## Abstract

Towards 1967, the accuracy of caesium frequency standards reached such a level that the relativistic effect could not be ignored anymore. Corrections began to be applied for the gravitational frequency shift and for distant time comparisons. However, these corrections were not applied to an explicit theoretical framework. Only in 1991 did the International Astronomical Union provide metrics (then improved in 2000) for a definition of space–time coordinates in reference systems centred at the barycentre of the Solar System and at the centre of mass of the Earth. In these systems, the temporal coordinates (coordinate times) can be realized on the basis of one of them, the International Atomic Time (TAI), which is itself a realized time scale. The definition and the role of TAI in this context will be recalled. There remain controversies regarding the name to be given to the unit of coordinate times and to other quantities appearing in the theory. However, the idea that astrometry and celestial mechanics should adopt the usual metrological rules is progressing, together with the use of the International System of Units, among astronomers.

## 1. The genesis of atomic time scales

When Essen and Parry, at the National Physical Laboratory (NPL) in the UK, began to provide in July 1955, in an operational mode, the frequency of their standard based on the hyperfine transition of caesium (Cs-133), the frequency inaccuracy was estimated to be in the range of 10^{−9} to 10^{−10} in relative value [1]. (In this paper, uncertainties and frequency differences will be expressed in relative values.) The NPL atomic standard was employed at a few day intervals to calibrate local quartz clocks, after adoption of a conventional value of the frequency of the caesium transition. Thus, a local integrated atomic time scale could be realized. At this epoch, radio emissions existed at very low and stable frequency (VLF) for communication purposes. The evaluation and publication of their frequency referred to the NPL caesium standard provided a means of dissemination of the atomic frequency. Later, when other caesium frequency standards appeared, the common reception of VLF emissions provided a method of frequency comparisons.

An almost immediate application was to construct mean atomic time scales by integration over the frequency. This required an agreement on the value of the caesium frequency and on the origin of the time scales. In 1958, a new definition of the second based on Ephemeris Time, i.e. on the orbital motion of the Earth, was in preparation. It was desirable that the caesium frequency be coherent with this future definition (adopted in 1960), rather than with the current second based on the rotation of the Earth, which was longer by approximately 2×10^{−8}. These considerations let us adopt the value proposed by Markowitz *et al*. [2]: 9192631770 Hz, when referred to the second of Ephemeris Time, a value retained in 1967, for the atomic definition of the second, that is still in use. Let us observe that, in contrast with the usage, the re-definition of a basic unit in 1960 introduced a deliberate step in its size.

By agreement between time laboratories, but not officially, the event 1958 January 1 d 0 h 0 m 0 s in Universal Time (based on the rotation of the Earth) was given the same date in the various atomic time scales.

The atomic time scale established by the Bureau International de l'Heure (BIH) was initially one of these integrated atomic times. Then, in conformity with its international missions, the BIH realized an average time scale based on the data from all relevant laboratories. The mode of construction was modified several times in order to follow the scientific and technical advances, but without loss of continuity since 1955. This is explained in the BIH reports and summarized in [3,4]. In 1971, the BIH atomic time was recognized by the 14th Conférence Générale des Poids et Mesures under the name International Atomic Time (TAI; a name that we applied retrospectively during the period 1955–1971).

## 2. Introduction of general relativity in the metrology of time

The mean atomic times were initially computed by averaging the data from standards, operating on the ground, regardless of the gravitational frequency shift owing to their altitude: this shift of approximately 10^{−13} km^{−1} being negligible. The only relativistic correction was that of the second-order Doppler shift generated by the motion of the atoms inside the standard, predicted by special relativity. As remarked by Will [5, p. 8],
by 1960 […] The attitude toward the theory seemed to be that, whereas it was undoubtedly of importance as a fundamental theory of nature, its observational contacts were limited to the classical tests and cosmology […] as a consequence, general relativity was cut off from the main stream of physics.

General relativity (GR) progressively penetrated the field of time metrology under pressure from the increasing accuracy and stability of atomic time standards. For example, in 1967, when the fourth session of the Comité Consultatif pour la Définition de la Seconde (CCDS) prepared the current definition of the second, the relative inaccuracy of its realization was 1×10^{−12}, still exceeding the gravitational shift in all ground laboratories. Nevertheless, the role of GR was evoked briefly at this session. Should the second be referred to a stated gravitational potential (at sea level, for example), or at the location of the standard? A short but excellent report issued as a result of work at the Physikalische Technische Bundesanstalt (PTB) was presented [6], which clearly explained the role of proper time and coordinate time; this report had only one defect: it arrived too early. At this session the CCDS only stated in a ‘Declaration’ that an atomic definition of the second can be formulated in compatibility with the relativistic theories. The proposed definition of the second itself brought no indication in this respect.

In the 1970s, there were still some doubts on the validity of GR for complex quantum devices as atomic time standards. Several tests were organized: a flight of caesium clocks around the world in both directions [7], and a flight of a hydrogen maser in a rocket [8]. The predicted effects of GR were confirmed. Although the relative uncertainty of some of these tests was low, they were important, at least through their psychological effect, and the relativistic effects began to be accounted for in time and frequency comparisons. From 1969 to 1990, it was common practice to calibrate the radio time links between laboratories by carrying caesium clocks in commercial flights (this picturesque method was then forbidden by air lines on account of the risk of fire…). As we will see, synchronization and, consequently, time comparisons have no absolute sense in GR. These tests and calibrations required a convention that takes into account the trajectory of the clocks. Somewhat surprisingly, the pilots never refused to provide their flight data.

Although the application of ‘relativistic corrections’ was justified, their use without insertion in a full treatment of space–time reference was not entirely satisfactory and presented some risks, in particular omission or duplication of corrections. A great improvement was the adoption by the International Astronomical Union (IAU), in 1991, of a resolution on the definition of space–time reference systems in the relativistic framework.

The interest of the astronomers is explained by the modelling of the motion of celestial bodies whose positions are precisely observed (as a consequence of the progress of measurement of time and frequency) and whose interactions are purely gravitational. Treaties on relativistic celestial mechanics [9–11] are devoted in a large part to the reference systems and to the methods of observation such as radar and laser ranging, interferometry. They were followed by more complete developments. These documents are rather obscure for non-specialists. We will remain here at a low theoretical level, which is sufficient to recall the basic principle and to define the time scales in use, especially on the Earth and its vicinity. We will insist on the link with metrology, and see that there are still divergences of interpretations and controversies.

## 3. Metric, proper time and coordinate time

In GR, gravitation is seen as a property of a curved space–time, described by a metric tensor, as explained in any textbook. In order to perform computations, one has to select coordinate systems in which the components of the metric tensor are expressed as a function of the only quantity which is assumed to be concretely measurable, the *proper time* of an observer.

There is, in principle, great freedom to choose the coordinate system. However, one is guided by a criterion of lesser complexity, which leads us to adopt approximations, valid in limited spatial domains at the required accuracy. In the Solar System, two main systems of coordinates are defined, one centred at the barycentre of the Solar System, the Barycentric Celestial Reference System (BCRS), the other centred at the centre of masses of the Earth (including its fluid envelopes), the Geocentric Celestial Reference System (GCRS). (We use in this paper the nomenclature recommended by the IAU.) The post-Newtonian approximations provided by the IAU in 1991 were not sufficient for celestial mechanics, in particular because they did not distinguish the dynamically and kinematically non-rotating references. Completed metrics were introduced in 2000, in harmonic coordinates. However, we will use the 1991 metric, because it is much simpler and is still sufficient for the metrology of time on Earth and in its vicinity, at the level of 10^{−18} in relative frequency, at least up to the orbit of geostationary satellites. Recommendation I of IAU A4 (1991) Resolution states
…that the four space–time coordinates (

The quantity *x*^{0}=*ct*, *x*^{1}, *x*^{2}, *x*^{3}) be selected in such a way that in each coordinate system centred at the barycentre of any ensemble of masses, the squared interval d*s*^{2} be expressed with a minimum degree of approximation in the form:
3.1
where *c* is the velocity of light, *τ* is the proper time and *U* is the sum of the gravitational potentials of the above ensemble of masses, and of a tidal potential generated by bodies external to the ensemble, the latter potential vanishing at the barycentre.*t*(=*x*^{0}/*c*) is the *coordinate time* in the considered coordinate system. We now give a few details on the quantities involved in equation (3.1).

### (a) Proper time

‘Proper time’ may be a source of confusion. This expression designates, in the metric, a theoretical concept. Proper time is supposed to be directly measurable with an appropriate clock. However, often the same expression is used for the physical output of a designated local clock. Perhaps a more satisfactory expression should be used in this latter case.

We postulate that the frequency of the caesium transition on the world line of the atom provides the proper time of the theory. However, we need this frequency at some connector of a device. This requires corrections, for physical perturbations and relativistic effects (velocity of atoms, gradient of gravity inside the device, etc.).

Clearly, the unit of *τ* is concretely the second, as defined in the International System of Units (SI). However, one should note that the SI definition is rather the definition of an ideal realization. If a new definition based on another atomic transition leading to a more accurate realization is adopted, then the frequency of this transition will be fixed so that the new realization of the second will be within the measurement uncertainties: the second appears as an ideal realization to which one tends asymptotically.

### (b) Coordinate times

In the BCRS and the GCRS, the coordinate times are called

Barycentric Coordinate Time (TCB),

Geocentric Coordinate Time (TCG).

The IAU provides the theoretical elements for the transformation between these coordinate times, which is sometimes expressed as a sum of secular and periodic terms. Both TCB and TCG are ideal times. They can be realized on the basis of the TAI, which is defined as a coordinate time as explained in the following sections. There are still controversies about the name of the unit of coordinate time. This will be considered later, as well as the problem of the origins.

### (c) Gravitational potential

In equation (3.1) (and similarly in the 2000 metric) applied to the BCRS, the Sun has a predominant role. Its potential is evaluated by *GM*_{Sun}/*r*, where *G* is the constant of gravitation, *M*_{Sun} is the solar mass and *r* is the coordinate distance (*r*^{2}=(*x*^{1})^{2}+(*x*^{2})^{2}+(*x*^{3})^{2}). The product *GM* has the dimension L^{3} T^{−2}. With the definition of the metre, the only unit that must be realized is that of time, the second, unless a non-SI unit is adopted for distance, *r*.

In the case of the GCRS, the tidal potentials, mainly of the Moon and of the Sun, are added to the potential of the Earth. The main component *GM*_{Earth}/*r* is also completed by an expansion in spherical harmonics representing the actual potential affected by the irregular distribution of masses.

### (d) Orientation of the systems

The coordinate times TCB and TCG are not affected by the orientation of the reference systems, and by their rotation rate. Nevertheless, we give a few indications on the adopted orientations.

In the BCRS, the metric let free the orientation. The initial orientation was fixed by the equator and equinox positions in 2000 and was realized by a catalogue of angular coordinates of quasars. Subsequently, improved coordinates were chosen so that they bring no rotation (within the uncertainties) with respect to the previous ones: a curious but unavoidable concept, as for the definition of the second, where the realizations contribute to generate the ideal system to which one tends asymptotically. This system is called the International Celestial Reference System. Its realizations are called International Celestial Reference Frames (ICRF*x*), where *x* is a number identifying the version.

The orientation of the GCRS is derived from that of the BCRS, with the convention that the angular coordinates of the quasars in BCRS and GCRS are identical. Thus, the GCRS is *kinematically* non-rotating, but the relativistic geodetic precession introduces a dynamical rotation and Coriolis terms in the equations of the motions in the GCRS.

The next step is to define a Geocentric Terrestrial Reference System (GTRS) co-rotating with the Earth related to the GCRS by a spatial rotation. This requires knowledge of the five parameters that describe the rotation of the Earth: coordinates of the pole of rotation with respect to the Earth and in space, and the Universal Time, UT1. In both the GCRS and the GTRS, the coordinate time is TCG. A specific GTRS, called the International Terrestrial Reference System (ITRS), is initially oriented in conformity with international conventions, by the position of the pole of rotation of the Earth in 1900 and by the Greenwich meridian. The realizations of ITRS are called International Terrestrial Reference Frames (ITRF*xxxx*), where *xxxx* is the year of realization and identifies the version. The successive versions statistically keep the initial orientation. A model of the tectonic plate motions is adopted in order to realize a condition of ‘no global rotation’ (the uncertainties of coordinates at the surface of the Earth are of the order of the millimetre, their variations are of a few centimetres per year). Needless to say, the ITRS and the ITRF are particularly important for everyday applications of positioning; in particular, the reference system of the Global Positioning System (GPS), WGS84, agrees closely with the ITRS. The ultimate level of accuracy is required for Earth sciences. In these developments, the coordinate time should be TCG. However, this was not estimated as satisfactory for reasons that are explained in the following section.

### (e) Origin of coordinate times

The origin of the coordinate time scales and of their realizations (time scales) is a rather confusing topic. A time scale contains implicitly its origin according to the dates attributed to events. For coordinate times, TCB and TCG, the origin is defined with reference to the TAI so that, at the event *TAI*=1977 January 1, 0 h 0 m 0 s exactly at the geocentre, the readings of TCB and TCG are 1977 January 1, 0 h 0 m 32.184 s exactly. The reason for this time offset is given below.

## 4. From the Geocentric Coordinate Time to the International Atomic Time

The first atomic times scales at the end of the 1950s, including the first forms of TAI, were established without considering the effects of GR. They were in fact ‘scaled’ geocentric coordinate time scales, but this was recognized officially much later. We recall this evolution.

At the surface of the Earth, the sum of the gravitational potential and the potential of the centrifugal force generates a frequency shift of approximately 7×10^{−10}. If TCG had been the basis of dissemination of time on the Earth, then all users of the second (of proper time) would have had to apply the large correction of −7×10^{−10}, which corresponds to a time drift of 22 ms yr^{−1}. In order to avoid this inconvenience, it was decided in 1991 to define a Terrestrial Time (TT) *as a time scale differing from* TCG *by a constant rate, the unit of measurement of* TT *being chosen so that it agrees with the SI second on the geoid* (IAU Resolution A4, Recommendation 4). In 2000, in order to avoid intricacy and temporal changes inherent in the definition and realization of the geoid, the IAU adopted a conventional value of the frequency shift (*scaling factor*) corresponding closely to the potential at the geoid level.

The origin of TT is fixed by the convention that, at 1977 January 1, 0 h 0 m 0 s TAI, the value of TT is 1977 January 1, 0 h 0 m 32.184 s exactly. The time offset is the difference between the former Ephemeris Time and Universal Time at the beginning of 1958 when TAI and Universal Time coincided. By this decision, together with the definition of the second in 1967, the Ephemeris Time may be considered as an extension of TT in the past.

Thus, TAI is a realization of a coordinate time. It is not a proper time although its scale unit is close to the second of proper time as realized by a caesium frequency standard fixed on the rotating Earth and located at the geoid level. In every location, the access to the second of proper time through TAI requires a relativistic transformation based on the potential and the motion. We insist on this point, because there are still frequent errors of interpretation which may be due to the smallness of the relativistic effects on the ground: 10^{−13} in relative value per kilometre of altitude, for fixed clocks.

TAI is not directly disseminated. The basis of timing on the Earth is the Coordinated Universal Time (UTC), a compromise defined since 1972, so that
4.1
*n* being an integer changed when necessary to maintain the condition that |*UTC* – *UT1*| be less than 0.9 s, where UT1 is a precisely defined form of Universal Time. The changes of *n* since 1973 occurred at irregular intervals ranging from 1 to 7 years. In the intervals between these steps, UTC is also a coordinate (without the final ‘d’) time.

## 5. International Atomic Time and Terrestrial Time TT(BIPM*xy*)

The TAI was conceived at the BIH as the product of a worldwide cooperation and as an operational scale. This was essential to ensure reliability (no interruptions) and accessibility. This cooperation was total all over the planet, ignoring political barriers and in spite of the cost of transmission of data. This spirit was maintained when the Bureau International des Poids et Mesures (BIPM) took over the responsibility of TAI in 1988, with some restrictions for countries which are not members of the Meter Convention.

The methods of computation of TAI, which are essentially still in use, were introduced in July 1973 with the algorithm ALGOS optimized for the frequency stability over 1–2 months, completed in January 1977 by a ‘steering’ in order to ensure accuracy of the frequency. The details can be found in BIH reports; for the present organization see Arias [4]. We recall only the basic principles. Each participating laboratory *i* maintains an approximation of UTC, denoted UTC(*i*), and sends the differences *UTC*(*i*) – *H*_{i,j} of each of its atomic clocks *i*,*j* at 5 day intervals to the BIPM, together with the data for time links. Thus, all the clocks, approximately 350, are inter-compared. ALGOS produces an intermediate time scale denoted as the Echelle Atomique Libre (EAL) and then the steering process based on the calibrations of the EAL frequency by primary caesium standards gives TAI and UTC.

The availability of TAI is provided by monthly *Circular T*, giving the values of *UTC*–*UTC*(*k*) at 5 day intervals for approximately 70 laboratories. Then TAI is obtained through equation (4.1). In most cases, the total uncertainty is below 10 ns and may be only 2 ns for the best equipped laboratories. *Circular T* also gives daily corrections to system times of GPS and of the similar Russian system GLONASS in order to obtain UTC, with a global uncertainty of the order of 10 ns for GPS, and some hundreds of nanoseconds for GLONASS.

The frequency accuracy of TAI may differ from the averaged frequency of primary standards by approximately 5×10^{−15} (in December 2010). However, this difference is published with a total uncertainty of approximately 5×10^{−16}. *Circular T* also gives the possibility of referring the frequency of TAI to individual primary standards.

The above method of computation and dissemination of TAI and UTC was devised for optimum use of the stability of clocks, accuracy of frequency standards and of time comparisons. It may have to be changed as a consequence of changes in the relative quality of these three components. In particular, the frequency stability of industrial caesium clocks might become insufficient with regard to the increasing accuracy of primary standards.

As an operational time scale, TAI is definitive as soon as it is made available. Thus, an event receives a definitive time tag in TAI. This is a very particular aspect of the responsibility of the persons in charge of TAI: an operational time scale retains indefinitely the memory of all defects in its realization.

As a consequence of the above constraint, the retro-processing of past data produces improved time scales by removal of some omissions (such as the effect of blackbody radiation in caesium standards) and some causes of perturbation (such as a seasonal effect). It also offers the possibility of a better use of the data of primary standards. At the epoch when millisecond pulsars were discovered, the need for optimized atomic time scales led to realizations of TT denoted as TT(BIPM*xy*), where *xy* are the last digits of the year of production [12,13]. A new version is not an extension of the previous one: it is a new scale. These time scales are accessible by tables of differences *D*=*TT*(BIPM*xy*) − *TAI* − 32.184 s. By definition of the origin of TT, the value of *D* was 0 at the beginning of 1977; it reached 27 μs in 2009, which is far from being negligible in some astronomical applications.

## 6. Barycentric Coordinate Times

The TCB is mainly of interest for celestial mechanics and space navigation. Its difference from TT (and TAI) increases at a rate of approximately 0.5 s yr^{−1}. It was judged as inconvenient and even dangerous that the argument of ephemerides of celestial bodies be so different from the time scale TAI in general use. Similar to the definition of TT, a coordinate time named Dynamical Barycentric Time (TDB) is defined using a scaling factor as a linear function of TCB. This scaling ensures that TDB follows TT in the long term, the difference being less than 2 ms. Such a decision is, however, the source of complexity, as often happens with a departure from the conceptual purity for practical convenience, as we will see in the following.

Figure 1 summarizes the relations between the theoretical times and the realizations of TT, TAI and TT(BIPM*xy*). From left to right, it shows the theoretical definitions. From right to left, it shows how the theoretical times and the proper time of an observer (hence, the second of proper time) can be realized through access to time scales TAI, UTC and TT(BIPM*xy*).

## 7. Metrological aspects of the measure of time in relativity context

We have already mentioned that confusion between proper time and TAI sometimes persists. We have seen that the duplication of coordinate times by application of scaling factors increases the difficulties of understanding a subject which is intrinsically complex. We will now mention other topics that remain controversial.

### (a) Unit of relativistic coordinates

Some authors consider the relativistic coordinates as dimensionless [14], others give a special name to their unit, such as the ‘TCB second’ or a global name such as ‘graduation unit’. I was myself in favour of the latter name. However, after long discussions with eminent metrologists, Quinn and de Boer, I agreed that it was simpler to name ‘second’ the graduation unit. Thus, more generally, all quantities having the dimension of time have the second (without any qualifier) as their unit, even if they have different natures, such as time interval and reading of a time scale. If the logic of this point of view seems rather obscure, then it is possible to consider it as a convention which has the merit of being in agreement with the quantity calculus. It also agrees with the metrological rule that the unit does not define a quantity. These problems have been considered recently [15,16], but without reaching a consensus among astronomers. Curiously, the notation of the differences in time readings is expressed quite naturally in the form of
7.1
(sometimes called *algebraic notation*), which does not introduce specific units. When one has to designate the interval between two second markers of a time scale T, the wording *unitary scale interval of* T was employed by the CCDS, but *scale unit of* T is usually employed. (A rule, specific for metrology of time, is that the same acronym is used for the designation of a time, in Roman, and its reading, a quantity, in italics.)

### (b) Consequences of the scaling factors of dynamical barycentric time and terrestrial time

As seen before, the product *GM* for celestial bodies intervenes in the components of the metric equation (3.1). When using TCB and TCG, i.e. ‘natural’ coordinate times without scaling, this product is independent of the system of reference where it is used: *G* is a physical constant in proper units and *M* is a relativistic invariant. However, these nice properties are lost when TDB and TT are employed. We cannot enter into the subtleties of this problem here, which cannot be solved unambiguously because the metrics to which TDB and TT pertain have not been specified. Two conflicting points of view have their partisans.

Some authors consider that the metric remains unchanged with the same definition of the quantities that are involved, but that different units are introduced and named, for example TDB-units. Thus, the value of

*GM*in TDB-units is different from its value in SI units. Space coordinates are also expressed in TDB-metres. However, such a change of units also changes the unit of proper time, i.e. introduces a non-SI system of units when one applies the rules of the quantity calculus to equation (3.1).Others consider that the scaling introduces new quantities which are expressed in SI units.

Point of view (ii), which is advocated by some astronomers (see Guinot [16]) is gaining acceptance. There is a consensus for using common rules for the nomenclature; these rules are, for example, adopted in the latest issue of the Conventions of the International Earth Rotation and Reference Systems Service (IERS) [17].

### (c) The astronomical units in the Solar System

Until about 1970, only angular observations of planets providing their orbital periods were precisely measured. Using Kepler Laws, it was possible to obtain their relative distances, but without a precise reference to the metre, the uncertainty being about 10^{−4}. This led to the introduction of an *astronomical unit of length*, ua, whose definition appears in table 7 of the 2006 SI Brochure (*non-SI units whose values in SI units must be obtained experimentally*). The ua has a convenient size in celestial mechanics: it is approximately equal to the mean of the Earth–Sun distance. In this context, the basic quantity *GM*_{Sun} for the Sun receives a conventional value.

The introduction of radar ranging to planets towards 1970 provided a much better value of the ua in metres, the relative uncertainty now being 2×10^{−11}. Some astronomers, for example Capitaine *et al*. [18], have proposed a new definition of the ua as a conventional number of metres, the consequence being to consider *GM*_{Sun} as a quantity to be determined experimentally. This appears more logical, as the possible variations of the mass of the Sun and of *G* are the subjects of investigations. This would make the Solar System dynamics compatible with the SI. The pros and cons of this new definition of the ua are still being debated.

In both concepts, the ua, such as the metre, must be considered as units of proper length [19]. On account of the spatial extent, the definitions must be restricted to a very small sub-multiple of the ua.

## 8. Concluding remarks

The role of astronomers in the introduction of GR in metrology might lead one to think that it is only a subject of interest for them. It is true that precise ephemerides for the Solar System need a relativistic theory of gravitation. These ephemerides are needed for exploration of the Solar System, and for knowledge of its formation and its future, with consequences for the apparition of life.

However, a more immediate impact of GR for humanity is its application to devices in orbit around the Earth. An example is the development of global satellite positioning systems such as GPS, GLONASS, future GALILEO and others. These systems, and other time–frequency systems, such as Doppler ranging on satellites, laser ranging on artificial satellites and on the Moon, very long baseline interferometry on quasars and artificial probes, could not operate without taking GR into consideration. Besides their practical applications, for positioning on the Earth (navigation, geodesy) and in telecommunications, they are now essential tools for geophysics, and for oceanography where displacements at the millimetre level can be measured.

We cannot hide the fact that GR, in contrast with the simplicity and beauty of its basic principles, leads to mathematical difficulties. As we have seen, these difficulties are further enhanced by using scaling factors for convenience which may be applied or not.

For example, the necessity to define TAI so that its scale unit has a duration close to that of the second of proper time at the surface of the Earth is clear. However, should we use it in geodesy? The versions of the ITRF are compatible with TT, except from ITRF94 to ITRF97, which were in conformity with the non-scaled TCG. These changes affect the radial component of coordinates by 4.4 mm at sea level, which is not negligible and which has to be taken into account in oceanography, with risks of misinterpretation.

In space, the coordinate time TCB has started to be used for ephemerides. Some very precise observations of positions of stars from space (project GAIA of the European Space Agency) will use TCB.

I add some remarks on the production of time scales.

Time and frequency are easily transmitted by radio, at all levels of accuracy, free of charge. This is most convenient, but a consequence of this is a lack of interaction between users and producers: it seems quite natural to get time. This free access to time had always been true, since the advent of radio time signals at the beginning of the twentieth century. Time has, nevertheless, a cost.

Even when time was provided by astronomical observations, and could be read on the sky without any risk of interruption, coordination was required. This led to the creation of the BIH, which was conceived in 1911, taking as its model the organization of the Metre Convention. However, the First World War stopped the progress of the Hour Convention, and the BIH became an international service of the IAU (joined later by the International Union of Geodesy and Geophysics and the International Radio Scientific Union). The Bureau, located at the Paris Observatory, was generously supported by the observatory, which paid the quasi-totality of expenses.

When I developed the concept of TAI at the BIH, I was conscious of its future importance and also of its fragility: an interruption is irremediable and even a defect can hardly be corrected. I was convinced that the construction of TAI should be entrusted to an inter-governmental body. For several years, a physicist of the BIPM was detached from the BIH, then the section of the BIH in charge of time was transferred to BIPM and finally the full responsibility of TAI was taken over by the CIPM and the BIPM. This smooth transition led to the present situation, which I find fully satisfactory.

## Acknowledgements

It is my great pleasure to thank all the persons who made it possible, members of the CIPM, Director of the BIPM, Presidents of the Paris Observatory and members of the team of BIH who moved to BIPM. I feel most rewarded by the competence of the present team in charge of TAI at the BIPM.

## Footnotes

One contribution of 15 to a Discussion Meeting Issue ‘The new SI based on fundamental constants’.

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