International Atomic Time (TAI, from the French name Temps Atomique International) is a highprecision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid. It is the principal realisation of Terrestrial Time, and the basis for Coordinated Universal Time (UTC) which is used for civil timekeeping all over the Earth's surface. As of 2009, TAI was exactly 34 seconds ahead of UTC: an initial difference of 10 seconds at the start of 1972, plus 24 leap seconds in UTC since 1972; the last leap second was added on 31 December, 2008.^{[1]}^{[2]}
Time coordinates on the TAI scales are conventionally specified using traditional means of specifying days, carried over from nonuniform time standards based on the rotation of the Earth. Specifically, both Julian Dates and the Gregorian calendar are used. TAI in this form was synchronised with Universal Time at the beginning of 1958, and the two have drifted apart ever since, due to the changing motion of the Earth.
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TAI as a time scale is a weighted average of the time kept by over 200 atomic clocks in about 70 national laboratories worldwide. The clocks are compared using satellites.^{[3]} Due to the averaging it is far more stable than any clock would be alone. The majority of the clocks are caesium clocks; the definition of the SI second is written in terms of caesium.^{[4]}
The participating institutions each broadcast, in real time (in the present), a frequency signal with time codes, which is their estimate of TAI. Time codes are usually published in the form of UTC. These time scales are denoted in the form TAI(NPL) (UTC(NPL) for the UTC form), where NPL in this case identifies the National Physical Laboratory, UK.
The clocks at different institutions are regularly compared against each other. The International Bureau of Weights and Measures (BIPM) combines these measurements to retrospectively calculate the weighted average that forms the most stable time scale possible. This combined time scale is published monthly in Circular T, and is the canonical TAI. This time scale is expressed in the form of tables of differences UTCUTC(x) and TAITA(x), for each participating institution x.
Errors in publication may be corrected by issuing a revision of the faulty Circular T or by errata in a subsequent Circular T. Aside from this, once published in Circular T the TAI scale is not revised. In hindsight it is possible to discover errors in TAI, and to make better estimates of the true proper time scale. Doing so does not create another version of TAI; it is instead considered to be creating a better realisation of Terrestrial Time (TT).
Atomic timekeeping services started experimentally in 1955, using the first caesium atomic clock at the National Physical Laboratory, UK (NPL). Early atomic time scales consisted of quartz clocks with frequencies calibrated by a single atomic clock; the atomic clocks were not operated continuously. The "Greenwich Atomic" (GA) scale began in 1955 at the Royal Greenwich Observatory. The United States Naval Observatory began the A.1 scale 13 September 1956, using an Atomichron© commercial atomic clock, followed by the NBSA scale at the National Bureau of Standards, Boulder, Colorado. The International Time Bureau (BIH) began a time scale , T_{m} or AM, in July 1955, using both local caesium clocks and comparisons to distant clocks using the phase of VLF radio signals. Both the BIH scale and A.1 was defined by an epoch at the beginning of 1958: it was set to read Julian Date 2436204.5 (1 January 1958 00:00:00) at the corresponding UT2 instant. The procedures used by the BIH evolved, and the name for the time scale changed: "A3" in 1963 and "TA(BIH)" in 1969.^{[5]} This synchronisation was inevitably imperfect, depending as it did on the astronomical realisation of UT2. At the time, UT2 as published by various observatories differed by several centiseconds.
The SI second was defined in terms of the caesium atom in 1967, and in 1971 it was renamed International Atomic Time (TAI).^{[6]}
Also in 1961, UTC began. UTC is a discontinuous time scale composed from segments that are linear transformations of atomic time, the discontinuities being arranged so that UTC approximated UT2 until the end of 1971, and UT1 thereafter. This was a compromise arrangement for a broadcast time scale: a linear transformation of the BIH's atomic time meant that the time scale was stable and internationally synchronised, while approximating UT1 means that tasks such as navigation which require a source of Universal Time continue to be well served by public time broadcasts.^{[7]}
In the 1970s, it became clear that the clocks participating in TAI were ticking at different rates due to gravitational time dilation, and the combined TAI scale therefore corresponded to an average of the altitudes of the various clocks. Starting from Julian Date 2443144.5 (1 January 1977T00:00:00), corrections were applied to the output of all participating clocks, so that TAI would correspond to proper time at mean sea level (the geoid). Because the clocks had been on average well above sea level, this meant that TAI slowed down, by about 10^{−12}. The former uncorrected time scale continues to be published, under the name EAL (Echelle Atomique Libre, meaning Free Atomic Scale).^{[8]}
The instant that the gravitational correction started to be applied serves as the epoch for Barycentric Coordinate Time (TCB), Geocentric Coordinate Time (TCG), and Terrestrial Time (TT). All three of these time scales were defined to read JD 2443144.5003725 (1 January 1977 00:00:32.184) exactly at that instant. (The offset is to provide continuity with the older Ephemeris Time.) TAI was henceforth a realisation of TT, with the equation TT(TAI) = TAI + 32.184 s.^{[9]}


