Time Scales

The concept of time has been refined throughout history, and new understanding usually produces a new time scale. The list in this web page aims mostly at describing when and why new time scales were developed. At the end of this web page are links to other web pages which better explain the definitions of various time scales.
Earth rotation time
Historically the most obvious indicator of the passage of time has been the diurnal cycle of earth rotation. The day is the fundamental element of all calendars.

The rotation of the earth under the moon and sun produces tides. Reckoning time by tides is sufficiently simple that rocks can do it. Sedimentary rocks called tidal rhythmites contain records of earth paleorotation dating back three billion years.

Apparent Solar Time
Local Time -- sometimes LT
Apparent Solar Time has been used since prehistory. It is reckoned at any location by observation of obvious phenomenon such as sunrise, sunset, or passage through the meridian (noon). Reckoning time by sunrise and sunset is sufficiently simple that plants can do it.

Reckoning time by local apparent noon is sufficiently simple that anyone with a stick in the ground can do it. The ellipticity of the earth's orbit and the obliquity of the earth's equator produce a variation in the duration of a day reckoned by apparent noon. The variation is known as the ``equation of time'', and it is large enough that a pendulum clock is stable enough to measure it. The ``equation of time'' is best visualized in combination with the annual variation in the latitude of the sun in order to produce the analemma.

The earliest almanacs tabulated the ``equation of time''. Until 1930 in the British Nautical Almanac and 1935 in the American Ephemeris and Nautical Almanac the position of the sun was tabulated at apparent noon as well as at mean noon.

Mean Solar Time -- sometimes MST
The principles behind mean solar time and the ``equation of time'' were known to Ptolemy. By the middle of the 19th century personal timepieces were sufficiently accurate and sufficiently widespread that civilization began to run on mean solar time instead of apparent solar time. In this case ``mean'' means the average obtained by considering the rotation of the earth in the absence of the annual variations caused by obliquity and eccentricity. Telegraphs were particularly strong drivers of mean solar time because they began to require synchronization of human activities over large distances.
Julian Day Number
A decimal integer count of consecutive days beginning on January 1, 4713 B.C in the proleptic Julian calendar. The Julian Period of 7980 years is a combination of the 19-year Metonic cycle of 235 months, the 28-year cycle of the Julian calendar, and the 15-year cycle of the Roman indiction. The scheme was invented by Scaliger in 1582 who realized that all three cycles were in year 1 during that conveniently prehistoric year. (Note that the ISO 8601 format used elsewhere in this document is inappropriate here because it specifies the Gregorian calendar where the year is always positive.)
Julian Date -- JD
In 1849 John Herschel published a treatise suggesting that astronomers (who preferred to use the same date for all of the observations of a single night) should adopt JD as an indication of the number of mean solar days (and decimal fractions thereof) elapsed since JD 0.0 which was at Greenwich mean noon of -4712 January 1 (using the astronomical reckoning of the years in the proleptic Julian calendar).
Modified Julian Date -- MJD
In keeping with civil usage and the International Meridian Conference of 1884 where days are reckoned from midnight, and also for the sake of convenience of not handling such large numbers, the MJD was defined in the 1950s as ( JD - 2400000.5 ). MJD 0.0 corresponds to 1858-11-17T00:00:00. (Two URLs which attribute the origin of MJD to artificial satellite tracking at SAO are found in Austria and Australia.)

The IAU has had a love/hate/love relationship with MJD. In 1973 the IAU resolved that it should be used. In the mid-1990s the IAU seriously discussed the possibility of recommending that the term MJD should not be used because several other quantities with the same name but different definitions have been in use in various contexts. Finally (?) in Resolution B1 of the XXIIIrd General Assembly in 1997 the IAU recognized that when properly defined the term MJD may be used. (This may have been another case of capitulation to practical reality akin to that of the 1935 IAU resolution regarding GMT which basically admitted that no action by the IAU could prevent the use of the term.)

Subsequent to the creation of time scales other than Greenwich Mean Time, forms of JD and MJD expressed in those time scales have also been used to indicate elapsed time measured in ephemeris days and in multiples of 86400 SI seconds. As recommended by the IAU in 1997 any current application which requires precision better than one minute, or any historical application which requires precision better than several hours, should take care to indicate which time scale is associated with the use of JD or MJD.

It should also be noted that the use of JD or MJD for the UTC time scale is problematic and ambiguous at the precision of one second. JD and MJD express the elapsed count of some form of ``day'' as real numbers along a presumably unsegmented, continuous number line. The UTC time scale (and, historically, GMT as used in practical situations before the advent of UTC) contains changes in rate and discontinuities. In particular, there is no obvious way to represent a leap second of UTC (or the smaller leaps present in the available forms of GMT and UTC before 1972) using JD or MJD notation.

Local Mean Time -- LMT
Local Mean Time is the Mean Solar Time for any given longitude around the earth, so it differs at every longitude. Anyone with a stick in the ground, an almanac, a calendar, and a clock can reset that clock to Local Mean Time every day at local apparent noon.
Standard Time
Standard Time is the mean solar time of some conventionally chosen, standard (and hopefully nearby) meridian.

The needs of railroad schedules produced the adoption of standard time zones within which every railway station clock shared the same mean solar time. The UK railways began to adopt Standard Time in 1840, and the US railways adopted Standard Time in 1883.

Daylight Saving Time -- DST
Summer Time
Cynically, daylight saving time is what governments decree to promote productivity by hurrying people off to work earlier so that they don't have time to see what a nice day it is and decide to go fishing instead.
Realistically, the general public almost everywhere greatly enjoys getting up earlier because that allows extra sunlight after the end of the work day.
Cosmic Time
A term used by some of the delegates to the 1884 International Meridian Conference in Washington to designate the time on the prime meridian. Other delegates employed the term Universal Time when describing the same concept.
Greenwich Mean Time -- GMT
The mean solar time of the Greenwich meridian.

Prior to the long sequence of usages below it is relevant to point out one thing:
GMT does not now have, and never has had, leap seconds.
For the only time scale with leap seconds see UTC.
Nevertheless, the practical and historical reality is that the available forms of GMT have always had leaps. The leaps happened every time any official clock was reset to agree with earth rotation.

Some agencies currently assert that GMT is currently used as a synonym for UTC. Below is a history of meanings which have been applied to GMT. There is no current definition of GMT which is authoritative in all contexts.

GMT started during 1675/1676
On 4 March 1674 ( Julian calendar, Old Style = 1675-03-14), King Charles II appointed John Flamsteed as the first Astronomer Royal. In June 1675 a warrant founded the Royal Greenwich Observatory, and the foundation stone was laid in August. In July 1676 Flamsteed began residence in the Observatory.

References to GMT before this time cannot have had any contemporary meaning. They are probably better interpreted as indicating what is now known as UT.

in the British Royal Navy until 1805
The time of the Greenwich meridian with the hours reckoned from midnight and days reckoned from noon.
in the British Nautical Almanac from around 1780 until 1833
The data were tabulated according to the apparent solar time of the Greenwich meridian.
GMT starting in 1834
Noting that chronometers were already in use by most ships which relied on astronomical observations for navigation, and in conformity with the report from a committee of ``the most distinguished navigators and astronomers of the empire'', the British Nautical Almanac began to tabulate phenomenon based on mean solar time.
GMT in civil contexts
The mean solar time of the Greenwich meridian with the hours and days reckoned from midnight.
GMT on 1883-11-18
The US and Canadian railways adopted standard time zones based on the mean solar time of meridians spaced at 15 degree intervals west of Greenwich.
GMT in 1884-10
The mean solar time of Greenwich attained a unique distinction at the International Meridian Conference held in Washington during October. By international vote it became the one time, the cosmic time, the universal time which most nations agreed to use.

The exact wording of the protocols had a curious effect in England because it indicated that the transit instrument then in use at the Greenwich Observatory should define the prime meridian. All of the maps of England, however, used the meridian occupied by the previous transit instrument at Greenwich. By strict interpretation of the IMC results, all maps of England suddenly had incorrect values of longitude.

GMT in 1895/1896
In 1895 Simon Newcomb produced expressions which gave a precise definition of the ``fictitious mean sun''.
Newcomb's expressions were adopted for use starting in 1901 at a conference of the directors of the principal national ephemerides in Paris in 1896.
These expressions were the mechanism for converting sidereal time to universal time until 1984.
GMT from 1903 through 1920
During the late 19th century it had become common for observatories to connect their clocks to telegraph lines and transmit time signals regionally. Early in the 20th century various national time bureaus began to emit radio broadcasts of time signals for the sake of setting the clocks globally, and especially for ships at sea.
In 1911 the Observatoire de Paris began to monitor radio broadcasts of time signals and compare them.
In 1912 la Conference Internationale de l'Heure de Paris recommended the creation of an international time bureau to collect and compare the observations of time broadcasts from all over the world.
The Bureau International de l'Heure (BIH) was created in 1913, but the Great War interfered with international aspects.
The official organization of the BIH occurred in 1919 under the auspices of the new International Astronomical Union (IAU), and the BIH was in full operation during 1920.
The BIH routinely monitored radio broadcast time signals, published their differences, and studied the issues involved in determining longitude and mean solar time.
GMT on 1918-03-19
Although the term GMT was not explicitly used, the standard time for legal purposes in the United States specified by 15USC261 (the Calder Act) was defined to be based on the mean astronomical time of meridians spaced at 15-degree intervals west of Greenwich; i.e., GMT.
GMT in astronomy before 1925
The mean solar time of the Greenwich meridian with the hours and days reckoned from noon.
GMT in the British astronomical almanac before 1925
The mean solar time of the Greenwich meridian with the hours and days reckoned from noon.
GMT in the British astronomical almanac beginning in 1925
The mean solar time of the Greenwich meridian with the hours and days reckoned from midnight.

Within the pages of the British Nautical Almanac and Astronomical Ephemeris the time 00:00:00 GMT had previously meant noon, but starting this year 00:00:00 GMT now meant midnight. Sadler (1978) indicated that the use of the same name ``GMT'' for a quantity entirely opposite in meaning to the original term was by order of the Admiralty.

GMT according to the IAU beginning in 1925
an ambiguous term

Because the British Nautical Almanac had declared the value of what had once been noon now to be midnight the IAU recognized that the term ``GMT'' had been rendered useless as a precise term in most archival and practical contexts. Anyone encountering a document containing the term ``GMT'' could only be certain of its meaning if the document were verified to have originated before 1925. For documents after 1925 there would be no way to be certain whether the author had meant ``old GMT'' or ``new GMT''.

GMT according to radio broadcasts starting in 1927
The International Radio Consultative Committee (CCIR) was created to regulate radio broadcasts around the world. Because radio broadcasts were the most readily available form of time signals, the CCIR gained authority over the meaning of the civil time scale.
GMT according to the IAU starting in 1935
In the context of astronomical ephemerides, the mean solar time of the Greenwich meridian with the hours and days reckoned from midnight; i.e., UT.
This was basically capitulation, or more positively, an acknowledgement of the ongoing tendency to continue using the term ``GMT'' despite its ambiguity.
GMT after 1939
Using observations gathered by the International Latitude Service (ILS) the BIH began publishing the corrections from UT0 to UT1. Initially the corrections were only available for previous years. Eventually the BIH published predictions for the current year and it became possible for the various observatories and time services to adjust their values of UT accordingly.
GMT according to navigational almanacs
through the 1950s
UT
GMT according to many radio time signal
broadcasts through the 1950s
UT as determined by transit observations from the observatory affiliated with the radio station. This was before the seasonal variations of UT2 had been codified, so depending on the observatory the values would initially have been UT0 and later something approaching UT1.

Through this era it was typical to reset the master clocks controlling the radio broadcasts by a fraction of a second whenever it was indicated by the transit observations. These clock resets were, in effect, ``leap milliseconds'', and they were consistent with the way that mechanical clocks had always been reset in order to keep track of mean solar time. Tabulating the differences between various radio broadcasts had been a principal mission of the BIH from its inception, and only through those records can the meaning of old radio broadcasts be interpreted.

GMT according to many radio time signal
broadcasts starting in 1956
UT2 as determined by transit observations from the observatory affiliated with the radio station. (Note that many observatories based their time scales and signals on transit observations reduced with conventional values for their longitudes. Before 1984 the conventional longitudes were inconsistent at a level of several hundredths of a second of time.)
GMT according to astronomical almanacs
since 1960
The term GMT ceased to be used.
GMT according to many radio time signal
broadcasts in the 1960s
the earlier form of UTC which used frequency offsets from the atomic second along with annual steps of 50 ms to 100 ms in an effort to match the predicted value of UT2
GMT on 1966-04-13
Although the term GMT was not explicitly used, the standard time for legal purposes in the United States specified by 15USC261 was clarified and reaffirmed to be based on the mean solar time of meridians spaced at 15-degree intervals west of Greenwich; i.e., GMT.
GMT according to navigational almanacs
since the 1970s
UT1
GMT according to the IAU since 1976
A resolution at a joint meeting of IAU Commissions 4 and 31 urged that the term GMT should be replaced by UT0, UT1, UT2, or UTC as is appropriate. Sadler (1978) reports that the wording of this resolution was amended by Commission 31 and that some members of Commission 4 were unaware of the final content until after its adoption.
GMT during the 1980s
The determination of time using astronomical observations of stellar transits with meridian circles ceased completely, having been replaced by VLBI and laser ranging. The ``conventional longitudes'' of the meridian circles around the world, which had been inconsistent by several hundredths of a second of time, became historical artifacts. In the new, globally self-consistent world of coordinates based on VLBI and satellite geodesy the longitude of Greenwich ceased to be zero , and the timekeeping role formerly held by the Greenwich meridian was conceptually assumed by the nearby, but tectonically moving international meridian. For all practical and official purposes, GMT as a precise quantity defined in accord with the 1884 International Meridian Conference had ceased to exist. Nevertheless, anything that might qualify to be called GMT remains within 0.1 second of the values of UT1 or UT2.

These many usages for GMT recall a bit of childhood nonsense:

"When I use a word," Humpty Dumpty said, in a rather scornful tone, "it means just what I choose it to mean - neither more nor less."
"The question is," said Alice, "whether you can make words mean so many different things."
"The question is," said Humpty Dumpty, "which is to be master - that's all."
-- Lewis Carroll, Through the Looking Glass

Greenwich Mean Astronomical Time -- GMAT
A new name for the mean solar time of the Greenwich meridian with the hours and days reckoned from noon which was coined by the IAU in 1928. It was to be used when describing the old meaning of GMT which had been in use until 1925. Of course this new term did not alleviate the ambiguity in the meaning of GMT in existing usage.
Greenwich Civil Time -- GCT
In 1928 the IAU approved the use of this term as a synonym for Universal Time. The US almanac used this term from 1925 until 1952 to indicate that days were being reckoned from midnight. The British almanac could not be convinced to use the term GCT, and continued to use the term GMT with the new astronomical meaning.

Part of the argument against GCT was that the legal civil time of Greenwich was set forward one hour in the summer. In 1935 the IAU recognized that the ambiguity caused by the disagreement between astronomical usage and civilian usage would never permit complete adoption of GCT. The term GCT was discontinued by the IAU at the Vth GA in 1935. Starting in 1939 the US almanac used ``GCT or UT'' until 1952 when it switched to UT alone.

Weltzeit -- WZ
In 1928 the IAU approved the use of this term as a German language synonym for Universal Time. In 1948 the IAU recommended that WZ (and UT) should be used by astronomers only to designate Greenwich mean solar time reckoned from midnight. Germany is one of the nations that has adopted UTC as the basis of legal time, and Weltzeit continues to be used to this day with the colloquial meaning often being UTC.
Universal Time -- UT
The term Universal Time was used by some delegates to the 1884 International Meridian Conference to indicate GMT reckoned from midnight. In 1928 the IAU approved the use of this term as a replacement for the term GMT which had been rendered ambiguous in 1925. The IAU decision to employ the name Universal Time indicated that it is intended to be a subdivision of the ``Universal Day'' which was adopted as part of Resolution V of the IMC

In 1948 the IAU recommended that UT (and WZ) should be used by astronomers only to designate Greenwich mean solar time reckoned from midnight. Through the 1950s UT was used as the independent variable of the ephemerides.

It is important to note that Universal Time has always been a conventional construct based on measurements of sidereal time. It is not easy to measure the position of the sun with great precision. Even if it were easy the solar measure would still have to be converted to UT by application of some conventional formulae including the ``equation of time''. From 1895 until 1984 the conventional formulae for UT were those of Newcomb which were based on observations of the sun. As pointed out by Aoki et al. (1982), Newcomb's expressions were designed to give a quantity which incremented uniformly in the reference frame used during the early 1890s. Nevertheless, Newcomb knew that his expressions for the fictitious mean sun would eventually deviate from the position of the actual mean sun.

Decades of BIH intercomparisons of radio broadcast time signals from around the world had revealed that the variation of latitude caused by polar motion caused the time derived from stellar transit observations to result in different values of UT at different observatories. The BIH had also determined that the seasonal variations in earth rotation were reasonably predictable. At its IXth GA in 1955 the IAU, via its Commission 31 (Time), directed the BIH to publish corrections for the seasonal variations of UT. Although there do not seem to published records, Markowitz (president of IAU Comm. 31) reportedly held further discussions with the BIH and the international time services, and they produced definitions and nomenclature for three distinct versions of UT. The BIH complied in 1956, and the new versions of UT came into common use.

UT0
UT0 was the raw measure of UT based on transit observations at a single observatory. Until 1984 these transit observations would have been reduced using the FK3 and FK4 catalogs which were based on Newcomb's formulae. UT0 is not corrected for the effects of polar motion which means that different observing stations determine different values. The correction from UT0 to UT1 is at most about 0.035 s. The modern techniques for measuring earth orientation (which became the prevalent means of observation by the 1980s) simultaneously produce UT1 and polar motion directly, so UT0 is effectively not used anymore. The UT0 time scale has no official name.
UT1 before 1984
UT1 was UT0 with corrections added for polar motion such that, ideally, all observing stations would agree on its value. In practice, the agreement never happened in real time, but only after the fact in the publications of the BIH. The values of UT1 produced through 1984 did not agree with each other because most observatories employed conventional (one might say traditional, or even historic) values for their longitudes. The conventional values of longitude were known to be inconsistent with each other at the level of several hundredths of a second of time. The longitudes had always been that way, and most observatories did not wish to modify their published longitude or introduce a discontinuity in the time scales which they produced. The UT1 time scale has no official name, but early mentions of it in publications by the BIH used the term ``Temps Universel, compte tenu du mouvement du pole''.
UT2
UT2 is constructed from UT1 by adding an empirical formula to remove the effect of the annual seasonal variations in the rotation of the earth. In that sense UT2 is more smooth than UT1, and it provided a better gauge of ``mean'' for mean solar time. The correction from UT1 to UT2 is at most about 0.035 s. The UT2 time scale has no official name, but early mentions of it in publications by the BIH used the terms ``Temps Universel uniforme provisoire'' and ``provisional Uniform Universal Time''. Before the year 1970 measurements of the random variations in the rotation of the earth using the precision made possible by atomic clocks had revealed UT2 as a futile exercise, for there are other variations in the rate of UT1 -- some of which are predictable, and some which are not. Nevertheless, UT2 remains as much in effect now as it ever was.

Sadler (1978) provided a detailed review of the history of mean solar time, GMT, and all forms of UT before 1984.

During the 1970s new techniques for observing earth orientation were proving to be far more precise and accurate than previous means. These included satellite observations (laser and radio), lunar laser ranging (LLR), and very long baseline interferometry (VLBI). Traditional optical transit measurements of stars had always been limited to observations at night, and certain systematic effects had never been seen.

UT1 since 1984
The changes adopted by the IAU in 1976, 1979, and 1982 were implemented in the ephemerides starting in 1984. At the same time the celestial reference system of the FK5 catalog came into use. Since 1984 Newcomb's non-relativistic expressions for UT which had been based on observations of the sun, but which did not exactly track it in the long run, ceased to be used. They were replaced by new expressions for UT1 which no longer refer explicitly to the location of the sun.

Aoki et al. (1982) gave the expression for UT1 which came into use in 1984 and they explain why it is no longer based on the sun.

UT1 since 1997-02-27
At the XXIInd GA in 1994 IAU resolution C7 recommendation 3 indicated that the equation of the equinoxes should be amended by the addition of new complementary terms. This change was needed in order to refine the definition of the origin of coordinates from which earth rotation was measured to give accuracy better than a milliarcsecond. In order to avoid any discontinuity in UT1 the change was implemented on 1997-02-27 when the difference between the old and amended expressions was zero. Capitaine and Gontier (1993) demonstrated that the difference has a principal period of 18.6 years and amplitude of 0.176 milliseconds.
UT1 since 2003
At the XXIVth GA the IAU 2000 resolutions recommended a complete change in the basis for measuring earth rotation to begin in 2003. Capitaine et al. (2000) gave the expression for UT1 which came into use in 2003. Capitaine et al. (2003) amplify the disconnect from the sun, and they show that the difference from the previous version of UT1 is as much as 2 microseconds over the next few decades and 50 microseconds over the next 200 years. With these new changes UT1 is no longer based on GMST, but rather on ERA (see below).

The current version of UT1 is exactly what is needed for geophysical investigations. It permits evaluation of the length of day (LOD) with a precision that reveals changes due to storm systems and changes in ocean currents. But in continuation of a trend that began over a century ago, there is really no publicly available measured quantity which can indefinitely be used as an authoritative value of mean solar time. Indeed, Fukushima (2001) demonstrated that in about 360000 years the value of UT1 given by the IAU 2000 resolutions will differ by a full day from the count of calendar days experienced by people living on the earth.

UT1R
UT1R is UT1 after a conventional model for tidal forces has been removed. UT1 indicates the instantaneous orientation of the earth around its axis. There are many periodic tidal forces which perturb the rotation of the earth. The IERS provides on-demand plots of earth orientation parameters. When the tidal forces are removed the graph of UT1R becomes visibly smoother than the graph of UT1.
UT2R
UT2R is UT2 after application of the same tidal model as in UT1R. In effect, this is a measure of earth rotation after all predictable components have been removed. Plots of UT2R give a rough indication of the unmodellable components of UT1; the short period fluctuations are largely due to weather and the long period fluctuations are largely due to the core of the earth.
UT for civil purposes in the far future
According to Aoki et al., the old Newcomb expression (implemented in 1901) for the fictitious mean sun deviated from the true mean sun by 0.020 s/(century*century). It is not clear whether the new FK5-based expressions of Aoki et al. (implemented in 1984), or whether the new NRO-based expressions of Capitaine et al. (implemented in 2003), arrested this acceleration, for that was not the goal of either change. If the new expressions did not remove the acceleration between the fictitious mean sun and the true mean sun then UT1 should continue to indicate mean solar time to about one second for about 1000 years. If the new expressions did remove the acceleration between the fictitious mean sun and the true mean sun then UT1 should continue to indicate mean solar time to within about one second for more than 5000 years. The paper by Fukushima, however, indicates that the IAU 2000 resolutions based on Capitaine et al. will result in a much more significant difference between UT1 and mean solar time within 1/4 of a precessional cycle, which is less than 6000 years.

The goal behind the new expressions defining UT1 has been to ensure continuity of the value and rate of UT1 at the instants of change. These new expressions very closely track the hour angle of the mean sun because they were designed to match a quantity which once did that, but there is no longer a quantity specifically designed to indicate the hour angle of the mean sun. Continuity and uniformity of UT1 has been deemed more important.

Historically no attempt has been made to create expressions for UT which will be valid for more than a few centuries. Demanding a better expression for mean solar time is not immediately reasonable because, in a Clintonesque sense, it depends on what the meaning of the word ``mean'' means. In particular,

  • Should the ``mean'' be a mean over a century, a millennium, or ten millennia?
  • Should the zero point of the mean be set at the beginning of that interval or some time during the interval?
  • Should the value of such a hypothetical new mean solar time be matched to the current value of UT at the start?
  • Would that matching require a leap second?
  • How far is it reasonable for a conventional expression for mean solar time to deviate from ``true'' mean solar time?
  • Given that UT is understood to be nonuniform, should a hypothetical new mean solar time accept that there will be millisecond variations in LOD and abandon the goal of being uniform at that level?

The UTC time scale which currently serves as the basis for all civil time is defined to be calculated from UT1. If civilization continues to desire the use of mean solar time then UT1 will eventually fail to serve that need.

Within the next millennium the IAU will have to consider defining and naming a new version of UT to serve as the quantity which is measured by analemmatic sundials. A name for that time scale might perhaps be Analemmatic Universal Time (UTA).

Sidereal Time -- sometimes ST
The hour angle of the Vernal Equinox. The length of the sidereal day is about 23h 56m of mean solar time. Each tropical year the number of sidereal days exceeds the number of mean solar days by one. The sidereal day differs from the inertial rotation period of the earth because the equinoxes precess around the ecliptic with a period of around 23000 years. Despite being a more fundamental indication of the actual rotation period of the earth, there is no calendar in common use which counts sidereal days.
Greenwich Apparent Sidereal Time -- GAST
The Greenwich hour angle of the true (instantaneous) Vernal Equinox of date, which includes the ``nutation in right ascension'' or ``equation of the equinoxes''. Because of nutation GAST was known not to increment uniformly even before variations in earth rotation were known. The equation of the equinoxes can be as large as 1.2 s, which is small enough that many telescope pointing systems ignore it.
Greenwich Mean Sidereal Time -- GMST
The Greenwich hour angle of the mean Vernal Equinox. In this case ``mean'' means the average obtained by considering the precession of the Vernal Equinox in the absence of nutation, which has a principal period of 18.6 years. Before the variations in earth rotation had been observed GMST was presumed to increment uniformly.
Books on fundamental astronomy historically contained detailed treatments of the formulae regarding GAST and GMST because for most of the past few centuries these were the means by which earth rotation was measured with precision. Measuring the transits of stars with known catalog positions produces values of Sidereal Time, and using the conventional formulae gives values of Universal Time.

From 1895 through 1984 the Vernal Equinox was the location on the non-relativistic celestial sphere defined by Newcomb's expressions. UT1 was determined from GMST using Newcomb's formula. Nevertheless there were several instances of potential discontinuity in UT1 when new fundamental catalogs of stars were adopted.

In accordance with IAU resolution from 1976, 1979, and 1982, in 1984 a new set of astronomical constants came into use along with a switch from the FK4 star catalog to the FK5. From 1984 into 1997 the Vernal Equinox was defined by the expressions in Lieske et al. (1977). UT1 was determined from the expressions in Aoki et al. (1982), who also point out that the new expressions and catalog resulted in shifts of the longitudes of some observing stations.

From 1997-02-27 through the end of 2002 there was an additional correction to the equation of the equinoxes based on IAU 1994 resolution C7 recommendation 3. This correction was required by the vastly increased precision that VLBI had contributed to the measurement of earth orientation.

Based on IAU recommendations in 2000, starting in 2003 the Vernal Equinox was abandoned as the coordinate origin for measurement. A point with some of the original properties has been resurrected by Capitaine et al. (2003). They also point out that the effort to maintain continuity of UT1 had invalidated the classical interpretation of GMST and the equation of the equinoxes.

At the GA in 2006 the IAU approved resolutions which explicitly contain a new definition for the ecliptic, and thus for the equinox.

Since 1984 GMST has not been the Greenwich hour angle of the mean equinox, and the equation of the equinoxes has not been the true right ascension of the mean equinox. Beginning in 2003 UT1 is no longer determined from GMST, but from the Earth Rotation Angle (ERA).

Defining the Vernal Equinox to an accuracy of one arcsecond is easy, but the rapid motions of the rotation pole of the earth and the non-planarity of its orbital motion hinder precise definition of the equator and ecliptic. The Vernal Equinox is not well defined at a precision of one milliarcsecond. This ambiguity became evident during the 1970s as VLBI began to contribute to earth orientation measurements, and it became problematic during the 1980s as VLBI and other new techniques replaced traditional optical astrometric measurements. By the year 2000 there were at least three different definitions for the location of the equinox being used for various purposes. VLBI precision is approaching microarcseconds, and it is hard to measure anything when the origin of measurement is not known as well as the measurement itself can be made.

Earth Rotation Angle -- ERA or theta
In 1979 Guinot proposed the non-rotating origin (NRO) as a new and unambiguous scheme for defining earth rotation. Capitaine (1986) gave an early description of the differences between the traditional and NRO-based schemes, and the implications of the NRO were studied through the 1990s. In the literature through the year 2000 the ERA was known as the ``stellar angle'' (not to be confused with a ``sidereal angle'', which would refer to an equinox).

At the XXIVth GA in 2000 the IAU resolved that the equinox-based scheme for determining UT1 should be replaced by a NRO-based scheme beginning in 2003. This change was sufficiently fundamental that in 2002 the IERS held a workshop entirely devoted to exploring the implications of the change. The terminology and pedagogy for these new elements of fundamental astronomy remain open questions which are even now being considered by the IAU Working Group on Nomenclature for Fundamental Astronomy.

ERA is the first officially sanctioned quantity whose name explicitly disavows that earth rotation is time. This reflects a change in the purposes of IAU Commissions 19 and 31 over the course of history. Initially Comm. 31 (Time) was solely concerned with earth rotation, and Comm. 19 was solely concerned with polar motion. Now earth rotation is handled by Comm. 19, Comm. 31 primarily considers atomic time, and Comm. 4 continues its long history with dynamical time.

Fukushima (2001) pointed out that the non-rotating origin (NRO) introduced by the IAU 2000 resolutions for the measurement of ERA and UT1 actually rotates significantly over long time intervals. In particular Fukushima showed that precession of the equinoxes will cause the non-rotating origin (previously referred to as the CEO and now to be called the CIO) to circle entirely around the sky over an interval of approximately 360000 years. (Other papers on the implications of the IAU 2000 resolutions regarding time scales and reference frames are mentioned below at the end of the section on Fully Relativistic Time.)

The above forms of earth rotation time are consistent with the nomenclature that has developed throughout history. In conjunction with its orbital motion, earth rotation naturally produces the days, weeks, months, and years which are counted by calendars. Earth rotation time traditionally and evenly subdivides into 24 hours of 60 minutes of 60 seconds. In the sexagesimal notation used for these subdivisions the time tag 12:00:00 has long been understood to indicate that the sun is nearly overhead.

Earth rotation time is robust across an interruption in civilization because it is derived directly from observation. It is a straightforward matter to recover earth rotation time to a precision of microseconds even after an interruption of a century, and it will always be easy to recover to better than a second.

Although rocks, trees, fishes, bugs, little furry creatures, and most of humanity reckon time by the rotation of the earth, physicists reserve the term for a more uniform concept. The irregularities in the rotation of the earth mean that no form of earth rotation time measures time in the sense used by physicists. All forms of earth rotation time are now better described as ``time-of-day''. In the vocabularies of most of the languages of the world the long history of the words for ``time'' has been to mean ``time-of-day''. In order for ``time'' to have a simple relationship with a calendar, that ``time'' must be a form of ``time-of-day''. In the general population there is not yet a clear understanding of the distinction between the old traditional meaning of time and the new physical meaning.

Dynamical time
Dynamical time means time determined by comparing observations of the motions of objects with physical models that describe that motion. The celestial bodies in the solar system move like hands of a clock. Using a theory of motion for those bodies it is possible to read the hands of the clock and determine what time they are telling. But that dynamical time has no relation to the rotation of the earth.
Non-relativistic dynamical time
At the Vth IAU GA in 1935, Comm. 4 resolved that all national ephemerides should use the same value for the Gaussian gravitational constant (k) when calculating the motions of the planets. The president of Comm. 4 was E.W. Brown who was renowned for having developed a workable theory of the motion of the moon. Brown was tasked with ascertaining a value of k which was acceptable to all parties and reporting that value at the 1938 GA. Brown died just prior to the 1938 GA, but the agreeable value of k had been determined. At the VIth GA in 1938 Comm 4 adopted the value 0.017202098950000; this was the original value used by Gauss and later by Simon Newcomb for his tables. The value of k fixes the scale of the solar system in astronomical units, but in retrospect it also fixes the duration of the day. Thus, the rate of what would eventually be called Ephemeris Time was irrevocably fixed in 1938.

Newcomb had suspected that the variations in the motion of the moon were directly correlated with variations in the motions of the inner planets, and Spencer Jones (1939) demonstrated the correlation unequivocally. This was direct evidence that the rotation of the earth varied on a time scale of decades. It meant that Universal Time was not uniform and therefore not suitable for use when calculating ephemerides.

Newtonian Time
A name proposed by Clemence (1948) for a time scale defined by Newton's laws of motion; i.e., what would soon become known as Ephemeris Time.
Ephemeris Time -- ET
From 1927 through 1948 various papers had suggested that time might be measured by the motions in the solar system. In 1950 the Conference on the Fundamental Constants of Astronomy held by the CNRS in Paris recommended that the IAU adopt a time scale based on orbital motions as described by Newcomb's tables. In 1952 the IAU VIIIth GA resolved that Ephemeris Time should be created and used in ephemerides. In 1960 the ephemerides switched from using UT to ET.

Because Newcomb's tables had been based on astronomical observations from the 18th and 19th centuries, the length of the ephemeris day happened to match the length of the mean solar day from around the year 1820.

The difficulty with Ephemeris Time is that it can only be measured in retrospect after reducing observations of the orbital motions of bodies in the solar system. The motion of the sun with respect to background stars is extremely difficult to measure. The motion of the planets, except perhaps Mercury, is too slow to provide a precise measure. As a result, the primary means for determination of Ephemeris Time were observations of the motion of the moon as compared with the theory of Brown.

During the 1960s it became evident that there were deficiencies in Brown's analytical theory of the moon. Several corrections to the analytical theory were named by IAU Comm. 4 during the 1960s, and each correction resulted in a new form of Ephemeris Time.

ET0
Named at the XIth GA of the IAU in 1961 and based on the Improved Lunar Ephemeris (ILE) that was tabulated in the ephemerides from 1960 through 1967. This used the old (1950) system of astronomical constants.
ET1
Named at the XIIIth GA of the IAU in 1967 and based on the ILE with the new (1964) system of astronomical constants and some corrections to terms in Brown's lunar theory. This version of the ILE was tabulated in the ephemerides from 1968 through 1971. Serious flaws in ET1 were evident by 1970.
ET2
Named at the XIIIth GA of the IAU in 1967 and based on the the ILE further corrected with new calculations of the solar perturbations. This version of the ILE was tablulated in the ephemerides beginning in 1972. By 1973 ET2 was already known to have deficiencies.

During the 1960s it also became evident that the ever increasing numerical abilities of computers provided a workable alternative to analytical theories. Ephemerides of the motions of bodies in the solar system began to be calculated directly by numerical integration. The numerical integrations incorporated relativistic effects which Newcomb could not have known to include in his expressions. The passage of time on the surface of the earth was being measured much more practically by atomic clocks. Atomic time agreed well with the time indicated by observations of the solar system compared to numerical integrations. Also, it was not clear whether ET was proper time or coordinate time. This inevitably led to the demise of Ephemeris Time. At the XIVth IAU GA in 1970 Guinot suggested that Ephemeris Time could be replaced altogether by using atomic time alone, but by 1973 it was understood that dynamical time and atomic time might differ despite the best of intentions.

The almanacs and ephemerides continued to be based on Ephemeris Time and on the analytic theories rooted in Newcomb's expressions through the end of year 1983.

The definition of Ephemeris Time set a precedent for the nomenclature of time which has created some confusion. The expression used for the mean longitude of the sun in ET was the same expression from Newcomb which was used for the calculation of UT. ET was a strictly uniform time scale not related to the rotation of the earth, and UT was a non-uniform time scale directly related to the rotation of the earth. But the fact that both used the same formulae meant that both were reported using the traditional nomenclature for time which had always been based on rotation of the earth. Values of UT and ET were given using multiples and divisions of days; i.e., calendar years, calendar months, hours, minutes, and seconds.

Relativistic dynamical time
At the XVIth General Assembly in 1976 the IAU adopted resolutions which called for sweeping changes to the basis for almost all astronomical calculations. Until this point almost all calculations had been based on the expressions created by Simon Newcomb in 1895. The new system was intended to bring astronomy from the era of Newtonian dynamics built entirely on earth-based observations into the era of relativity, radar, man-made satellites, and interplanetary spacecraft. The IAU adopted a new system of astrnomical constants, but the accompanying FK5 star catalog and reference frame was still constructed according to traditional optical astrometric methodologies. Also in 1976 the IAU defined two new forms of time which were intended to serve as relativistic replacements for Ephemeris Time. In order to give time for study and implementation of these changes it was resolved that they would not be used in the ephemerides until 1984. Coincidentally this was 100 years after the International Meridian Conference.
Terrestrial Dynamical Time -- TDT
The concept for TDT was adopted by the IAU in 1976 and the name TDT was adopted by the IAU at the XVIIth GA in 1979. It came into use in the ephemerides in 1984 and was used through 2000. But by 1987 TDT was already deemed to be a misnomer because there is nothing dynamical about it. It was not clear whether TDT was intended to be a measure of proper time or coordinate time. In 1991 the IAU redefined TDT and renamed it TT.
Barycentric Dynamical Time -- TDB
TDB was intended to be the relativistic equivalent of ET for the purposes of calculating planetary ephemerides, but its history has turned out to be far more complex than was expected at its inception.
TDB in 1976
The concept and original definition for TDT was adopted by the IAU at the XVIth GA.
TDB in 1979
At the XVIIth GA the name TDB was adopted for use with the concept and definition from the previous GA.
TDB in 1984
TDB came into active use as the new expressions and systems for astronomy were implemented in the Astronomical Almanac (which replaced the previously separate ephemerides of the US and UK) and the other ephemerides. In practice the quantity called TDB was actually the independent variable of the DE20x series of planetary ephemerides from JPL.
TDB in 1987
Ongoing discussion of the 1976 definition of TDB had revealed that it was ill defined because it lacked a precise definition for the epoch of its origin, it lacked a metric for transformations to the time experienced by other observers, and because the definition for the rate at which it ticked was not sensible.
TDB in 1991
The IAU defined TCB as a rigorously correct independent variable for planetary ephemerides. The resolution offered that TDB could continue to be used for some purposes despite its inadequately rigorous definition.

Despite resolutions that TCB should be used for all solar system calculations, the ephemerides and many other papers on solar system dynamics continued to use the name TDB for their independent variable.

TDB in 1998
Standish defended the ongoing use of what was being called TDB by publishing a paper which defined Teph and demonstrated that it was a linear transformation of TCB.
TDB in 2005
The IAU Working Group on Nomenclature for Astronomy created presentations and explanations which recommend that the original 1976 definition of TDB be forgotten because it was never used. They agree that the Teph defined by Standish and used in the ephemerides since 1984 has always been what TDB was intended to be. Each ephemeris has its own version of TDB.
TDB in 2006

The IAU GA in Prague approved several resolutions including one that re-defined TDB.

By so doing TDB has effectively been converted from a Platonic or theoretical time scale into a practical one which is tied directly to JPL DE405.

Guinot and Seidelmann (1988) described the difficulties with the 1976/1979 resolutions and proposed changes that were later implemented.
Rigorously correct relativistic time
In 1991 the IAU resolved that a fully relativistic and inertial reference system should be created, and also defined two new forms of fully relativistic time. In 1994 the IAU specified a list of extragalactic radio sources to be used in defining a reference frame consistent with that reference system. In response the IERS coordinated the International Celestial Reference System (ICRS) and the International Celestial Reference Frame (ICRF). In 1997 the IAU resolved that the ICRS and ICRF should come into use starting in 1998.
Geocentric Coordinate Time -- TCG
TCG was defined by the IAU at the XXIst GA in 1991, and its definition was clarified by the IAU at the XXIVth GA in 2000. It has not explicitly come into use in any ephemerides, but it is defined to have a linear relationship with TT. The unit of TCG is the SI second (9192631770 cycles of the cesium resonance) in a coordinate reference frame that moves with the center of the earth. Because clocks on the surface of the earth rotate within a gravity well, a clock using the SI second of TCG ticks faster than a clock using SI seconds of TT or TAI. TCG ticks faster than TDB (and TT and ET) by about 7 parts in 10 billion, or about 20 milliseconds per year. Consequently, the values of physical constants (including the length of the meter) to be used with calculations using TCG differ from the traditional values of physical constants. Various scientific unions have recommended the use of TCG for all measurements made in the terrestrial environment, but the formidable tasks of changing the values of constants in software mean that most such measures continue to use TT.
Barycentric Coordinate Time -- TCB
TCB was defined by the IAU at the XXIst GA in 1991, and its definition was clarified by the IAU at the XXIVth GA in 2000. It has not yet come into use in any ephemerides. The unit of TCB is the SI second (9192631770 cycles of the cesium resonance) in a coordinate reference frame that moves with the center of mass of the solar system. Because clocks on the surface of the earth move and rotate within several gravity wells, a clock using the SI second of TCB ticks faster than a clock using SI seconds of TT or TAI. TCB ticks faster than TDB (and TT and ET) by about 1.5 parts in 100 million, or about half a second per year. Consequently, the values of physical constants (including the length of the meter) to be used with calculations using TCB differ from the traditional values of physical constants. Various scientific unions have recommended the use of TCB for all measurements made in the solar environment, but the formidable tasks of changing the values of constants in software mean that most such measures continue to use Teph (often believing that to be TDB).
independent variable of the ephemerides -- Teph
Teph is the name which has been coined to denote the independent variable that has been used in numerically integrated ephemerides since the 1960s. Standish (1998) demonstrated that Teph is a linear transformation of TCB that ticks at a rate equal in some mean sense to the rate of TT. Teph is a realization of the goal that ET and TDB tried to attain.

Each different ephemeris has a different instance of Teph. Typically the values of Teph closely match the values of TT over the interval of the observations which were used to construct the particular ephemeris. Any instance of Teph is a barycentric coordinate time scale which has 0.01720209895 as the value of the Gaussian gravitational constant.

In early discussions of the IAU Working Group on Nomenclature for Fundamental Astronomy it has been suggested that the various instances of Teph might someday be given an official name something like Barycentric Ephemeris Time.

In 2005 the IAUwgNfA has decided that Teph is what TDB was always meant to be, and they are recommending that the two be considered synonymous.

Seidelmann and Fukushima (1992) described TCG and TCB and the reasoning behind them. Vondrak (2002) described the IAU 2000 resolutions which clarified TCG and TCB and the reasoning behind them. Soffel (2002) and Petit (2002) provided further details about the IAU 2000 resolutions which clarified TCG and TCB. Two detailed reviews of the IAU 2000 resolutions and their implications for time and fundamental astronomy are by Seidelmann and Kovalevsky (2002) and Soffel et al. (2003) ( preprint here).

Dynamical time is robust across an interruption in civilization because it is derived directly from observation. As long as the historical record of astronomical observations is preserved it is a straightforward matter to recover dynamical time to a precision of milliseconds even after an interruption of centuries.

Atomic Time
Although there had been previous efforts to build atomic resonators, Atomic Time as we now know it came into being in 1955 when Essen and Parry at the UK NPL created the first workable clock using the cesium resonance. By 1958 the cesium resonance had been compared with astronomical observations of the ephemeris second, and the atomic second of 9192631770 Hz was born. Thus 86400 atomic seconds match the length of one ephemeris day, but the mean solar day has been longer than that for quite a while. So atomic time has no relation to the rotation of the earth.
Stepped Atomic Time -- SAT
A form of time scale used in long-wave radio broadcast time signals of the US and Germany during the 1960s. The carrier frequencies and most second intervals were atomic seconds, but there were frequent steps of 100 ms to 200 ms inserted in order to match UT2. These steps were the precursor to leap seconds in the later form of UTC. In 1966 broadcasts of this time scale were classified as experimental by CCIR Recommendation 374-1.

In particular, SAT was used by the long-wave transmissions of WWVB in the US and the PTB in Germany. Some devices manufactured by Hewlett-Packard for automatically synchronizing with broadcast time used WWVB, and were therefore synchronized with SAT, not UTC. Complete records of all the steps applied to SAT are not readily available. As a result it can be difficult to determine a relationship with sub-second precision between historical timestamps expressed in SAT and in TAI.

International Atomic Time -- TAI
TAI is the continuation of time scales which began with the first cesium atomic clock in 1955. The value all existing atomic time scales (and by extrapolation the value of TAI) was equal to that of UT2 on 1958-01-01, but that date was before high-precision international coordination of time had begun. Guinot (2000) points out that because in 1958 the values of UT1 used by various observatories differed by several hundredths of a second of time, so also did their values of UT2.

The name TAI was officially proposed in 1970 and adopted in 1971. Beginning in 1977 TAI has been constructed by steering the frequency of what is now called EAL with an offset. Since 1980 TAI has been a "realization of TT", a coordinate time, in conformance with the definition approved by the IAU in 1991, but TAI does not officially incorporate the clarifications to TT that the IAU adopted in 2000. Guinot (1986) explored the ways in which clocks contributing to TAI measure a proper time.

TAI has always been a statistical combination of the available ensemble of atomic clocks. The differences between TAI and various other atomic time scales are published monthly by the BIPM in Circular T. TAI has not ticked uniformly throughout its history, but once a TAI has been assigned to an event its value is never revised. The variations in TAI can be traced via TT(BIPMxx). The initial results of the meeting about the calculation of TAI held on 2004-03-31 are now online from the BIPM.

A.1
The first atomic time scale was constructed by the USNO in 1959 and was extrapolated back to 1956. It was set equal to the UT2 of the USNO as of 1958-01-01.
AM,
A3, TA
In 1961 the BIH constructed a time scale named AM using radio broadcasts based on three atomic clocks. This was renamed A3, more clocks were added from 1967 through 1969, new statistical algorithms were employed, and the name became TA. This series of time scales has been extrapolated back into 1955 using broadcast time signals based on the original cesium clock at NPL. In 1971 the BIH atomic time scale became TAI.
TAI since 1977-01-01
By the mid 1970s it was evident that the scale unit of TAI was not equal to the SI second at sea level. On 1977-01-01 the frequency of TAI was reduced by one part in 1012, and the frequency of TAI has been steered since that time.
Echelle Atomique Libre
(Free Atomic Time Scale) -- EAL
Starting 1977-01-01 the un-steered combination of atomic clocks which had formerly been TAI has been known by the new name EAL.
TAI since 1995
By 1995 it was evident that blackbody radiation was affecting the frequency of cesium clocks, and that the true SI second should be measured at 0 Kelvin. Over the interval from 1995 to 1998 the length of the TAI second was decreased by about 2 parts in 1014 until it corresponded as closely as possible to cesium atoms at absolute zero.
TA(k)
Various atomic time scales which contribute to TAI are maintained in real time by various laboratories around the world. For example, the designation TA(NIST) refers to the atomic time scale that is maintained at the US National Institute of Standards and Technology, and TA(PTB) refers to the atomic time scale maintained at the German Physikalisch-Technische Bundesanstalt. The differences between various instances of TA(k) are published monthly by the BIPM in Circular T.
GPS time
The GPS satellites adopted a time scale which was synchronized with UTC in 1980, and it has been steered in close synchrony with TAI since then. Therefore the difference TAI - GPS has been 19 s to within a microsecond. In effect, this means that GPS time is another variant of TA(k).
Galileo System Time -- GST
The European navigation satellite system Galileo will have a time scale based on TAI. The design specifications indicate that GST will be kept within 50 ns of TAI 95% of the time. In effect, this means that GST will be another variant of TA(k).
International Time -- TI
The time scale named at the ITU-R SRG 7A colloquium in Torino on 2003-05-30 as a likely candidate for radio broadcast time signals at some point in the future. TI would be a purely atomic time scale offset from TAI by a fixed integer number of seconds. In order to avoid discontinuities for systems using radio broadcast time signals the offset would be equal to the offset of UTC at the instant of switching from UTC to TI. The nominal year at which the switch would occur is 2022.

Atomic time is not robust across an interruption in civilization because it depends on the continuous operation of complex equipment. If civilization were disrupted the existing atomic time scales would be lost. The precision to which a new civilization could match new atomic time scales to the current ones would depend upon astronomical observations. If dynamical time were the only available scheme, then the match would not likely be as good as a millisecond.

Terrestrial Time -- TT
TT was defined by the IAU in 1991 as a clarification of what TDT was intended to have been. Seidelmann and Fukushima (1992) described TT and the reasoning behind it. TT has been used in the ephemerides since 2001. TT is intended as a Platonic ideal, for there is no single realization of it. TT is a coordinate time scale for a reference frame which moves with the geocenter, but TT ticks at a rate equal to that of clocks on the rotating geoid. Therefore TT is a linear transformation of TCG.

TT can be realized by various methods, but the most practically available form is derived directly from TAI. Irwin and Fukushima (1999) have provided the best relationship between TT and TCB. Soffel (2002) and Petit (2002) provided further details about the IAU 2000 resolutions which clarified TT.

TT(TAI)
TT(TAI) = TAI + 32.184 s

This is TT calculated simply by presuming that TAI has been free of defects since it read 1977-01-01T00:00:00. The value of 32.184 s is the best available estimate of the difference between TDT and TAI on that date.

TT(BIPMxx)
This time scale is an effort to ascertain corrections to the values of TAI based on retrospective studies of the behavior of the clocks which have contributed to TAI. The procedure for computing it was first described by Guinot (1987) when TT(BIPM87) was published. The current instance is TT(BIPM04) created in 2004 and plotted here.
TT(pulsars)
Several international scientific unions are preparing to recommend that a new time scale be constructed from radio astronomical measurements of pulse arrival times of an ensemble of pulsars. This time scale would be used to provide an independent means of measuring the defects of TAI inferred from TT(BIPMxx).

Terrestrial Time is not currently robust across an interruption in civilization because its principal realization depends on atomic time. If civilization were disrupted then TT could be reconstructed to a millisecond precision using dynamical time. TT(pulsars) might provide a way to achieve microsecond precision, but this possibility will not be clear until after that new time scale has been in operation for many years.

The forms of dynamical, atomic, and coordinate time above are not based on earth rotation. They have no connection with days in the traditional sense; thus they have no simple relationship with the concept of a calendar. It is important to remember that the 24-hour cycle of tags like 12:00:00 really only makes sense for earth rotation time.

To their credit, the BIPM do report TAI and TT using modified Julian date (MJD) notation. Nevertheless, it remains commonplace to use the traditional calendrical and sexagesimal notations when counting the seconds which are defined by these time scales. (Indeed, for the sake of human cognition this notational convenience is very nearly a requirement.) Unfortunately, that usage leads to even greater confusion about the meanings of time scales.

Denoting TAI with a tag in the form 1958-01-01T00:00:00, and denoting TT, TCG, or TCB with a tag in the form 1977-01-01T00:00:00 should be considered as a convenience only. They are merely counts of elapsed time where one anonymous and indistinguishable second follows another. It is very appropriate to count these forms of time using decimal notation from the epochs represented by those tags. But there is no observable event that happens cyclically at 12:00:00 for dynamical, atomic, or coordinate time -- the entire notion of such a cyclical process is contrary to their uniformly-incrementing conceptual definitions.

Coordinated Universal Time -- UTC
UTC does not fit into any one of the above categories, but it is dependent on them. UTC has always been both Universal Time and Atomic Time as provided by radio broadcast time signals. UTC has been a practical time scale. The nature of the goals it has been intended to meet and the proceedures for meeting those goals have changed over the years.

Initially the name UTC was not used. The process of broadcasting synchronized signals was called coordination, and the resulting signals were called coordinated. Prior to the advent of atomic clocks it had not been possible to keep the broadcast time scales of widespread systems synchronized to within a millisecond.

The original goal of UTC was for radio broadcasts around the world to be synchronized with each other while providing a time which matched the expected value of UT2 as closely as could be predicted in advance. The length of the second of UTC was adjusted (``elastic seconds'' or ``rubber seconds'') at the beginning of each year, and any accumulated error caused by mis-prediction of the rate of UT2 was corrected by applying occasional steps of 50 to 100 milliseconds to the value of UTC.

UTC during 1960
An experiment by the US and UK to use the same system for broadcast time signals. This was a natural extension of the 1955/1958 collaboration of Markowitz, Hall, Essen, & Parry (1958) where the US radio broadcast time signals of UT2 had been used to calibrate the frequency of the cesium transition and the rate of Ephemeris Time. By so doing, the longstanding differences in time broadcasts which had been caused by inconsistencies in the ``conventional longitudes'' of the observatories were reduced from several hundredths of a second of time to less than a millisecond.
UTC from 1961 through 1971
The responsibility for coordinating the frequency offsets and steps was transferred to the BIH. A table of the frequency offsets and steps is available from the IERS, which is the organizational descendant of the earth rotation portions of the BIH.

Cautionary note:
During this same period some radio broadcasts were providing SAT (see above). Also, at least until 1967 the Soviet Union and China were broadcasting another form of time coordinated in the USSR independently of the BIH.
Before assigning absolute meaning, any time-stamp from this era intended to be used with sub-second precision should be subjected to historical scrutiny about the mechanisms of its provenance. This includes the origin of the POSIX epoch at 1970-01-01T00:00:00.

UTC in 1963
The details of the original form of UTC were codified in CCIR Recommendation 374. As yet this broadcast time scale had no official name. The US NBS continued to announce their WWV signals as Greenwich Mean Time.
UTC in 1965
The BIH started calculating UTC based upon its atomic time scale (which later became TAI).
UTC in 1967
The CCIR adopted the names "Coordinated Universal Time" (for English) and "Temps Universel Coordonne" (for French) along with the single abbreviation UTC (for all languages). As such, the CCIR became the defining authority for the time scale named UTC.
The IAU noted this nomenclature at its XIIIth General Assembly in Prague.
The canonical ordering UTC is consistent with neither French nor English, but it is consistent with the UT0/UT1/UT2 nomenclature scheme. Despite the canonical ordering, it remains common even today to see usage where the letters are permuted (and worse misnomers such as Consolidated Universal Time, Universal Correlated Time, Universal Coordinating Time, Universal Time Calibrated, etc.).
UTC in 1969
Despite resolutions calling for an international and interdisciplinary committee to study options for radio broadcast time signals, in 1969 CCIR study committee VII-1 unilaterally deemed that radio time signals should broadcast atomic seconds with occasional full second leaps.
UTC in 1970
In 1970-01 the CCIR unilaterally decreed that on 1972-01-01 (in less than two years) broadcasts of UTC would begin using the new scheme. This was codified in the text of CCIR Recommendation 460. The maximum difference DUT1 = (UT1 - UTC) was specified as 0.7 s, which prompted the creation of signals encoding DUT1 which can only indicate values up to 0.7 s.
The CCIR failed to send a letter informing the IAU of the change, so the IAU was unable to respond officially at its General Assembly in 1970. That made it impossible for the IAU to produce an official response before the IAU GA in 1973, which was after the change would be implemented.
UTC starting in 1972
At the end of 1971 a special offset of -0.1077580 seconds was applied to step UTC so that ( TAI - UTC ) was exactly 10 seconds. Henceforth the length of the UTC second has matched the length of the TAI second, and the value of UTC has been adjusted via one second leaps to keep it within a second of UT1.
UTC in 1973
The IAU recognized that UTC provided mean solar time and recommended its use for civil time. The IAU gave more advice on modifications to the leap second scheme.
UTC in 1974
The first revision of the document defining UTC was issued as CCIR Recommendation 460-1. It incorporated advice from the IAU GA in 1973 and raised the maximum allowable difference of (UT1 - UTC) from 0.7 s to 0.9 s.
UTC in 1975
The CGPM resolved that UTC provides both atomic frequency standards and UT (or mean solar time) and endorsed its use for civil time. As a result, legislative bodies in some countries began to adopt UTC as a precisely defined replacement for GMT in the basis of their legal time.
UTC on 1977-01-01
Because the rate of TAI was reduced by one part in 1012, the rate of UTC was reduced by the same amount. Therefore, before this date UTC seconds were shorter than they currently are.
UTC in 1978
The second revision of the document defining UTC was issued as CCIR Recommendation 460-2.
UTC in 1982
The third revision of the document defining UTC was issued as CCIR Recommendation 460-3.
UTC in 1986
The fourth revision of the document defining UTC was issued as CCIR Recommendation 460-4.
UTC in 1988
The responsibility for maintaining UTC was split between two agencies. The responsibility for keeping TAI was transferred from the BIH to the BIPM. The responsibility for monitoring earth rotation, determining UT1, and announcing the need for leap seconds was transferred to the newly created IERS. After around a century of operation the BIH and the ILS ceased to exist as these responsibilities were combined into the IERS.
UTC in 1992/1993
The CCIR was reorganized to become the ITU-R, and the defining document for UTC was renamed ITU-R TF.460.
UTC from 1995 through 1998
In 1995 a CCTF working group determined that the length of TAI seconds was longer than the SI second because the clocks contributing to TAI were not corrected for the effects of blackbody radiation. Over the next three years the frequency of TAI was steered to reduce the length of its seconds by about 2 parts in 1014. Therefore the length of UTC seconds was also reduced. This change is evident as the final kink in the plot of TT(BIPM04).
UTC in 1997
The fifth revision of the document defining UTC was issued as ITU-R TF.460-5.
UTC since 1999
Klepczynski publicly suggested discontinuing leap seconds, and the CCTF wrote a letter to various international scientific unions which started the ongoing process of reconsidering the future of leap seconds.
UTC in 2002
The sixth revision of the document defining UTC was issued as ITU-R TF.460-6.
UTC(k)
Approximations to UTC are maintained in real time by various laboratories around the world. For example, the designation UTC(NIST) refers to the approximation to UTC that is maintained at the US National Institute of Standards and Technology, and UTC(NPL) refers to the approximation to UTC maintained at the UK National Physical Laboratory. The differences between the various instances of UTC(k) are published monthly by the BIPM in Circular T.
UTC in 2007 ?
As of 2004-09 the index of contributions to WP7A on the ITU website contains a new document from the United States whose title says it is a proposed revision of ITU-R TF.460-6 (the defining document for UTC). Although it is not possible to see the content of that document, it seems likely that it is a revision of this archival document on the FCC website from the United States Working Party 7A that holds the federal charter to interact with the ITU-R.

The archival document from USWP7A proposes that UTC should switch to having leap hours on 2007-12-21.

UTC in 2012 ?
On 2005-09-19 the USWP 7A released the 2005 version of its Proposed Revised Recommendation ITU-R TF.460-6. The document was not approved by the State Department, but its text would have ceased adding leap seconds as of 2012-12-21. The fact that this date would have been the same as the end of the Mayan calendar long count was a source of some amusement.
UTC in 2022 ?
According to the Potential Alternative to the Leap Second developed at the Colloquium on the UTC Timescale held by ITU-R SRG 7A in Torino on 2003-05-28/30:
UTC will cease to exist.
UTC will be replaced by the purely atomic time scale named TI which is described above.
UTC has always been a compromise between the needs for atomic frequency and time interval and the needs for mean solar time. As a result, UTC is the only form of time that has leap seconds. UTC is the only form of time which can have a second labelled ``23:59:60'', or which might perhaps omit a second labelled ``23:59:59''.

On the other hand, the leaps which have been introduced in UTC (milliseconds before 1972 and full seconds since 1972) are nothing new for civil time. Prior to atomic clocks there were no practically available clocks which were as stable as earth rotation. Even the best temperature-controlled quartz crystal clocks needed to be reset -- i.e., leaped -- regularly to agree with astronomical observations. Throughout the long history of developing clocks for timekeeping it had always been that way. Prior to 1960 the leaps had been applied individually, by each local timekeeping agency, for its own set of time signals, as deemed necessary by the astronomers running the transit instrument at the local observatory. The only real change that happened in 1972 was to agree that the leaps should be full atomic seconds, coordinated internationally, and that there should be a nomenclature scheme for referring to those leap seconds.

The possibility of changing UTC to omit leap seconds means ignoring astronomy and disconnecting civil time completely from the rotation of the earth. It would make the progression of civil time predictable, but time tags such as 12:00:00 would be completely unrelated to having the sun overhead at noon. Over the passage of centuries the difference between 12:00:00 and noon would become increasingly obvious.

Note also that if UTC is redefined without being renamed, the result will be the same sort of archival chaos as was created by the British Admiralty when it redefined GMT in 1925. Because the definition of UTC has always been a compromise, anyone finding the term UTC in a document will not be sure of its intended meaning even if the document originated while UTC had leap seconds. After such a change it will be unclear whether authors intended the use of ``old UTC'' or ``new UTC'', or whether the difference is important at all.
This question will have to be asked: Should ``UTC'' be interpreted simply as a conventionally-available atomically-regulated civil time, or should it be interpreted as a form of mean solar time?
Persons reviewing computer source code and documentation will have to ascertain whether the original intent of authors and system operations involving any quantity called UTC require a time scale with properties that match mean solar time or not. Legal systems which have relied on the fact that UTC is a form of mean solar time may require revision. Legal and operational systems which seem to work at first may fail later as the difference between UTC and UT1 grows. Changing the characteristics of UTC without changing the name may seem easy at first, but it has widespread consequences of potentially considerable cost which must eventually be paid.

UTC without leap seconds would be inconsistent with the nomenclature established by resolution V of the 1884 International Meridian Conference and adopted by the IAU, and also inconsistent with the 1975 CGPM resolution on UTC.

The robustness of UTC across an interruption in civilization is schizophrenic specifically because UTC is a combination of two incommensurate concepts. Inasmuch as UTC is a vehicle for communicating mean solar time, UTC is robust because by its own definition it admits that the conventional value of mean solar time need not be accurate to much better than one second. Inasmuch as UTC is a vehicle for atomic time, UTC cannot be robust because atomic time is not.

POSIX time
The current standard for this time scale is IEEE P1003.1 or POSIX.

In 2003 Landon Curt Noll submitted some historical views on how POSIX got the way it is to the LEAPSECS mailing list.

The current standard defines seconds since the epoch ignoring the existence of leap seconds. As a result, the rationale admits that not all POSIX seconds have the same length, and it is also fuzzy about the definition of the epoch.

To put it simply, the POSIX standard is self-inconsistent. A rigorously defined time scale should either be a count of mean solar seconds, or atomic seconds. POSIX tries to be both and as a result it cannot address leap seconds meaningfully.

POSIX time shares most of the caveats of Julian Date (above). There are two main distinctions between POSIX time and the forms of Julian Date. First, POSIX time is an integer count of seconds instead of an arbitrary-precision real number of days. Second, the quality of clocks and the representations of integers in computing hardware place severe restrictions on both the precision of instants of time and the useful span of dates which can be represented by POSIX time.

See the related online bibliography page for more ruminations on the POSIX time scale.

Microsoft Windows file time
Microsoft Windows defines its file time as ``the number of 100-nanosecond intervals that have elapsed since 12:00 A.M. January 1, 1601 Coordinated Universal Time (UTC).''

The year 1601 is prior to the development of reasonably accurate escapements for clocks. The year 1601 is prior to the development of the telescope.

As noted above, nothing that could possibly be called UTC existed prior to 1960. UTC has always been an atomically-regulated time scale. Prior to atomic clocks all practical time keeping was performed in subdivisions of the day. Subsequent to atomic clocks it becomes necessary to decide whether a time scale is counting calendar days or SI seconds.

For values subsequent to 1972 trying to do both means that Microsoft Windows file time faces the same problem as POSIX time. For values prior to 1956 there is no possible way to attribute an unambiguous meaning to a Microsoft Windows file time. The whole notion is utter bilge.

See the related online bibliography page for more ruminations on the Microsoft Windows file time.

Microsoft .NET Framework DateTime Structure
The .NET framework from Microsoft takes the above notion even farther into fantasyland.

According to the docs on msdn the DateTime structure "represents dates and times with values ranging from 12:00:00 midnight, January 1, 0001 Anno Domini (Common Era)" using "100-nanosecond units called ticks, and a particular date is the number of ticks since 12:00 midnight, January 1, 0001 A.D. (C.E.) in the GregorianCalendar calendar".

According to calendar historians, at that date the Roman empire under Augustus was probably still engaged in the process of having no leap years at all (in order to correct for having one every three years starting in the year Julius died). This is not to mention the fact that the Common Era would not be defined for another millennium, the Gregorian Calendar for another half millennium after that, and the atomic chronometer another four centuries after that.

Network Time Protocol (NTP)
Dr. David Mills at the University of Delaware began implementing the Network Time Protocol (NTP) in the early 1980s. The current versions of NTP are able to keep computers all around the Internet synchronized to better than one millisecond. Dr. Mills has written this book on NTP as a definitive reference.

Principal documentation for NTP can be found at the web site of Dr. David Mills and at the NTP project web site. The IETF has an active working group on NTP and provides status of the effort.

It is almost certainly a mistake for me to write anything further about NTP, but its characteristics place it on this page.

The NTP timescale is kept and exchanged via an unsigned 64-bit fixed point integer where the upper 32 bits represent integer seconds and the lower 32 bits represent fractions of seconds to a resolution of around 200 picoseconds. The origin of the current NTP era is 1900-01-01T00:00:00 UT, and the NTP counter will wrap around in the year 2036. Given that UTC with leap seconds originated in 1972, and that atomic time did not exist before 1955, it is not clear that any meaning dare be attributed to the fractional bits of the NTP clock during most of the first half of the present NTP era.

The NTP counter ignores leap seconds. As such, its practical properties are very similar to POSIX time. NTP ticks in SI seconds, but its counter accumulates mean solar seconds. At the sub-second level NTP time corresponds directly with TAI or UTC since 1972. At the resolution of one second NTP corresponds to mean solar time. Differences NTP over long spans of time correspond to the historical tradition where ``time'' means earth rotation angle.

Local Civil Time -- sometimes LCT
Local civil time is that which is decreed by the local authorities. No decision by the IAU, ITU, IERS, BIPM, CGPM, URSI, or any other international organization can dictate the time scale used for legal purposes in any jurisdiction. The laws of many localities have not changed since GMT was the basis for worldwide time. Other localities changed their laws to adopt UTC as the basis for legal time after the IAU, CGPM, and other international organizations recommended its use.

The properties that are suitable for LCT remain an open question. Some kind of solar time has been the basis for most calendrical schemes since the dawn of history. Any form of solar time is guaranteed to be non-uniform, and hiding that non-uniformity has been a goal for centuries. The non-uniformity is too subtle for humans to notice, but the number of human-created systems which can detect that non-uniformity continues to increase.

Atomic time is necessary to many systems used by civilization. Current applications for navigation require that everyone be able to agree on its value to about 10 nanoseconds. Mean solar time is traditional as civil time and necessary in order to construct a calendar that counts days. Current applications for civil time require that everyone be able to agree on its value to about 10 milliseconds. There is little dispute that it is far more important for everyone to be able to agree on the value of civil time to within 100 nanoseconds than it is for civil time to have a value that tracks mean solar time to within 100 milliseconds.

Humanity could adopt perfectly uniform atomic time now at the expense of letting our descendants figure out how to return to mean solar time if they so desire.
We could admit that both mean solar time and atomic time are important at the expense of retrofitting all timekeeping systems, legal systems, and the general populace with the understanding that there are two different kinds of time.
The relative merits of these and other options are not yet clear.
Perhaps by forcing the question might we trigger civil timekeeping chaos where different jurisdictions choose different answers to the questions?


Bibliography of works not directly cited above


Other web pages on time scales


Thanks go to John Seago for providing some references above.
Steve Allen <sla@ucolick.org>
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