The Future of Leap Seconds

This is a work in progress which attempts to catalog all of the openly-available information about the international regulatory process which may result in

the discontinuation of leap seconds in radio broadcasts of time signals

the redefinition of the word "day" such that it no longer has any connection to the rotation of the earth nor to longitude on the earth

See also:

Some of these events may have explicit presentations about the ongoing process looking into redefining broadcast time signals. Other events may only reference it tangentially as a result of the presence of members of the international time and frequency community.

2023 late in the year: ITU-R World Radio Conference

In 2015-11 the ITU-R WRC decided not to decide about leap seconds until the WRC in 2023, and to invite other international agencies to study the issues. In general the ongoing discussions are being done privately, and there has been very little public information about the proceedings. Details about plans for the future of leap seconds, time scales, and radio broadcast time signals may not become available for several more years.

2016-12-31T23:59:60: IERS Bulletin C52

The 27th leap second will be introduced into the radio broadcast time scale that is currently known by the name UTC. After this the difference between TAI and UTC will be 37 seconds.

2016-12: BIPM in Nature

2016: 27th leap second news related to computing systems

"Curiouser and curiouser!" cried Alice (she was so much surprised, that for the moment she quite forgot how to speak good English)

-- Lewis Carroll, Alice's Adventures In Wonderland

Aside from all the URLs of documents on this web page, one summary of the situation is in the Report of the IAU Working Group on Coordinated Universal Time (UTC) which was completed in 2014 April. The UK NPL has another good summary of the leap second in UTC issue and how the ITU-R has faced it.

The best available collections of scholarly articles on the subject of leap seconds in UTC are the proceedings of the 2011 meeting Decoupling Civil Timekeeping from Earth Rotation ( hardcover and CDROM) and the proceedings of the 2013 meeting Requirements for UTC and Civil Timekeeping on Earth ( hardcover and CDROM).

One significant impediment to the ITU-R is its own Radio Regulation 2.5 which reads:

Whenever a date is used in connection with Coordinated Universal Time (UTC), this date shall be that of the prime meridian at the appropriate time, the prime meridian corresponding to zero degrees geographical longitude.

Another impediment to progress within the ITU-R is that the phrasing of the question and the drafts of new versions of TF.460 have always resembled a Catch 22 . The process of preparing documents for the ITU-R is largely performed in an atmosphere of diplomatic secrecy. The understandable result is that many avoid public responses.

Civil time has always been some form of solar time (i.e., time-of-day), but there have been many other ways of reckoning time. During the past few centuries the basis of most civil time has been mean solar time, and this was adopted for legal purposes almost everywhere by international vote in 1884. In 1928 Universal Time became the official name for the quantity which best indicates the mean solar time of the Greenwich meridian (or GMT).

Since their inception early in the 20th century radio broadcasts of time signals have provided a form of mean solar time because that served a dual purpose both for navigation and for civil time. Fractional second leaps were routinely introduced into the broadcasts in order to keep clocks running on mean solar time. In the 1950s atomic resonators became available, and the atomic second was adopted with a different length than the mean solar second. In the 1960s radio broadcasts began to be based on atomic chronometers with numerous fractional second leaps in order to track mean solar time. Since 1972 radio broadcasts have provided Coordinated Universal Time (UTC) which serves a further purpose; it always uses atomic seconds and tracks mean solar time by inserting occasional full second leaps. As decades have passed, radio broadcast time signals have become used by an increasing number of systems which need atomic frequency; some of these need elapsed time and others need unique timestamps. Throughout the history of civil time it has always been the case that clocks are reset to agree with the rotation of the earth. That is the distinction between a clock and a chronometer.

The Proceedings of the Colloquium on the UTC Timescale give the best available look at the openly public deliberations. As the process continues it has become clear that some representatives to the ITU-R intend to urge the ITU-R to act unilaterally and recommend the broadcast of an atomic timescale which would continue to be called UTC but which would not have leap seconds. This ignores existing international agreements about the nature of time. This also ignores the results of the colloquium in Torino which recommended that if broadcast time signals are changed to omit leap seconds then the resulting new atomic time scale should have a new name other than UTC. See the 2005-05 Recent Event entry below for links to the details.

It remains unclear whether or how such new broadcasts of purely atomic time would include information about mean solar time. Broadcasts of purely atomic time would presumably be intended to serve the needs of systems, but a change from broadcasting Universal Time would have unknown effects on civil and legal time -- and ultimately on people.

There is an existing operational example of how it could be possible to satisfy both kinds of needs for time. It is not clear that the people trying to change broadcast time signals are interested in that sort of compromise.

The International Telecommunications Union (ITU) controls the document that defines the broadcast of UTC in time signals. The document is named ITU-R TF.460. The current version is number 6, dated 2002-02.

According to ITU-R TF.460-6, UTC is maintained by the BIPM with assistance from the IERS. According to this web page and other statements the BIPM is responsible for the calculation of TAI. However all statements from the BIPM indicate that they leave the determination of the integer number of seconds between UTC and TAI (i.e., leap seconds) to the IERS. The explanatory supplement to IERS bulletins A and B acknowledges that they are responsible for determining leap seconds, and that they do it in conformance with ITU-R TF.460.

The evolution of ITU-R TF.460 over its past few versions gives some insight into the ongoing process. All of these recent revisions recommend that broadcast time signals conform to UTC. They all define DUT1 as the predicted value of (UT1 - UTC), recommend the broadcast of DUT1, and give a coding scheme to transmit DUT1 for differences as large as 0.8 s.

CCIR 1970 Plenary Assembly Document VII/1008 The draft version which became CCIR Rec. 460 originally included the phrase "or integral multiples thereof" in section 2. (This is the closest that the world ever got to having a "double leap second", but please see the time scales document about the ANSI and ISO standards which mistakenly believed that UTC did have such a thing.) CCIR Recommendation 460 (1970) This is the original recommendation requiring radio broadcasts of time signals to use atomic seconds with occasional full-second leaps to track UT. This was approved by the Plenipotentiary meeting of the International Radio Consultative Committee (CCIR) in 1970-01. Note that it only uses the term Universal Time (UT). It does not name the time scale as UTC, and it gives no instructions about how to implement leap seconds. (The text is only available because it was reprinted by the US National Bureau of Standards.) CCIR Recommendation 460-1 (1974) This revision presumably incorporated the advice from the IAU General Assembly in 1973 which indicated that the tolerance between UTC and UT1 needed to be as large as 0.9 seconds.

The text of this document and its next 2 revisions are not easily available. CCIR Recommendation 460-2 (1978) CCIR Recommendation 460-3 (1982) CCIR Recommendation 460-4 (1986) This revision was renamed ITU-R TF.460-4 in 1992/1993 when the CCIR was reorganized as the ITU-R. ITU-R TF.460-4 (1986) This revision predates the activation of the IERS. It parenthetically remarks that "GMT may be regarded as the general equivalent of UT". It states that the definitions of terms for earth rotation are available from the glossary in The Astronomical Almanac . ITU-R TF.460-5 (1997) This revision predates the discussions about discontinuing leap seconds in UTC. It omits the parenthetical remark about GMT. It states that the definitions of terms for earth rotation are available from the IERS. ITU-R TF.460-6 (2002) This revision occurred during the discussion process for discontinuing leap seconds. In addition to DUT1, this revision defines DTAI as (TAI - UTC). It recommends that broadcast time signals provide DTAI, but it does not give any coding scheme for doing so.

There is, however, a major problem with this document as the definition for the distribution of time signals -- it is proprietary. Nevertheless, it is cited as the defining document for UTC, and thus for civil and systems time in many other standards. As a result there is widespread misconception about the content of the document and the rules for inserting leap seconds. There is also widespread ignorance of the history behind the current form of UTC and the problems that form was designed to address. There are also widespread examples of systems which have been designed to think they are using UTC when they are actually incapable of doing so. Finally, as a result of the invention of leap seconds, systems designers and the general public have not had to recognize that time-of-day (universal time) and time interval (atomic time) are two distinct and incommensurate quantities.

Because the text of the document that defines UTC (ITU-R TF.460) is under the purview of ITU-R, the principal action to contemplate omitting leap seconds from UTC appears to have originated in Study Group 7, Working Party 7A.

The names and dates of files in the on-line archives of the ITU are visible to all. In general the content of ITU publications is only available to those who pay the ITU (however the ITU does permit anyone to obtain three recommendations annually free of charge). The following documents seem to be relevant:

Reports are available regarding the content of two of the meetings of the SRG. One meeting was in Geneva in 2001-05, and another was in Paris 2002-03. Reports from the Geneva meeting indicate that another meeting may have occurred concurrently with the 2001-11 meeting of PTTI in Long Beach. Reports from the Paris meeting indicated that the only option for change to UTC that the SRG was considering was to discontinue leap seconds altogether after some date yet to be determined. However reports during 2003 seem to indicate that the SRG has modified its opinion; see below.

The Istituto Elettrotecnico Nazionale Galileo Ferraris in Torino hosted a Colloquium on the UTC Timescale called by ITU-R SRG 7A. Various opinions on the future of leap seconds were presented. No branch of the ITU appears to have provided any links to the announcement of this meeting, but links to the text of the announcement were available elsewhere as seen below in the sections on IAU, IERS, and NIST. The advance notices indicated that the SRG would present its consensual opinion on the future of leap seconds, but reports from the colloquium indicate that there was nothing resembling a consensus. A hint regarding the supposed nature of the consensual opinion is visible below in the link to Ron Beard's presentation at the 41st CGSIC meeting.

The agenda considered financial aspects (costs and opportunities) for several disciplines, but not for astronomy.

The LEAPSECS archives also contain the Agenda and Call for Papers to the ITU SRG 7A on the Future of the UTC Time Scale. It has been available to subscribers of LEAPSECS.

Early reports of the colloquium indicate that, beginning in about 20 years, radio broadcast time signals may indeed use a timescale that does not contain leap seconds. The best available summary appears to be that which Markus Kuhn posted to the LEAPSECS discussion list. Inasmuch as I understand the result of the colloquium, I have calculated the consequences of the scheme outlined at Torino.

Within the archives are copies of many documents from various organizations that are not freely available from any other source. The LEAPSECS list has been invaluable in tracking the proceedings. Without the contributions from its members most of the content of this web page would not be evident.

It appears that the contents of the LEAPSECS list have been openly archived beginning in 2003-01. (Particularly large messages and messages with attachments are not archived, and it takes up to a week before messages appear in the index.) This archive has one of the few openly available postings about the colloquium in Torino on 2003-05-28 where the ITU-R WP 7A SRG gathered opinions on the future of leap seconds.

The Earth Orientation Department of the US Naval Observatory is part of the IERS. The provide general introductory background information about earth orientation which includes earth rotation -- i.e., when will it be noon?

The distinction between the fields of expertise represented by these two departments of USNO lies at the core of the dilemma for UTC. The notion of time most evident over the course of human history is the diurnal noon/midnight cycle. A century ago it became evident that earth rotation is not a precise timekeeper. A generation ago atomic time replaced astronomy as the means for practical timekeeping. UTC with its leap seconds is a hybrid of these two incommensurate goals.

At the 24th General Assembly (Manchester, 2000-08) the IAU passed several resolutions; resolution B2 addresses UTC. This establishes a working group to cooperate with URSI, ITU-R, BIPM, and IERS on leap seconds and UTC.

The responsibility of handling resolution B2 falls to Division I whose main web page is here. The formation and membership of a working group can be seen in section 3.3 of the 1999/2002 Division I Report. The identities of the IAU representatives to ITU-R and to the SRG on UTC are visible on page 36 of Information Bulletin 90.

IAU Division I had one of the few openly available postings about the colloquium in Torino on 2003-05-28 where the ITU-R WP 7A SRG gathered opinions on the future of leap seconds.

IAU Commission 31 (Time/Temps) is part of the Division I effort. Their activities page contains pointers to several relevant documents:

The triennial report for 1996/1999 This contains references to the 14th CCTF meeting of 1999-04 which is covered in its own section below. The triennial report for 1999/2002 This is available as MIME types application/pdf and application/postscript. Section 2 is about the 15th CCTF meeting (see below). It ends with a cryptic sentence that implies a desire to preserve the leap second, and that seems outside the report of the CCTF itself. Section 5 is about ITU SRG 7A and mentions the surveys performed by the URSI and the IERS.

At the 25th General Assembly (Sydney, 2003-07) Division 1 of the IAU had two meetings on July 17 and 21 where the issue of UTC was on the agenda. These consisted solely of reports and there was no official action.

The International Union of Radio Science (URSI) Commission J (Radio Astronomy) has created a Working Group J.2 to address the issue of the leap second. As seen below, this working group appears to have existed by 1999-11-09.

On behalf of URSI Working Group J.2, Demetrios Matsakis of USNO began to send out an initial survey about discontinuing leap seconds on or before 1999-11-09. Judah Levine of NIST was assisting in disseminating this survey. By 1999-12 it appeared in the IERS gazette, and it started a significant discussion in the USENET newsgroup sci.astro.fits.

The web page for Working Group on the Leap Second (J.2) openly contains the text of the survey, along with notes on its distribution. The results of the survey became available in 2000-07. They are available in the WG web page as well as in the archives of the LEAPSECS mailing list via the link above. (Note that the WG web page contains some invalid pointers to the LEAPSECS archive.)

The resolution approved by URSI at the 2002 General Assembly is available as text/html and also to subscribers of the LEAPSECS mailing list via the link above. A draft of the second questionnaire to all URSI members is also available to LEAPSECS subscribers and to anyone via the links above.

The revised website of URSI contains this page with the most current information regarding another survey taken in late 2003.

The BIPM also combines the measurements of an ensemble of atomic chronometers around the world in order to produce International Atomic Time (TAI). The BIPM acknowledges that TAI serves as the basis for UTC which is the de facto , and in some localities the de jure , basis for most forms of legal time. They note that in 1975 the CGPM resolved that UTC provides both atomic frequency standards and UT (or mean solar time). However, the BIPM does not clearly advertise the defects of TAI that are evident in their TT(BIPMxx) data which produce the following plot.

The events of the 14th meeting on 1999-04-20/22 were summarized by bodies of the IAU and URSI. The Report of the 14th meeting is available on-line as a zipped file containing two files of MIME type application/pdf (French and English). The English text of section 4 on "The Future of Leap Seconds" begins on page 102. It describes report CCTF99-18 by McCarthy of USNO. This report seems to have introduced many of the problem elements seen in more recent presentations by McCarthy that are available via various links in this web page. McCarthy then suggested the formation of a working group. The CCTF did not believe that it had the authority to take action beyond the writing of a letter to be sent to other agencies, and the recommendation of the use of TAI for applications that require a continuous time scale.

The 14th CCTF meeting was held on 1999-04-20/22 (shortly after the 33rd CGSIC meeting at which Klepczynski suggested discontinuing leap seconds in UTC). One result of this meeting was a letter from the president of the BIPM to various concerned agencies (the text of this letter appears to be contained in the URSI 1997/1999 report linked above). This is supported by pages 275 to 276 in the English text of the proceedings of the 21st CGPM meeting (held in 1999-10) which are available as a zipped file containing PDFs in the two languages. It seems likely that the letter sent by the BIPM after this meeting was used as a significant excuse for the ITU activities relating to the redefinition of UTC.

The Report of the 15th meeting in 2001-06 is also available on-line as a zipped file containing two files of MIME type application/pdf (French and English). The English text of section 5 on the "Redefinition of UTC: Leap Seconds" begins on page 107. It mentions a report of ITU-R SRG 7A and three general options for the future of UTC. It also contains a poll of the CCTF members that indicates which option each preferred; there was a three-way split with no consensus whatsoever. The documents submitted to the 15th meeting include an early ITU document describing the formation of SRG 7A and the first report of SRG 7A.

In 2002-03 the IERS Explanatory Supplement to bulletins A and B briefly mentioned reasons behind the considerations for change in UTC.

From 2002-05 through 2002-06 the IERS performed a survey regarding the use of UTC. The results of the survey were complete by 2002-09. A large majority were satisfied by UTC with leap seconds and a majority thought it would be better not to change UTC. The comments attached to the results give a good indication of how various groups view the possibility of changing leap seconds.

The IERS is has one of the few openly available postings about the colloquium in Torino on 2003-05-28 where the ITU-R WP 7A SRG gathered opinions on the future of leap seconds.

The task of the IERS spans astronomical, geophysical, and meteorological disciplines. The IERS is finalizing a new draft of their conventions. The conventions provide a mathematically detailed and comprehensive view of the models, constants, and standards that underlie measurement of earth rotation. Also of technical interest are the proceedings of a 2002 workshop hosted by the IERS at which the evolution of the understanding of the meaning of the models and constants was discussed. Finally, it should be pointed out that UT1 no longer has any explicit relation to the position of the sun.

A NIST document from 1991 explains how the ITU process works and how their recommendations effectively correspond to international law.

NIST had one of the few openly available postings about the colloquium in Torino on 2003-05-28 where the ITU-R WP 7A SRG gathered opinions on the future of leap seconds.

On page 3 (page 2569 in the journal) of a 1999 article by J. Levine of NIST in Rev. Sci. Instrum. there is a reference to problems of representing UTC leap seconds which predates any of the official actions to redefine UTC.

A number of issues of Risks Digest (aka comp.risks) have pondered leap seconds:

Unix system time and the POSIX standard

Once Unix had become popular it became desirable to standardize the characteristics of the system, including the representation of time. The standards committees decided that POSIX time should be UTC, but the early POSIX standards inexplicably incorporated a concept which never existed in UTC -- the "double leap second". This mistake reportedly existed in the POSIX standard from 1989, and it persisted in POSIX until at least 1997. Some Usenet postings that shed more light on this are here, here, and especially here. One can only surmise that none of the authors of those sections of the ANSI C standard or POSIX standard had read the text of ITU-R TF.460, and that may mean that they did not understand the full implications of specifying a system that is supposed to track UTC. Any document with an unqualified reference to an instant with the time tag 1970-01-01T00:00:00 UTC hints that its authors did not understand the history of UTC. (And this also serves as strong example of why an international standard, upon which the operation of almost every system in the world depends, should not belong to an organization like ITU-R which does not openly publish it.)

Subsequent to the early POSIX standards, Berkeley Unix decided that the time_t value in the 4.4BSD kernel should count SI seconds and thus keep TAI, not UTC. This also appears to be the case for FreeBSD. Unfortunately, even this definition of the Unix epoch is subject to interpretation because TAI did not exist by that name until 1971, and because the length of TAI seconds was changed abruptly on 1977-01-01 and again gradually from 1995 through 1998.

The archives of the LEAPSECS discussion list contain an insider's view of the process by which the POSIX time standard evolved as seen by Landon Curt Noll.

The most recent discussions of the POSIX standard have occurred in the context of the PASC discussions mentioned previously, and they have had access to the text of ITU-R TF.460. The PASC archives are not easy to search, but many messages in this search appear to be relevant. A thread about seconds since the epoch started in late 2000. A thread about timestamps picked up in late 2004.

Most of the discussions, and the earlier versions of POSIX, predate the discussions on discontinuing leap seconds in UTC. Nevertheless it is interesting to see that after more than 15 years of effort the Unix communities have not yet been able to produce a consensus on a self-consistent interpretation of system time in the presence of leap seconds. The standard solves the problem in a fashion common to many legal compromises by being unspecific about some aspects of time. 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.

Basically, the standard says that POSIX time is UTC, except when it is not. POSIX seconds are nominally SI seconds, but for practical purposes POSIX time counts seconds of mean solar time. This self-inconsistent fuzziness was inevitable given that the standard must support compatibility with an interface that originated before leap seconds. On the other hand, almost all clocks, wristwatches, and other commonplace items keep time in a similarly fuzzy fashion. In reality they are all modelled on a clock with 24 hours of 60 minutes of 60 seconds of mean solar time. This was the notion of time as refined from the Babylonian era until the advent of leap seconds.

To put it another way, the POSIX standard recognizes that it is not reasonable to suppose that a Unix system clock cannot be reset. If a system clock can be reset, then it is not reasonable to require it to conform to the characteristics of atomic time. Throughout all of history it has been the case that clocks providing civil time are regularly reset. UTC has never been any different in this regard. In the absence of access to a clock which is never reset, it is most reasonable to expect POSIX time to follow the simple rule that there are 86400 seconds in a day.

There are always exactly 86400 mean solar seconds in a calendar day as counted by the POSIX time/calendar functions. There are usually 86400 SI seconds in a calendar day as counted by the POSIX time/calendar functions, but sometimes 86401 and maybe 86399. Only in special cases can it be presumed that POSIX systems do have access to a clock which cannot be reset; for such special cases it may make best sense to define a whole new kind of POSIX time interface. (And it is silliness to expect to extend a time scale with atomic characteristics into the calendar era prior to atomic chronometers. Almost any time stamp from before the year 1956 must be interpreted as having the characteristics of mean solar time, not atomic time.)

Any system which expects sub-second timing precision needs to be carefully designed taking into account all of the sources of delay and error. The POSIX time interface was not designed with the expectation that it would ever be used for applications which need sub-second timing precision. In more coarse language, what the hell are you thinking if you expect to use the system clock in your computer for precision timing?

So what does POSIX time really count?

time_t

time_t

Prior to the 1950s there was no practical means of marking and counting spans of time other than via earth rotation; all differences of long spans of times were really differences of earth rotation angle. Prior to the 1960s it was inconceivable that any sort of clock could exist that would never need to be reset. It was not until the 1960s that forms of atomic time became widely available and it began to be possible to measure time differences with sub-second accuracies using SI seconds over long intervals. By specifying time_t to be UTC, but ignoring leap seconds, POSIX effectively recognized that the underlying clock in a Unix system cannot be guaranteed to increment in lock step with the atomic chronometers of the world, and they chose the traditional meaning of time (of day) rather than the new meaning of (atomic) time.

Therefore POSIX time_t does not explicitly support applications which need a time-stamp in SI seconds, or which need to know the interval between two events in SI seconds. The Realtime and Advanced Realtime extensions to POSIX now offer two separate clocks; one is intended to provide current time-of-day (e.g., UTC), and one is intended to provide elapsed time (e.g., TAI). However this functionality may not be widely implemented for yet a while. Until then applications and users which need purely atomic time must implement their own mechanisms (e.g., LIGO ).

The Wikipedia article on Unix time has evolved into another good reference for the meaning of POSIX time.

time_t

It will be very good if the fate of leap seconds is decided well before POSIX has to consider how to store time after that date in 2038.

Note that 1970-01-01 is before the inception of leap seconds in UTC. The origin of the POSIX epoch was during the era of elastic seconds (or rubber seconds) of UTC. The length of UTC seconds from 1966 through 1972 was 3 parts in 108 longer than what was then believed to be the length of one SI second.

1970-01-01 is also before the time scale now called TAI had that name. The name TAI was proposed in 1970 and became official in 1971. Before that time it was simply TA, the atomic time scale of the BIH.

Furthermore, by the mid 1970s the frequency of TAI (and UTC) seconds was deemed to be too large by 1 part in 1012. So the length of (TAI and) UTC seconds from 1972 to 1977 was shorter than what is currently used as the conventional length of one SI second of TAI. This change on 1977-01-01 is plainly visible in the plot of TT(BIPM04) above.

Finally(?), in 1995 it was deemed that blackbody radiation was affecting the frequency of cesium chronometers, and that the true SI second should be measured at 0 Kelvin. So over the interval from 1995 to 1998 the length of the (TAI and) UTC seconds was decreased by about 2 parts in 1014 until it corresponded as closely as possible to cesium atoms at absolute zero.

For these reasons it is extremely tricky to try to calculate how many SI seconds have elapsed since the POSIX epoch. Indeed, it is probably best not to consider the POSIX epoch to be expressed in UTC at all, but rather as just plain UT. That is to say, although there was atomic time at the inception of the POSIX epoch, and although the time services of many countries in the world were in agreement to millisecond precision, practically all clocks on 1970-01-01 were ticking mean solar seconds and being reset as needed to mean solar time. It is not reasonable to demand that the origin of the POSIX epoch have the characteristics of atomic time scales.

In summary

It is simple to count mean solar seconds since 1970-01-01 (to within one) because that number is available from the time_t provided by any POSIX compliant system with a correctly set clock.

provided by any POSIX compliant system with a correctly set clock. Counting the number of UTC seconds since 1970-01-01 is straightforward, for it is the above value plus the number of leap seconds since 1972-01-01.

Counting the number of TAI (and TA) seconds since 1970-01-01 is somewhat harder, for it requires taking into account the different length of UTC seconds before 1972 and the offsets introduced into UTC.

Counting the number of elapsed SI seconds since 1970-01-01 is harder still, for it requires correcting for all the changes in the length of TAI seconds which can be seen in TT(BIPM04).

How many leap seconds have happened since 1601-01-01?

The Microsoft Windows file time stamp specifies that it is in UTC. The meaning is necessarily ambiguous because nothing that might be called UTC existed before 1960, and until 1972 UTC used seconds of varying length and steps of milliseconds instead of full leap seconds. Indeed, GMT did not really exist as we know it until the International Meridian Conference in 1884, and GMT did not exist at all prior to the founding of the Royal Greenwich Observatory in 1676.

There are two time scales which can reasonably be extrapolated back to 1601: mean solar seconds of Universal Time (UT) and SI seconds of Terrestrial Time (TT). If these are treated in a fashion consistent with their current usage then it is possible to determine how many leap seconds would have happened since 1601. The answer comes from the astronomical studies of the quantity known as Delta T and Length of Day (LOD).

(See the rest of this answer as a series of plots.)

If the desired answer is the number of elapsed seconds of fixed length equal to one SI second as measured by chronometers on the surface of the earth then the time scale is TT. The number of leap seconds elapsed since 1601 is approximately -60 (yes, that is negative 60). This number can be broken down into two components. The number of leap seconds which would have been inserted from 1601 to 1900 is approximately -125. The number of leap seconds which would have been inserted from 1900 until now is approximately 65. This answer is of little practical use because there were no atomic chronometers during most of this historical interval, nor even any telescopes at its epoch.

If the desired answer is the number of elapsed seconds of mean solar time then the time scale is UT. The number of leap seconds elapsed since 1601 is zero because UT is a subdivision of calendar days; UT never has leap seconds. This answer is probably most consistent with the intended meaning of civil time stamps in practical use over the entire historical interval. As with POSIX time, however, it necessarily implies that not all seconds have the same length, for mean solar seconds are a measure of earth rotation rather than fundamental physics.

Similarly, if counting SI seconds on the surface of the earth, the number of leap seconds from year 0000 (or 0001) until 1900 was about -10000 (negative 10000 SI seconds), and the number of leap seconds from the conquest of Alexander the Great until 1900 was about -14500 (negative 14500 SI seconds). Again as above, for both of these dates, if counting days (i.e., seconds of mean solar time or UT) then the number of leap seconds is zero. In all cases it is imperative to choose whether the relevant time scale is intended to be counting SI seconds or mean solar days.

timezone offsets and summer/daylight time

zoneinfo

tz

"posix" This set of zoneinfo database entries considers a Unix time_t value to be equivalent to the number of mean solar seconds since 1970-01-01. Since 1972-01-01 its value matches UTC except during leap seconds. Every day has 86400 seconds. For correct time this requires that the system clock be retarded or reset backward at each leap second. This is the default provided with most Unix systems, and it is most consistent with POSIX. "right" This set of zoneinfo database entries considers a Unix time_t value to be equivalent to the count of seconds actually broadcast in radio time signals since 1970-01-01. It requires a file of leap seconds to be updated whenever a new one occurs. For correct time this requires that the system clock increment monotonically using TAI seconds. Despite its name, this is generally regarded as experimental and inconsistent with POSIX. This was the branch of code which was briefly used by default in 4.4BSD Unix.

Local civil authorities have demonstrated a tendency to modify the rules with little forewarning; e.g., the US during the energy crisis of the 1970s, much of Australia for the 2000 Olympics. The tz mailing list regularly receives reports that local civil authorities have changed the effective dates for daylight savings time transitions.

It is beyond the scope of the activities of the ITU-R, or any international organization, to dictate the nature of local civil time. If civil time is deemed to be able to tolerate secular excursions of a full half-hour from mean solar time, then implementing the first leap hour seems not much different than omitting a daylight transition. But it is not clear that secular excursions of half an hour are acceptable for legal purposes, and in the long run even leap hours start happening annoyingly frequently.

The most that can be asked of the ITU-R is that radio broadcasts continue to provide Universal (mean solar) time to an accuracy of 1 second or better. It is within the scope of the activities of the ITU-R to recommend that radio broadcasts which switch to a purely atomic time scale should also include sub-modulations which permit a machine to ascertain Universal Time. This would be a significant change, for setting a watch to the correct civil time simply by listening to raw radio signals might no longer be possible for an unaided human. It would be both simple and relatively cheap to create new radio receiving hardware which could use such embedded sub-modulations to reconstruct an audio signal that could mimic the existing broadcasts of UTC. But if civil time were to remain as mean solar time then even this would place a significant burden on the relatively many owners of radio-controlled clocks in favor of the relatively few owners of systems that require atomic time -- the many would have to upgrade their clocks in order to accommodate the few. In the case of most consumer-oriented radio-controlled clocks that means discard the old and purchase anew.

comp.bugs.4bsd from 1988-01-07 This thread on including leap seconds in the time functions of the C library was started by Bradley White, who later wrote the "right" code into the Olson library. comp.bugs.4bsd from 1988-01-12 This thread picked up after contact with David Mills who wrote the NTP software that is widely used to synchronize computers with UTC.

Markus Kuhn proposes UTS as a smooth option for Unix-like systems and other system clocks which do not like leap seconds. He has also proposed an API for ISO C which accommodates leap seconds.

David R. Tribble wrote a detailed proposal for extended range time types in the C and C++ languages. The proposal has not been adopted.

D. J. Bernstein has various notions about on UTC, TAI and UNIX Time . He also provides libtai, a library for storing and manipulating 64-bit dates and times that can give results for an interval of hundreds of billions of years. This is generally regarded as experimental.

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 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.

Version 4 of NTP includes a mechanism for transmitting the historical table of leap seconds, which means that NTP can be used to transmit TAI. However there is no programming interface for permitting a system running NTP to make use of this table of leap seconds, and the current uncertainty in the future of UTC is probably not helping to motivate the development of one.

Some countries have adopted UTC as their legal time. Among them appear to be France, Germany, Hong Kong, Korea, The Netherlands, New Zealand, Sweden, and Switzerland.

Many of the above links, however, must be taken with a grain of salt. Whereas UTC is currently the basis for legal time de facto almost everywhere, it is not always the basis of legal time de jure . Nevertheless it appears to be common for national standards bodies to claim that UTC is the legal time even if their laws refer to Greenwich Mean Time. In particular note the case of Australia as a whole vs. its province of New South Wales.

Legal time in the United Kingdom is based on GMT, not UTC. See the detailed history by Joseph S. Myers who also pointed out that the most recent attempt to make UTC the legal time of the UK "failed for lack of time".

Legal time in the United States was based on GMT until 2007-08-09. See the US Code here or at Cornell. While the US Code still indicated that legal time was GMT the publications of the NIST gave the impression that UTC was actually the legal time, and they justifie this by claiming that GMT no longer existed. (Whereas this was true in a pragmatic/technical sense, it was disingenuous to assert that the original meaning could not be recovered.) On 2002-11-19 bill S 3177 was introduced in the senate. It did not get past committee, but it contained language that would have modified 15 USC 261 to define standard time zones in terms of UTC instead of Greenwich mean time. It was in 2007 that the US congress passed a law indicating that US legal time was based on UTC, and it was 2007-08-09 when that was signed by the president.

The laws of many other countries refer to GMT as the legal time. Among these appear to be several Canadian provinces (Ontario, Saskatchewan, and Quebec), Ireland, Namibia, and the European Union (text/html or application/pdf).

As a result, in the United States and the United Kingdom, if a contractual agreement has clauses which specify time, but do not specify the time scale to be UTC, then for legal purposes the time would default to be based on mean solar seconds of GMT where leap seconds do not exist. In France, Germany and any country where the legal time scale is based on UTC, then the time clauses in the contract would default to be based on SI seconds of UTC, and leap seconds would count. In any location, however, a contractual obligation which is actually dependent on sub-second resolution had better be specific about the time scale.

It is reported that the national time authorities of 49 nations base their legal time scales on UTC. F. Pollastri provides a link with an old partial list of national time authorities. S. Young and LLRX.com provide a link with a historical analysis of legal time in the United States.

For the 2011 meeting on the Future of UTC held in Exton Pennsylvania John Seago and Kenneth Seidelman wrote Legislative Specifications for Coordinating with Universal Time which took a detailed look at the use of UTC and GMT in the existing international legislation on time.

Earlier, for the 2003 colloquium on UTC held in Torino Italy, John Seago and Kenneth Seidelmann wrote National Legal Requirements for Coordinating with Universal Time which was an earlier look.

Legal time on the Internet is UTC. (However, as noted above in the POSIX section, most computers do not keep true UTC, so the timestamps of Internet events near leap seconds may be imprecise or ambiguous.) UTC is specified by name in a great many other standards documents which span a wide range of disciplines. Even though Universal Time is not appropriate for the operations of many complex systems, the name UTC is thoroughly entrenched in systems that underline modern society.

Timestamps specified by UTC effectively have to be communicated in ASCII. Some archival data systems such as EOSDIS and CCSDS have explicitly recognized the problems posed by timestamps in UTC. Their standards documents distinguish between ASCII and binary representations of time, and they recommend the use of timestamps in both UTC and atomic time when necessary.

In summary, because UTC is internationally recognized as a form of mean solar time in accord with the International Meridian Conference of 1884 legal time everywhere is currently based on the rotation of the earth. This basis is a requirement if time is to be related to a calendar that counts days.

As detailed by links within this web page there are, nevertheless, ongoing efforts by individuals in the US NIST, the US Navy, the US Department of State, the US FCC, the ITU-R, the BIPM, the IERS, and other national and international organizations to break the connection between clock time and calendar date that was established by international vote in 1884 and thus change the basis of legal time everywhere from earth rotation to atomic oscillations.

The increasing ease and precision with which earth rotation could be measured obsoleted the entire notion of UT2. Therefore in 1972 when UTC was changed from mean solar seconds to SI seconds with leaps, it also began to be defined with respect to UT1. To a physicist it no longer makes sense to think of any form of mean solar time as time. For practical purposes of the measurement of intervals, time in the sense that relates to the evolution of physical processes is now most nearly measured by atomic time. UT in all its forms is actually a measure of time-of-day, which is really the earth rotation angle. For practical purposes of indicating the time-of-day for civil events, the differences between GMT, UT0, UT1, UT2, UT1R and UTC in its current form are insignificant (less than 0.9 second). All of them are versions of the mean solar time on the Greenwich meridian.

Here is the question for humanity: Which is the more fundamental unit of time, the day or the second?

Mean solar days are the fundamental element of modern calendars and thus of most legal systems of time. Universal Time has always been a measure of time-of-day expressed as fractions of mean solar days. UTC with leap seconds has been a practicable form for distributing that quantity.

SI seconds are a fundamental element of modern telecommunication and navigation systems. Atomic time has always been a measure of time interval expressed as SI seconds. Before the GPS satellites there was not a globally available means of distributing that quantity.

UTC in its current form with leap seconds will continue to work for over 1000 years. Atomic time without leap seconds will be off by an hour in 1000 years. If the ITU-R were to recommend that radio broadcasts provide only a form of leap second-free atomic time then the legislatures of the world would have to ponder whether to recognize that as a form of legal time, the grandfather clock owners of the world would wonder why having names for the aeons-old concept of time-of-day (i.e., 12:00 for noon and midnight) was no longer to be relevant to human society, and analemmatic sundial owners would be out of luck.

Systems that need atomic time are, of course, intended to serve the needs of people. The task that the ITU-R SRG 7A has tackled implies determining the nature and accuracy requirements for time as used by almost all the systems and peoples of the world. This is not an enviable task, but the SRG includes some of the smartest people in the world. The attempt of UTC to provide two different things and the broad misuse and misunderstanding of UTC with leaps may require the demise of that name in favor of two replacements: one that provides mean solar time of the origin meridian for civil purposes, and another that provides purely atomic time for systems. The ultimate solution may require almost everyone who deals with time to adopt new hardware and software that recognizes both time-of-day (in mean solar seconds) and elapsed time interval (in SI seconds).

Steve Allen <sla@ucolick.org>