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Extrapolations of the difference ( TI - UT1 )

For the past decade the ITU-R has been considering ceasing the insertion of leap seconds in the international recommendation about radio broadcasts of time signals. All drafts for the new version of ITU-R TF.460 have had an unacknowledged side effect: if adopted they would disconnect the progression of calendar days from the rotation of the earth. This would redefine the word "day" such that there would be no relationship between calendar date and the number of times the sun will have crossed the sky.

This web page contains tables of the growing magnitude of the difference between radio broadcasts and earth rotation along with plots of the daily differential between the two. Plots of the integrated difference in these tables are available on this web page. POSIX-based systems already have a mechanism that could avoid trouble from leap seconds as described on this web page.

The Colloquium on UTC held at Torino Italy

The Proceedings of the Colloquium on the UTC Timescale held by ITU-R SRG 7A in 2003 May were formerly online from the Italian Istituto Elletrotecnico Nazionale which hosted the meeting, but moved to INRIM until around 2011-03 when the INRIM web pages vanished. As of 2014-11 the Internet Archive Wayback Machine still has a few crawls of the original index and the conclusions of the colloquium.

At the colloquium held by the ITU WP 7A SRG in Torino on 2003-05-28/30 it was supposed that in about the year 2022 radio time signals would stop broadcasting UTC and start to broadcast a new timescale to be called TI. The initial value of TI would match UTC, and after that TI would increment using SI seconds with no leaps. After that time, UTC would effectively cease to exist.

In the years since the Torino colloquium the ITU-R process has continued. I attempt to track that process in my calendar and bibliography page. The most significant deviation from the plan outlined at Torino is that the ITU-R officials appear to be ignoring a significant part of the result of the Torino colloquium. The colloquium result called for the renaming of the time scale from UTC to TI. There are historical precedents which indicate why it is important to change the name.

It seems strange that the ITU-R should call for a meeting of world experts and then ignore their advice. In the intervening time there are now two schemes by which computers are able to perform correct handling of leap seconds.

Effects of disconnecting time from the sun

The reports of the colloquium do not make it clear whether any approximation to UT1 (earth rotation time-of-day) would continue to be included in radio broadcast time signals. As a result, it is not clear whether civil time would continue to track UT1 (as it always has done throughout history) or whether civil time would simply follow TI (atomic time). There are, however, significant sociological consequences which will result if civil time follows TI instead of UT1.

Over the passage of centuries the rotation of the earth is being decelerated by tidal friction from the moon and sun. This means that TI (atomic time) and UT1 (earth rotation time-of-day) would begin to differ, roughly quadratically over long term, as the rotation of the earth is slowed. Eventually that quadratically growing difference will accumulate to arbitrarily large values.

In about 600 years TI will be ahead of UT1 by half an hour, and in about 1000 years the difference will be a full hour. This means that when a TI clock says 12:00 it will still be an hour before noon in Greenwich. The situation in 1000 years is, of course, much the same as what happens all summer long as a result of civil summer/daylight time. However the difference does not stop growing at one hour.

In 3000 to 4000 years TI will be ahead of UT1 by half a day. This means that when a TI clock says 12 noon it will be the previous midnight in Greenwich according to UT1.

In 4000 to 5500 years TI will be ahead of UT1 by a full day. Differences of full day mean differences of calendar date, and day of week. This means that when a TI clock says 12 noon on Wednesday it will be the previous day in Greenwich -- noon on Tuesday -- according to UT1. It is not definite that human society 40 centuries from now will care about the discrepancy between the day on the (atomic) clock and the day as counted by their predecessors waking and sleeping cycles. On the other hand, the current notion of the seven day week has been in use for 30 centuries, and it is deemed quite important by much of the world population.

At Torino the proponents of omitting leap seconds supposed that the governments of the world might handle this situation using leap hours introduced into civil time by occasionally omitting the annual "spring forward" change to jump to summer/daylight time. However there are serious questions raised by the notion of a leap hour. Given that the first leap hour would not happen for centuries, it is not clear that any systems (legal or technological) would build in the necessary complexity for handling it. This seems to be likely even if the notion of the leap hour were built into the new radio broadcasts from their inception. This might mean that posterity would have to face a severe choice: either undertake an expensive and expansive Y2K-like systems review or face an eventual disagreement over what day of the week it would be.

Various values for the deceleration of the earth

The deceleration of the rotation of the earth has been a subject of scientific study for several centuries. It has been traced with some precision by researchers combing through records of astronomical events such as occultations, transits of Mercury and Venus across the sun during the past few centuries, and eclipses that date back over 2000 years. In astronomical tradition the difference between Universal Time (UT) and a truly uniform timescale (ephemeris time and/or atomic time) has been called Delta T. Delta T is effectively the integral of the difference between the instantaneous length of day (LOD) and 86400 SI seconds. Stephenson, Morrison, and others have painstakingly reconstructed earth rotation from ancient historical records of eclipses.

plot of length of day over past 2700 years PDF file SVG file

Among other things, this plot shows that if there had been atomic clocks during the time of Alexander the Great, we would have needed 4 hours worth of (negative) leap seconds since then to keep atomic time in step with mean solar time-of-day. Prior to the invention of the telescope there is no way to know what the smaller changes in LOD were like, but the overall trend of increasing LOD is clear. During the early Christian era, when the LOD was roughly constant at 27 ms shorter than the modern standard, an hour of Delta T accumulated in about 365 years (because 27 ms/day * 365.25 day/year * 365 year = 1 hour).

Lunar laser ranging studies have determined that the long term tidal deceleration should create a LOD change of 2.3 ms/day/century, which accumulates to 42 s/century2. However, over the interval with historic observations (about 2700 years) the deceleration has been less. This is presumably due to crust and mantle rebound after the most recent ice age; the LOD change is 1.7 ms/day/century, which accumulates to 31 s/century2. Furthermore, over the interval since the year 1620 the deceleration has been even less; the LOD change is 1.4 ms/day/century, which accumulates to 25.6 s/century2 but probably cannot persist indefinitely. Next is a detail plot of earth rotation over the past 250 years based mostly on good telescopic observations of occultations.

plot of length of day over past 250 years PDF file SVG file

Finally, over the past 30 years (coincidentally since the inception of leap seconds) the rotation of the earth's crust was accelerating . This acceleration was presumably due to changes of fluid circulation in the outer core of the earth. Historical investigations of earth rotation indicate that such accelerations are not unprecedented, and it should not be possible for the acceleration to continue for very many more years.

Note that there have been previous instances when the rotation of the earth's crust has accelerated more than it has since 1972. Note also that over the timescales of a human lifetime these "decadal fluctuations" are much more significant than the inexorable but slow tidal deceleration. The decadal fluctuations of the 19th century were large enough that Simon Newcomb suspected their existence. The torques which have caused the decadal fluctuations must briefly have been more than ten times larger than the tidal torques. Predicting these decadal fluctuations is effectively impossible, for that would correspond with an ability to predict the weather in the core of the earth.

plot of length of day over past 50 years PDF file SVG file

The number of leap seconds needed is proportional to the area between zero and the LOD curve. In particular note that when the LOD has been about 2.5 ms longer than 86400 SI seconds there have been leap seconds about every 400 days (because 2.5 ms/day * 400 days = 1 second), and when the LOD has been about 1 ms longer than 86400 SI seconds there have been leap seconds about every 1000 days (1 ms/day * 1000 days = 1 second).

From 1999 through 2004 the excess LOD was less than 1 ms, so there was no need for a leap second for more than 2000 days. If that acceleration had continued much longer then the LOD might have fallen under 86400 SI seconds -- then the IERS might have called for a negative leap second. There has never been a negative leap second, so no time keeping system has been tested with one. Indeed, many precision time keeping systems are known not to be prepared to implement a negative leap second.

Implementing the plan outlined at Torino

The difference between UT (earth rotation time-of-day) and the TI (atomic time) that was supposed in Torino will have much the same character as Delta T, but its value will be supposed to be zero in 2022. It is instructive to calculate a table of values to see how the difference grows. For the purposes of this table the difference ( TI - UT1 ) will be denoted DUTC. The table estimates the calendar year in which various values of DUTC will be achieved assuming each of the three values of deceleration noted above. Years which are farther into the future than should be reasonably extrapolated using any particular deceleration are omitted or in brackets. See this page for plots of the projected future deviation.

DUTC 25.6 s/century2
(since 1620)
31 s/century2
(observed over
2700 years)
42 s/century2
(long term)
notable event
1 s 2022-12 2022-10 2022-08 exceeds any previous deviation
2 s 2023-12 2023-08 2023-03 many telescope pointing systems fail
3 s 2024-11 2024-05 2023-10 exceeds current financial transaction tolerance
4 s 2025-10 2025-03 2024-05
5 s 2027 2026 2025 most telescope pointing systems fail
10 s 2031 2030 2028 lawsuits regarding events near midnight
20 s 2040 2037 2033
30 s 2049 2045 2039
1 m 2073 2065 2055 ambiguity for all legal time-stamping
(128 - 19) s 2095 2079 2057 GPS L1 signal format for (GPS - UTC) would overflow
if leap seconds continue to be inserted
2 m 2116 2102 2083 analemmatic sundials fail
3 m 2153 2134 2109
(256 - 19) s 2174 2149 2114 GPS L1 signal format for (GPS - UTC) would overflow
even if Delta t LS is unsigned
4 m 2187 2164 2133
5 m 2217 2201 2155
10 m 2345 2304 2249
20 m [2534] 2474 2391
30 m [2683] 2608 2505 first leap hour
1 h [3023] 2916 2768
1.5 h [3286] 3155 2972 second leap hour
2 h [3509] 3357 3145
2.5 h [3706] 3536 3298 third leap hour
3 h [3884] 3697 3436
3.5 h [4048] 3846 3564 fourth leap hour
4 h [4200] 3985 3683
4.5 h 4115 3794 fifth leap hour
5 h [4479] 4238 3900
5.5 h 4355 4000 sixth leap hour
6 h [4732] 4467 4097
6.5 h 4575 4189 seventh leap hour
7 h 4678 4278
7.5 h [4778] 4363 eighth leap hour
8 h [5180] [4875] 4446 full shift difference
(western 20th century standard)
12 h [5933] [5558] 5033 noon is midnight
18 h [6855] [6396] 5753
24 h [7633] [7103] 6360 Wednesday is Tuesday
36 h [8938] [8289] [7379] too far into the future ...
48 h [10038] [9289] [8237] ... to believe most extrapolations

The year 2022 ? ...

As seen in the table above, the long term effect of omitting leap seconds is inevitable even though the calendar year of any particular difference is impossible to predict. The most significant alteration of the above table would be determined by the date at which the ITU might decide to make a change in broadcast time signals. The year 2022 was offered at the colloquium in Torino as a reasonable compromise, but it is much farther into the future than many proponents for omitting leap seconds would like (indeed, some seem to promote omitting any further leap seconds in UTC starting immediately).

The last time that UTC was changed

The ITU decision process is claimed to be slow. Typically something as significant as changing the nature of all civil timekeeping is supposed to require review by and approval from a large ensemble of international bodies. Nevertheless, there is a precedent where the CCIR (the forerunner to the ITU-R) acted quickly and unilaterally, and that precedent is the original institution of the leap second.

The original scheme of UTC was instituted in the early 1960s. Old UTC attempted to track UT2 by introducing annual frequency changes and small offsets. By the late 1960s that scheme was recognized as silly and intractable. There was a growing need for atomic frequency, and the oft-changing frequencies broadcast with the original UTC were intolerable. In 1968 the CCIR created a working party to consider how radio broadcast time signals might be improved. With the radio reception and computational technology available in the late 1960s it was deemed impractical for radio broadcasts to provide both mean solar time and atomic time.

In 1969 a number of scientific unions called for an international and interdisciplinary study group to find a new scheme. Disregarding that call, the CCIR study group met in late 1969 and proposed the leap second scheme to the CCIR. At the plenary meeting in early 1970 the CCIR unilaterally decided to institute leap seconds -- beginning in 1972 -- with less than two years of advance notice. Furthermore, the CCIR failed to send a letter to the IAU notifying them of the impending change. Without official notification the IAU General Assembly in August 1970 had no basis for objecting to the impending change. Astronomers responded to the CCIR with a resolution stating that UTC with leap seconds represented the "optimum solution" in the face of "conflicting requirements" of users of time, but they could not take final action until the General Assembly held in 1973, which was after leap seconds had begun.

UTC was a hybrid both before and after 1972. The implementation of UTC as SI seconds with leaps continued to obscure the distinction between mean solar time and atomic time. In the intervening decades many systems have evolved which are capable of noticing that distinction.

... or the year 2007, or 2015, or 2022 ? Could a sudden change happen again?

In a word, yes.

By 2004-09 the index of contributions to WP7A on the ITU website contained 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 proposed that UTC should switch to having leap hours beginning just before the end of calendar year 2007. This document was widely disparaged by other delegations. In hindsight, the only plausible explanation for the US delegation proposing a "leap hour" was that the then current federal law said that legal time in the US was mean solar time, so at that date if the US delegates had proposed a purely atomic time scale their proposal would have violated US law. Subsequently the federal law has changed such that the basis for legal time in the US is now the time scale known as UTC.

Neverthless, a quick change has happened before In 1970 the decision to switch to leap seconds was made with less than two years of advance notice before the change in 1972. In the proposal above, the decision to switch to leap hours would be made with less than two months of advance notice. The effects of such a change are plotted in a sibling web page with plots of the expected time difference in the year 2100.

In the 21st century there are wristwatches with more computational capability than most astronomers had in 1970. It is no longer impractical for radio broadcast time signals to provide two time scales in a form accessible to modern receivers. Indeed, the US GPS satellites do exactly that, as do the European Galileo satellites, the Chinese BeiDou, and the Indian navigation satellies.

How long will UTC with leap seconds work?

The current rules for leap seconds in UTC are specified by ITU-R TF.460. They state that a leap second may be added (or subtracted) at the end of any month, but that first preference is given to June and December, and second preference is given to March and September. After the SI second was defined it became evident that the length of the SI second happens to match the length of the mean solar second at around the year 1820. If we start with the length of day in the year 1820 and calculate the tidal deceleration using the rates listed above, then the following predicted rates for the insertion of leap seconds applies.

leap rate 25.6 s/century2
(since 1620)
31 s/century2
(observed over
2700 years)
42 s/century2
(long term)
leap schedule
leap seconds do not happen every year
1 s/yr 2015 [1981] [1939] leap second at end of either June or December
leap seconds happen once or twice per year
2 s/yr 2211 2142 2058 leap second at end of every June and December
leap seconds happen two to four times per year
4 s/yr [2602] 2464 2296 leap second at end of every March, June, September, & December
leap seconds happen four to twelve times per year
12 s/yr [4167] 3753 3248 leap second at end of every month
ITU-R TF.460 is not capable of inserting enough leap seconds
1 s/week - [10223] [8031] leap second every week (or leap hour about every 70 years)
1 s/day - [60644] [45298] leap second every day (or leap hour about every 10 years)

This table shows that although leap seconds in UTC will become more and more frequent, the current scheme for UTC will almost certainly work for the next 1200 years. This gives plenty of time to develop a solution which satisfies the systems that need atomic time as well as civilizations that are accustomed to mean solar time.

Unless civilization decides that counting days and nights is irrelevant, civil time will want to remain synchronized with solar time, not atomic time. If civil time were to become atomic time with leap hours there would foreseeably come a time when that scheme would become quite annoying. It seems likely that human perceptions will always find a one second leap to be inconsequential, even if that happens once a day. My wristwatch is good to a little better than a second a day, so by this reckoning leap seconds in 40000 years will be no more annoying to a human than resetting my watch is today. It is difficult to say whether posterity would prefer one leap second a day or one leap hour every 10 years, and it is presumptuous for the current generation to declare that future generations will not wish to operate on solar time. Changing to atomic time now would place a burden on posterity in exchange for laziness on the part of contemporary designers of systems.

Throughout their history, radio broadcasts of time signals have expressly been for the purposes of navigation. Nevertheless, in support of navigation they have always provided the mean solar time which is also best suited for civil and legal purposes. Any change of the ITU recommendations is said to require unanimous agreement by its constituent nations. Those nations could argue that the long term broadcasts of mean solar time have resulted in a prescriptive easement which, in effect, requires radio broadcast time signals to continue to provide mean solar time in some form.

On-line references to tidal deceleration and Delta T

An estimate of the value of Delta T is needed for any calculation of the apparent locations of celestial bodies, especially eclipses. As a result many people have taken an interest in the rotation of the earth. Here are several web pages which cover various different aspects of the deceleration.

The quantity Delta T was provided by the USNO and IERS from the 1950s through the 1990s, but it is no longer used. By its formal definition, Delta T = ET - UT. The expressions for Ephemeris Time (ET) and for Universal Time (UT) in this context were non-relativistic and have not been in use since 1983. For many purposes Delta T can still be calculated as ( TT - UT1 ).

All clocks need to be reset

Until the 1920s no clock was as stable as earth rotation, and as a result it was broadly understood to be unavoidable that all clocks intended to keep Universal Time (and thus civil time) needed to be reset regularly to agree with earth rotation as established by astronomical observations. But by the 1930s clocks had become good enough to detect seasonal variations in the rotation rate of the earth, and clocks improved significantly over the next several decades.

Astronomers had been aware from the 18th century that the rotation of the earth was slowing with respect to the motions of celestial bodies. In 1935 the IAU opined that all ephemerides should employ the same value of the Gaussian gravitational constant (k) for their calculations. They resolved that the interested authorities be consulted in order to choose a suitable value for adoption at the next General Assembly. Meanwhile in 1936 and 1937 measurements of the seasonal variations in the rotation of the earth were published by two different research teams. At the General Assembly in 1938 the IAU adopted a value of 0.017202098950000 for k, and in so doing they defined both the length of the Astronomical Unit and the duration of the day. In 1938 the astronomers incorrectly believed that day was the mean solar day of the year 1900.0.

Having ascertained that Universal Time was not a uniform clock, astronomers proceeded to define the theoretical basis of a timescale suitable for use when calculating the motions of bodies in the solar system. This timescale became known as Ephemeris Time, and it was based on the observations that produced Newcomb's Tables of the Sun. The theory of Ephemeris Time was developed and refined through the late 1940s and 1950s during the same interval, and by the same experts, that were leading to the definition of the SI second. The day produced by the Gaussian gravitational constant used in Ephemeris Time was called the ephemeris day, and 1/86400 of the ephemeris day became the ephemeris second.

The SI second has always been shorter than the mean solar second ...

Atomic clocks employing cesium were in stable operation by 1955, and as of that date it was determined that the mean solar second corresponded to 9192631830 cycles of the resonance. But it was well known that the rotation of the earth was variable, and the international standards process was already preparing to adopt an SI second which matched the length of the astronomically-defined ephemeris second. Therefore it was deemed reasonable that the atomic second should be defined to match the ephemeris second that was based on observations of the orbital motions of bodies in the solar system. However the 18th and 19th century astronomical observations which were used to define the ephemeris second effectively meant that the ephemeris second matched the length of the mean solar second in around the year 1820, and the tides had slowed the rotation of the earth since then. In any case, by 1958, after three years of observations of the motion of the moon, it was determined that the ephemeris second was notably shorter than the mean solar second; it corresponded to 9192631770 cycles of the cesium resonance. Nevertheless, by 1960 the SI second had been defined to be the length of the ephemeris second, and this value quickly came into common usage by laboratories around the world. Not widely recognized at that time, however, were the long term consequences of adopting a standard SI second which was already different -- shorter -- than the mean solar second used for civil and navigational time.

In the 1960s it was soon demonstrated that atomic clocks were far more stable than earth rotation, and far more practical to measure than the motions of bodies in the solar system. As a result, in 1967 the SI second was redefined as 9192631770 cycles of the cesium resonance, thus matching the ephemeris second, thus matching the mean solar second of about the year 1820. Civil time, however, had long been based on Universal time as provided by radio broadcasts, and Universal time was also required for navigation. By its definition Universal time agrees with earth rotation, so the "second" of Universal time is a mean solar second with duration of 1/86400 of the current, and varying, length of day. Nevertheless, it was also deemed unavoidable that broadcast time must begin to transmit SI seconds of fixed length, and the length of the SI second had been measurably shorter than the length of the mean solar second from the epoch of its definition.

... so atomic clocks and TAI have always ticked faster than clocks based on the earth

The only way to broadcast seconds of fixed length yet still keep the value of the calendar date in agreement with the rotation of the earth is to incorporate leaps in Coordinated Universal time (UTC). This is the compromise in the current hybrid form of Coordinated Universal time. Standard frequency is available all the time, and the short term consequences of handling leaps are weighed against the long term consequences of civil time having no relation with the sun.

Leap seconds are just a way of saying that the "UTC clock" is being reset so that the calendar can count days of earth rotation. In effect, the atomic clocks that now define UTC have always run fast with respect to the sun, and in order to keep UTC in agreement with the sun we must occasionally reset it backward by a second. Despite their extraordinary accuracy, atomic clocks themselves are also effectively reset. The NIST publishes frequency steering that they undertake to keep UTC(NIST) in step with UTC(TAI). Except for the scale of the deviations this steering is not much different than the "elastic seconds" that were originally broadcast as coordinated Universal time.

The question for a clock keeper is, to what should the clock be reset?

For the ensemble of atomic clocks that contribute to TAI, the answer to that question is that they are reset to agree with each other. Atomic time is undeniably more stable than earth rotation time, but even during the relatively short history of atomic time the rules for resetting the clocks have been changed several times.

For civil time the answer has always been that clocks are reset to the sun. By its definition, Universal time must agree with the rotation of the earth. Therefore if broadcast time signals change and cease to include leaps then they must also change the name of the time being broadcast. That probably means a change in the name of the reference timescale as specified by innumerable legal and technical systems -- that is, every document, system and standard that refers to UTC may have to be changed.

TAI is not perfect

TAI is a statistical timescale which is produced at the BIPM by combining the reports from many atomic clocks around the world. Anyone who wants to find out what TAI it is now must mark the time with some local clock that contributes to TAI. Then some weeks after now when all clocks have been combined the difference between the local clock and TAI will be known. At that point it can be said what TAI it was at the moment of interest.

Beginning in 1987, however, the BIPM has published other timescales for extremely demanding applications such as pulsar timing. These timescales are known as TT(BIPMxx), where TT indicates that this is an estimate of Terrestrial Time and xx indicates the calendar year at which the estimate was made.

In effect, TT(BIPMxx) is an admission that there are defects in TAI. The latest version is TT(BIPM14) . TT(BIPM14) looks like this:

plot showing defects of TAI as inferred from TT(BIPM14)

There are several interesting features here. First of all, before 1977 the clocks contributing to TAI were not corrected for the gravitational redshift. Because most clocks are above sea level they tick faster than TAI should tick. Through the mid-1980s there is an annual wobble due to seasonal environmental changes at some of the clock sites. In 1995 a CCTF working group deemed that the clock frequencies should be corrected for thermal radiation, and the CIPM affirmed this in 1997. The steering of TAI to the corrected frequency occurred over three years from 1995 to 1998, and the final levelling of the curve over those years indicates that the frequency of TAI is now consistent with cesium atoms at 0 Kelvin.

Of particular interest is that the slope of TT(BIPM10) only reaches zero at the end of the plot. The description of the construction of TT(BIPMxx) indicates that several of the atomic clocks contributing to TAI are particularly good. The unwritten converse of this is that some of the clocks currently contributing to TAI are, to put it politely, not so good. Nevertheless, the presumed scale difference between the SI second and the TAI second that produces the non-zero final slope is less than the uncertainty in its measurement, so there is no urgent justification for rectifying it until there are better atomic clocks.

In order to provide an independent estimate of the validity of the atomic timescales there is now an international effort to construct a timescale based on the averaging of signals received from an ensemble of pulsars.

UT1 is not perfect

Ideally UT1 is the successor of UT which is the the successor of GMT which is the result of Simon Newcomb's expressions for the fictitious mean sun. However even Simon Newcomb knew that his expressions did not exactly track the mean motion of the sun during his lifetime. The non-relativistic Newcomb expressions were used until 1983 (which is probably far longer than they should have lasted) after which newer IAU expressions based on the 1976 IAU constants replaced them. Those expressions for UT1 were modified again in 1997, and an entirely new form of expressions for UT1 became active at the beginning of 2003. At present the IAU-approved expressions for UT1 contain no direct relation to the position of the sun. Nevertheless, the difference between the true mean sun and UT1 is almost certainly no more than a few hundredths of a second and not changing significantly.

If mean solar time is deemed relevant to human society, then sometime before the start of the 22nd century, or at latest before the next change in the definition of UT1, it would be good to verify when exactly the mean sun crosses the ITRS meridian. This is not a question which has yet been answered directly in the astronomical literature. There are probably only two or three people in the world who know the difference between UT1 and where the true mean sun now is. (Indeed, about this it would be quite appropriate to employ the Clintonesque phrase "It depends on what the meaning of the word `mean' means.")

GPS L1 receivers will fail

The newer constellation of GPS satellites (starting with Block IIF) will accommodate leap seconds for something like 30000 years. This is described by ICD-GPS-200 Rev. C, which is available from the US Coast Guard Navigation Center.

There are two significant additions in the Block IIF signals.
6.2.5 and indicate that bits 7 through 22 of word ten in page 25 of subframe 5 will be a 16-bit integer giving the calendar year (curiously it does not specify whether this is signed or unsigned, but the Control Segment has around 14000 years to clarify that point). indicates that bits 39 through 51 of L2 CNAV message type 1 will be a 13-bit unsigned integer which extends the range of the existing "Transmission Week Number" from 1024 weeks to 8192 weeks. This extends the ability of a GPS receiver to tell when it is from not quite 20 years to over 150 years, which should be longer than any GPS receiver is likely to last. Unfortunately, 30.3.2 indicates that message types 1 and 2 are temporary and will be replaced by the as yet undefined messages 7 through 9. This no doubt will reduce the likelihood that a GPS receiver will bother to use them.

By the time that there are too many leap seconds for the L1 format all of the earlier GPS satellites will be replaced. However, old ground-based GPS receivers will fail to accommodate leap seconds as described below. This is basically to say that sometime in the next 50 years it will be necessary to discard or upgrade all GPS equipment.

The L1 down-link data format for the GPS satellites stores the difference between GPS system time and UTC using a signed 8-bit quantity. This means that the maximum difference ( GPS - UTC ) that can be stored is 127 seconds. If leap seconds continue to be inserted into UTC, then the current fleet of GPS satellites and all receivers of GPS signals will become obsolete.

When will the GPS L1 data format fail? It depends on the deceleration of earth rotation. The approximate year of failure is 2057, 2079, or 2095 for decelerations of 42, 31, or 25.6 s/cy2, respectively. This means that a new series of GPS satellites and a new set of receivers must be designed and deployed sometime within the next century. In addition to the USCG link above, some news about GPS interface control documents is also available through the US Air Force.

Furthermore, navigational satellite systems such as GPS and Galileo place constraints on what can and cannot be used for civil time. Suppose that human society deems that atomic time should be used for system operations, but that some form of mean solar time other than UTC with leap seconds is desirable for civil purposes. This new form of mean solar time might have leap-milliseconds and be something like UTC was before 1972. It is not feasible to consider use of a time scale like this unless the satellite systems can broadcast it. Therefore it is imperative as soon as possible to decide what form of time is needed for civil purposes.

During the preparations for Y2K there were some lists of dates when various systems will fail. Among those lists was an obscure entry which reads

2072 (exact date TBD) Overflow of Milstar Operating System
The year 2072 is about in the middle of the expected window when the GPS leap second counter will fail. So it may be the case that MILSTAR uses the same counter.

The lifetime of individual satellites in these constellations is only expected to be 10 years. There is undoubtedly pressure to avoid having to redesign the down-link protocol, redesign the ground systems, retest the entire ensemble, work out how to handle the potentially awkward period of transition, and redeploy new versions of everything within such a short span of years. But do problems such as this really justify the demise of mean solar time for civil purposes?

An obvious short-term solution is to have all receivers estimate what Delta-tLS will be during any given year and have them guess how many times 256 seconds to add -- this is much the same as the way that the overflow of the 10-bit counter of weeks is handled. A longer term solution would be to construct a Diophantine equation which takes as inputs the 10-bit GPS week counter, the 8-bit GPS Delta-tLS, and the expected deceleration of the rotation of the earth in order to produce the likely number of 1024 week offsets and 256 leap second offsets that should be applied. Although the stochastic nature of the decadal oscillations in the rotation of the earth would eventually invalidate such an equation, building the result into GPS receivers is probably patentable.

So, what time is it?

The German magazine Der Spiegel opened its article on the redefinition of radio broadcast time signals with a joke:

A physicist, an astronomer, and a satellite technician are standing at a street corner. A passerby comes along and asks: "Pardon me, what time is it?"
The answer to the question depends on the needs of the questioner. In many cases human questioners merely want to have some idea how fast they have to rush to get to the next thing on their agenda, and it does not really matter what kind of time as long as everyone agrees.

By its design the SI second was never explicitly based upon the rotation of the earth. It happens that the SI second is currently reasonably close to the length of the mean solar second, and this gives the temporary illusion that SI seconds can be accumulated into minutes, hours, and days. But this close agreement will not persist indefinitely, and the disagreement is already uncomfortably large for some applications.

An interval of time consisting of 86400 SI seconds does not now and never did correspond to anything observable to anyone aside from an atomic clock keeper. There is no SI minute, hour, day, week, month, or year; there is only an SI second. As such, atomic time (TAI) is really nothing more than a count of SI seconds with a value currently approaching 1.5 billion. Purely atomic time cannot be used to construct anything that corresponds to what humanity has historically meant by the word "calendar". Ultimately, TAI does not indicate anything that can contribute to a calendar, for TAI knows nothing of earth rotations.

A calendar is composed of days, and days are rotations of the earth (less one per year). The original definitions of hours, minutes, and seconds are subdivisions of days. In that sense seconds must ultimately add up to days, so they should be mean solar seconds of Universal Time. In this case the answer to the question must be based on earth rotation.

Leap seconds were instituted in 1972 when radio broadcast time signals changed from counting "elastic seconds" (which by their definition evenly divided the day) to SI seconds (which have no relation to the day). The purpose of leap seconds is specifically to permit the broadcast of fixed length SI seconds while providing a value of time that stays in step with the day.

So, if someone asks us "What time is it?" then, like Monty Python's Arthur (King of the Britons), we must all learn to retort "What do you mean, African or European?" That is, we need to decide whether the question being asked is really "What fraction of a day is it?"

One more thing should be noted. Asking either an astronomer or a physicist (or, indeed, a satellite technician, after the European Union gets the GALILEO navigation satellites in orbit) "What time is it?" may result in too many answers.

A parable

One of the recurring reasons that is quoted for abolishing leap seconds in radio broadcast time signals is that air traffic control systems cannot tolerate them. Curiously, exactly the same argument was presented against leap seconds in 1970 when the decision to institute them was made. If air traffic control systems have a problem with leap seconds, how is it that no action has been taken to remedy this problem during the past 33 years?

Some of the proponents of discontinuing leap seconds have opined that the difference between mean solar time and atomic time is very small, and that it will hardly amount to anything during the next century. As shown above, however, the difference between mean solar time and atomic time grows quadratically, and eventually even leap hours become annoyingly frequent. Quadratic growth is familiar to everyone; it is the distance travelled by an object as it falls...

A bus full of passengers is travelling along a mountain road. The road is rough, the driver is annoyed by all the bumps, and a few of the passengers are cursing about the ride. The driver announces to the passengers that the trip would be much smoother if the bus ignored the road and drove off the precipice. The driver assures the passengers that so long as the bus is falling there will be no problem, but if the passengers lean the right way they will be able to choose between bouncing off occasional ledges or missing them and falling freely.
In 40000 years the figure eight of the analemma will have tilted back and forth twice; Polaris will have left the north pole, become the pole star again, and have left again. By then the bus passengers will either be dead or they'll have re-tooled the bus so that it can fly; they won't remember who the driver was let alone still be cursing him. It makes no sense to make any plans that far into the future.

Within 1000 years if there still are such things as wristwatches, they'll be self-aware and able to tell their wearer any kind of time. But a purely atomic civil time will have destroyed the utility of any sundial and have required contemplation of some sort of leap hour. The process of trying to jump a civilization back an hour or back onto mean solar time could make the effort that was invested in Y2K seem trivial. Before the bus drives over the precipice all the bus passengers deserve a chance to look at that first ledge on the way down and decide whether they really want that temporarily smooth ride, or whether they should tell the cursing passengers to get better seat cushions. Either way, some of the passengers are bound to curse the driver.

If civil time departs from UT, how can it ever get back?

UTC -- past, present, and future

The rest of this web page is largely editorial commentary.

The earlier form of UTC

The original form of UTC used from the 1960s through 1971 was a technological failure. With the observational and computational equipment of the era it was technologically infeasible to continue predicting and broadcasting seconds with frequency offsets and 50-millisecond leaps. With present levels of technology that scheme may be technologically feasible, but it does not make sense to broadcast rubber/elastic seconds as the primary signal. For shortwave broadcast time signals the 10 MHz carrier frequency should evenly divide the 1 kHz ticks and tones, which should evenly divide the 1 Hz second markers. Nothing else makes sense.

The present form of UTC

On the other hand, the current form of UTC used starting in 1972 has been a sociological failure. The manner in which it was adopted left implementors from various international scientific unions publicly apologizing to each other for years afterward. The proprietary nature of the standard document defining UTC has prevented its proper understanding and implementation. Whether by design or not, UTC with leap seconds has hindered the need to develop a vernacular vocabulary for talking about the differences between atomic time and Universal Time and the problems that arise for systems that must consider both.

At the time that UTC with leap seconds was adopted the world's best timekeeping experts had no consensus on the scheme, in 2001 at the 15th Meeting of the CCTF there was no consensus, and the report of the colloquium on the future of UTC held by the ITU-R SRG 7A in Torino in 2003 states that there was no consensus. Presumably in order to maintain collegiality at the meetings they all must attend regularly, write ups from those experts have tended to be conservatively politic and avoid discussion of aspects of UTC and timekeeping which even slightly controversial. Most discussions of the hows and whys of leap seconds are so dryly factual that they rouse no response in the average reader. There are few authoritative treatises about how to understand, interpret and implement the standard, or about the characteristics and deficiencies of systems which claim to have implemented UTC. Some systems and standards implementors evidently have not had access to the UTC standard itself (not that it is particularly enlightening in the absence of explanations).

UTC has also been a sociological failure because of the lack of clear ability to formulate questions and gather meaningful responses to questions about the implementation of leap seconds. It is not obvious whether the paucity of responses is due to a lack of understanding of the implications of the current situation and possible changes, or simply due to apathy, or due to security concerns about revealing system details, or all of the above.

Implementations of UTC

Many systems have adopted UTC as their timescale, but have chosen not to track the history of leap seconds. Perhaps such system choices are a result of these early sociological mishaps and other historical accidents of timescales. Ignoring leap seconds is practical, but self-inconsistent, and the inconsistency is becoming problematic in a growing number of places. Despite any claims to the contrary, such systems do not truly provide UTC. Instead they provide half-breed timescales that tick atomically (except near leap seconds) but count mean solar seconds of UT.

On the other hand, mean solar seconds of UT, or anything within about a second of that, remains more than accurate enough for many systems. This is especially true for systems whose clocks are not automatically synchronized with external time signals. It is no great surprise or problem that a wristwatch, grandfather clock, cuckoo clock, or electric clock (after a power failure) needs to be reset. The leap seconds of UTC are invisible to the social scheduling of human activity regulated by such clocks.

A full implementation of UTC must provide a way to calculate the difference of two times in SI seconds to sub-second accuracy. In order to do this, a full implementation of UTC must have a table of all leap seconds, and a way to keep that table updated as more leaps are inserted. Of course these abilities imply significant software and systems complexity to handle and validate times like 23:59:60.

Nevertheless, UTC with leaps is technologically feasible. There are systems which have demonstrated that it can be implemented properly, but these systems require manual oversight. There has never been any international agency with the will, authority, and resources to set up a practical and robust scheme detailing how UTC with leap seconds should be implemented, and there are no schemes which can be guaranteed to work automatically.

No implementation of UTC can provide a way to calculate the number of SI seconds remaining before some future UTC date. This is because of the unpredictability of earth rotation -- most especially due to the changing currents in the fluid outer core. So long as UTC continues the current scheme of leap seconds, the most practical way to characterize an estimate of the time remaining until some future civil date may be to claim that the estimate is given in mean solar seconds.

No implementation of UTC can provide a definite way to calculate the number of SI seconds elapsed since any date before atomic time. The historical measurements of earth rotation from the early telescopic era are not particularly trustworthy, and the measurements from before the telescopic era are truly rare and usually quite crude. The most practical way to characterize the estimate of the time elapsed since some historic cultural event is usually in mean solar seconds, or mean solar days (i.e., a calendar) if the event is long enough ago.

Where does the ITU-R go from here?

ITU-R SRG 7A was constituted in order to study Question ITU-R 236/7 The future of the UTC time scale . The preamble for the question asserts that "the occasional insertion of leap seconds into UTC creates serious difficulties for many operational navigation and telecommunication systems" even though no such difficulty or system has ever been openly documented. There are three carefully-worded components to the question:

  1. What are the requirements for globally-accepted time scales for use both in navigation/telecommunication systems, and for civil time keeping?
  2. What are the present and future requirements for the tolerance limit between UTC and UT1?
  3. Does the current leap second procedure satisfy user needs or should an alternative procedure be developed?

The question about UTC which is being considered by ITU-R SRG 7A is only one of several related questions being considered. Other ITU groups are considering ways to standardize the information provided in the radio broadcast time signals of all the different national standards agencies. Recognizing that TAI has deficiencies, the ITU is also joining with other agencies in recommending that another absolute timescale be constructed based on observations of pulsars. The question before SRG 7A is one which the ITU must answer but which requires participation by experts outside of the ITU.

The current ITU-R SRG 7A seems to recognize failures in precedents set by both forms of UTC. It is possible that the consideration for a change to UTC had to wait until most of parties involved in 1970s debacle had retired, and that the growing need to "do time right" has finally tipped the balance in favor of attempting a change. The broad membership of the SRG hints at a recognition that the sociological fiasco of 30 years ago must not be repeated.

The result of any change to broadcast time signals must have broad consensual support from all of the scientific unions. It must be possible for a broad spectrum of experts to agree with each other when they interpret the implications of any new system for particular applications.

The results of Torino

Early in the process of redefining leap seconds there were several surveys and questionnaires distributed to various users of time services. These were conducted by Communications Research Laboratories in Japan (only available to LEAPSECS subscribers), the International Union of Radio Science, and the IERS. All of these surveys occurred before the sorts of information in this web page were widely available. In all cases more of the responses favored keeping leap seconds in UTC than any other option. The ITU-R SRG 7A initially considered creating its own survey, but by 2002 they had decided that constructing a survey would be too much work and that the results would be uncertain, and the report of the Torino conference dismissed the notion.

The report of the Torino colloquium includes the following two sentences regarding the future of UTC.

Bibliography of works not directly cited above

Thanks for many of the references on this web page go to Jim Ray, Tom Van Baak, and all the contributors to the LEAPSECS mail list .
Steve Allen <sla@ucolick.org>
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