cannot serve as epistemic standards for measurement. The existence or lack of such truths can only be inferred from measurement outcomes in retrospect with the help of additional, metaphysical assumptions that are extrinsic to the practice of measuring. Indeed, were metrologists required to evaluate the accuracy and stability of their measuring instruments against such truths, metrology would be mired in scepticism. 19 Such truths or a lack thereof will thus not be considered legitimate epistemological explanans of success or failure in generating a stable network of clocks. The model-based account will accordingly remain metaphysically neutral and will neither presuppose nor deny any sort of realism about measureable quantities. 3.2 Conventionalist explanations Any plausible account of metrological knowledge must attend to the fact that metrologists enjoy some freedom in determining the correct application of the concepts they standardize, and should be able to clarify the sources and scope of this freedom. Traditionally, philosophers of science have taken standardization to consist in arbitrary acts of definition. Conventionalists like Mach, Poincaré, Carnap, and Reichenbach stressed the arbitrary nature of the choice 19 Metaphysical beliefs can still play a legitimate role in metrological practice indirectly through their psychological and social consequences. For example, metrologists may be psychologically motivated to accurately measure the value of a physical constant by their belief that the constant has an exact, mind-independent value. Their methods of accuracy evaluation would nonetheless be independent of the truth or falsity of their metaphysical beliefs, as clarified in (Tal [2011], pp ).

15 Making Time 311 of congruence conditions, namely, the conditions under which magnitudes of certain quantities such as length and duration are deemed equal to one another. In the case of duration, such conditions amount to a criterion of uniformity in the flow of time. Poincaré ([1898/1958]) argued against the existence of a mind-independent criterion of temporal uniformity. Instead, he claimed that the choice of a standard measure of time is the fruit of an unconscious opportunism that leads scientists to select the simplest system of laws ([1898/1958], p. 36). Reichenbach called these arbitrary choices of congruence conditions coordinative definitions because they coordinate between the abstract concepts employed by a theory and the physical relations denoted by these concepts (Reichenbach [1928/1958], p. 14). 20 Prior to such coordinative definition, there is no fact of the matter as to whether two given time intervals are equal ([1928/1958], p. 116). Which physical process is deemed uniform (for example, solar day, pendulum cycle, or radiation associated with an atomic transition) depends on considerations of convenience and simplicity in the description of empirical data rather than on the data themselves. The standardization of time, according to conventionalists, involves a free choice of a coordinative definition for uniformity. It is worth highlighting three features of this definitional sort of freedom. First, it is an a priori freedom in the sense that its exercise is independent of experience. One may choose any uniformity criterion as long as the consequences of that criterion do not contradict one another. Second, it is a freedom only in principle and not in practice. For pragmatic reasons, scientists select uniformity criteria that make their descriptions of nature as simple as possible. The actual selection of coordinative definition is thus strongly constrained by the results of empirical tests. Third, definitional freedom is singular in the sense that it is completely exhausted by a single act of exercising it. Though a definition can be replaced by another, each such replacement annuls the previous definition. In this respect, acts of definition are essentially ahistorical. Once a coordinative definition of uniformity is specified, conventionalists hold that the truth or falsity of empirical claims concerning temporal uniformity is completely fixed. How uniformly a given clock ticks relative to a specified uniformity criterion is purely a matter of empirical fact. The remaining task for metrologists is only to discover which clocks tick at a more stable 20 Coordinative definitions are required because theories by themselves do not specify the application conditions for the concepts they define. A theory can only link concepts to one another for example, linking the concept of uniformity of time to the concept of uniform motion but it cannot determine which real motions or frequencies count as uniform (Reichenbach [1928/1958], p. 14). This, of course, is true only under the very restrictive notion of theory that was accepted in the early days of logical positivism.

16 312 rate relative to the conventionally chosen process and to improve those clocks that are found to be less stable. In Carnap s own words: If we find that a certain number of periods of process P always match a certain number of periods of process P, we say that the two periodicities are equivalent. It is a fact of nature that there is a very large class of periodic processes that are equivalent to each other in this sense. (Carnap [1966/1995], pp. 82 3, my emphasis) We find that if we choose the pendulum as our basis of time, the resulting system of physical laws will be enormously simpler than if we choose my pulse beat [...] Once we make the choice, we can say that the process we have chosen is periodic in the strong sense. This is, of course, merely a matter of definition. But now the other processes that are equivalent to it are strongly periodic in a way that is not trivial, not merely a matter of definition. We make empirical tests and find by observation that they are strongly periodic in the sense that they exhibit great uniformity in their time intervals. (Carnap [1966/1995], pp. 84 5, my emphases) In contemporary timekeeping, the definition of the second also functions as a coordinative definition of uniformity. Recall that the current definition of the second, in addition to fixing a unit of time, also postulates that the period of electromagnetic radiation associated with a particular transition of the caesium atom is constant. Accordingly, a conventionalist like Carnap would explain the stability of contemporary timekeeping by a combination of two factors: on the social side, the worldwide agreement to define uniformity on the basis of the frequency of the caesium transition; and on the natural side, the fact that all caesium atoms under specified conditions have the same frequency associated with that particular transition. The universality of the caesium transition frequency is, according to conventionalists, a mind-independent, empirical regularity that metrologists cannot influence but only describe more or less simply. How does the conventionalist explanation of stability fare with respect to the actual methods used to standardize time? From a conventionalist point of view, the main task facing metrologists is that of detecting which of the hundreds of atomic clocks used to standardize time tick at a more stable rate relative to the defined caesium frequency. If the algorithmic manoeuvres employed in the calculation of UTC serve any epistemic purpose, it is to detect these stable clocks. A conventionalist, in other words, would view UTC as an indicator for regularities in the frequencies of clocks, regularities that may be described more or less simply but are themselves independent of human choice. The reproducibility of contemporary timekeeping would accordingly be explained by the reliability with which the UTC algorithm detects those underlying regularities. The idea that UTC is a reliable indicator of mind-independent regularities gains credence from the fact that UTC is gradually steered towards the

17 Making Time 313 frequency of primary standards. As previously mentioned, primary frequency standards are rigorously evaluated for uncertainties and compared to each other in light of these evaluations. The fact that the frequencies of different primary standards are consistent with each other within uncertainty bounds can be taken as an indication for the universal regularity of the caesium frequency. Assuming, as metrologists do, that the long-term frequency stability of UTC over years is due mostly to the contribution of primary standards (Audoin and Guinot [2001], p. 251), one can plausibly make the case that the algorithm that produces UTC is a reliable detector of a natural regularity, namely, the fact that all caesium-133 atoms have the same frequency associated with the specified transition. The conventionalist analysis nevertheless leaves unexplained the success of the mechanisms that keep UTC stable in the short-term, when UTC is averaged over weeks and months. These mechanisms include the ongoing redistribution of clock weights, the limiting of maximum weight, the slicing of steering corrections into small monthly increments, and the increasingly exclusive reliance on Hewlett Packard clocks, among others. One way of accounting for these short-term stabilizing mechanisms is to treat them as pragmatic tools for facilitating consensus among metrological institutions. I will discuss this approach in the next subsection. Another option would be to look for a genuine epistemic function that these mechanisms serve. To a conventionalist, this means finding a way of vindicating these self-stabilizing mechanisms as reliable indicators of an underlying empirical regularity. As a reliable indicator is one that is sensitive to the property being indicated, one should expect the relevant stabilizing mechanisms to do less well when such regularity is not strongly supported by the data. In practice, however, no such degradation in stability occurs. On the contrary, short-term stabilization mechanisms are designed to be as insensitive to frequency drifts or gaps in the data as is practically possible. It is rather the data that are continually adjusted to stabilize the outcome of the calculation. As already mentioned, whenever a discrepancy among the frequencies of different secondary standards persists for too long it is eliminated ad hoc, either by ignoring individual clocks or by eventually replacing them with others that are more favourable to the stability of the average. Frequency shocks introduced by new clocks are numerically cushioned. Even corrections towards primary standards, which are supposed to increase accuracy, are spread over a long period by slicing them into incremental steering adjustments or by embedding them in a memory-based calculation. The constancy of the caesium period in the short-term is thus not tested by the algorithm that produces UTC. For a test implies the possibility of failure, whereas the stabilizing mechanisms employed by the BIPM in the short-term are fail-safe and intended to guard UTC against instabilities in the data.

18 314 Indeed, there is no sign that metrologists even attempt to test the goodness of fit of UTC to the individual data points that serve as the input for the calculation, let alone that they are prepared to reject UTC if it does not fit the data well enough. Rather than a hypothesis to be tested, the stability of the caesium period is a presupposition that is written into the calculation from the beginning and imposed on the data that serves as its input. 21 This seemingly question-begging practice of data analysis suggests either that metrological methods are fundamentally flawed or that the conventionalist explanation overlooks some important aspect of the way UTC is supposed to function. Below I will argue that the latter is the case, and that the seeming circularity in the calculation of UTC dissolves once the normative role of models in metrology is acknowledged. 3.3 Constructivist explanations As we learned previously, UTC owes its short-term stability not to the detection of underlying regularities in clock data, but rather to the imposition of a preconceived regularity on that data through algorithmic manoeuvres. Constructivist explanations for the success of standardization projects make such regulatory practices their central explanans. According to constructivists, standardizing time is not a matter of choosing which pre-existing natural regularity to exploit; rather, it is a matter of constructing regularities from otherwise irregular instruments and human practices. Bruno Latour and Simon Schaffer express this position in the following ways: Time is not universal; every day it is made slightly more so by the extension of an international network that ties together, through visible and tangible linkages, each of all the reference clocks of the world and then organizes secondary and tertiary chains of references all the way to this rather imprecise watch I have on my wrist. There is a continuous trail of readings, checklists, paper forms, telephone lines, that tie all the clocks together. As soon as you leave this trail, you start to be uncertain about what time it is, and the only way to regain certainty is to get in touch again with the metrological chains. (Latour [1987], p. 251) Recent studies of the laboratory workplace have indicated that institutions local cultures are crucial for the emergence of facts, and instruments, from fragile experiments [...] But if facts depend so much on these local features, how do they work elsewhere? Practices must be distributed beyond the laboratory locale and the context of knowledge multiplied. Thus networks are constructed to distribute instruments and 21 My point concerning the possibility of failure is not meant to invoke any particular criterion of testability, such as falsifiability or severity. Rather, my point is that UTC should not be thought of as a hypothesis to be tested at all. UTC is not an estimator of a mind-independent parameter whose value metrologists are trying to approximate, but an abstract artefact in its own right that metrologists attempt to stabilize (much like their attempts to stabilize material artefacts).