User:Jonathan W/histJan06/leap second

A leap second is an intercalary, one-second adjustment that keeps broadcast standards for time of day close to mean solar time. Leap seconds are used to keep time standards synchronized with civil calendars, the basis of which is astronomical.

Broadcast standards for civil time are based on Coordinated Universal Time (UTC), a time standard which is maintained using extremely precise atomic clocks. In order to keep the UTC broadcast standard close to mean solar time, UTC is occasionally corrected by an intercalary adjustment, or "leap", of one (1) second. Over long time periods, leap seconds must be added at an ever increasing rate which corresponds to a parabola near 31 s/century&sup2; (see &Delta;T).

Reason for leap seconds
Leap seconds are necessary because time is measured utilizing stable atomic clocks (TAI or International Atomic Time), whereas the rotation of the Earth has been slowing down. Traditionally, the second has been defined as 1/86400 of a mean solar day (see solar time). This is determined by the rotation of the Earth around its axis and its orbit around the Sun; time was measured by astronomical observations. However, the solar day has gradually become 1.7 ms longer every century, due mainly to the tidal acceleration of the Moon. The SI second that is counted by atomic time standards has been defined in such a way that its length matched the nominal second of 1/86400 of a mean solar day between 1750 and 1892. Since that time the length of the solar day has been slowly increasing. Therefore the time as measured by the rotation of the Earth has been accumulating a delay with respect to atomic time standards. From 1961 to 1971 the rate of atomic clocks was constantly slowed down in order to stay in sync with the rotation of the Earth (before 1961, broadcast time was synchronized to astronomically determined Greenwich Mean Time). From 1972 onwards, broadcast seconds have been exactly equal to the length of the SI second chosen in 1967 as a certain number of atomic vibrations. UTC is counted by atomic clocks, but is kept approximately in sync with UT1 (mean solar time) by introducing a leap second whenever necessary. This happens when the difference UT1&minus;UTC is approaching 0.9 seconds, and is scheduled either between 30 June and 1 July of a year, or between 31 December of the current and 1 January of the next year. On January 1, 1972, the initial offset of UTC from TAI was chosen to be 10 seconds, which approximated the total difference which had accumulated between UT1 and TAI since 1958, when TAI was defined equal to UT1 (GMT). The table above shows the number of leap seconds added since then. The total difference between TAI and UTC is 10 seconds more than the total number of leap seconds.

Take care not to confuse the difference between the length of the mean solar day and the SI day, with the leap second adjustment (which is approximately 0.7 seconds per year). This erroneous line of reasoning confuses velocity with traveled distance (in time). The correct reason for leap seconds is not the difference, but rather, the sum of the difference between the length of the SI day and the mean solar day (currently about 0.002 seconds), over a given period of time. Note that the actual rotational period varies on unpredictable factors such as tectonic motion and has to be observed rather than computed.

For example, assume you start counting the seconds from the Unix epoch of 12:00:00AM on January 1 1970 with an atomic clock. At midnight on that day (as measured on UTC), your counter registers 0 seconds. After Earth has made one full rotation with respect to the mean Sun, your counter will register 86400.002 (once again, the precise value will vary) seconds. Based on your counter, you can calculate that the date is 12:00:00AM on January 2 1970 UT1. After exactly 500 rotations, your counter will register 43,200,001 seconds. Since 86400 × 500 is 43,200,000 seconds, you will calculate that the date is 12:00:01AM on May 16 1971 (exactly 500 days after January 1 1970) as measured in atomic time (UTC), while it is only 12:00:00AM on May 16 1971 in solar time (UT1). If you had added a leap second on December 31 1970 to your counter, then the counter would have a value of 43,200,001 seconds at midnight on May 16 1971 and allow you to calculate the correct date. The actual system involving leap seconds was set up to allow TAI and UT1 to have an offset of 0 seconds on January 1, 1958.

While tidal braking will slow down Earth's rotation, this will cause the amount of SI seconds in a mean solar day to increase from approximately 86400.002 to 86400.005 over the course of 100 years.

Announcement of leap seconds
The announcement to insert a leap second is usually issued whenever the difference between UTC and UT1 approaches 0.7s, to keep the difference between UTC and UT1 from exceeding ±0.9 s. After UTC 23:59:59, a positive leap second at 23:59:60 would be counted, before the clock indicates 00:00:00 of the next day. Negative leap seconds are also possible should the Earth's rotation become slightly faster; in that case, 23:59:58 would be followed by 00:00:00.

Leap seconds occur only at the end of a UTC month, and have only ever been inserted at the end of June 30 or December 31. Unlike leap days, they occur simultaneously worldwide; for example, a leap second on 31 December was observed as 6:59:60 pm U.S. Eastern Standard Time. It is the responsibility of the International Earth Rotation and Reference Systems Service (IERS) to measure the Earth's rotation and determine whether a leap second is necessary. Their determination is announced in Bulletin C, typically published every six months.

Historically, leap seconds have been inserted about every 18 months. However, the Earth's rotation rate is unpredictable in the long term, so it is not possible to predict the need for them more than six months in advance. Between January 1972 and December 1998, the IERS gave instructions to insert a leap second on 22 occasions. The interval between 1998-12-31 and 2005-12-31, the most recent leap second, is the longest period since the system was introduced without a leap second.

Note that leap seconds have nothing to do with leap years.

Leap seconds are also not included directly in GPS time, though a regularly broadcast message notes how far GPST and UTC are apart.

Proposal to redefine UTC and abolish leap seconds
On July 5, 2005, the Head of the Earth Orientation Center of the IERS sent a notice to IERS Bulletins C and D subscribers, soliciting comments on a proposal before the ITU-R Study Group 7's WP7-A to eliminate leap seconds from the UTC broadcast standard before 2008. (The ITU-R is responsible for the definition of UTC). The Wall Street Journal noted that the proposal was considered by a US official to be a private matter internal to the ITU as of July, 2005. It was expected to be considered in November, 2005, but the discussion has since been postponed. Under the proposal, leap seconds would be technically replaced by leap hours as an attempt to satisfy the legal requirements of several ITU-R member nations that civil time be astronomically tied to the Sun.

Many commentators consider the proposal to be flawed in many ways.


 * Little justification for changing UTC has been presented.
 * No serious analysis of the costs of the change (or not making a change) has been attempted.
 * The meaning of the term UTC in existing documents (technical and legal) and existing software will become ambiguous. All references to UTC will have to be reviewed to ascertain whether the original intent was to be mean solar time or to be atomic time or simply to be the conventional civil time scale which happens to be in current use.
 * All reported surveys inquiring about a change to UTC produced results which did not indicate that any change was desired.
 * Two timescales that do not follow leap seconds are already available: International Atomic Time (TAI) and GPS time. GPS time is easily obtained with inexpensive receivers.
 * The time indicated by sundials would no longer bear a fixed relation to civil time, but
 * United States Federal Law indicates that the legal time of the US is based on mean solar time.
 * The CGPM (general congress of weights and measures, the international force behind the SI) recommendation to use UTC is predicated on the fact that the leaps keep it reasonably close to mean solar time.
 * When the proponents convened an international colloquium in 2003 they were told not to change UTC (because that would confuse everyone about its meaning), but to define a new time scale whose purpose was to serve their needs. They were also told that leap hours were not acceptable.
 * The process of discussing the proposals has been mostly shrouded in secrecy for years. Relevant ITU documents and meetings are not publicly available.

On the other (pro) side of the discussion are several arguments. Some of these have only become relevant with the recent wide-spread proliferation of computers using UTC as their internal time representation. For example, as things presently stand, it is not possible to correctly compute the elapsed interval between two stated instants of UTC without consulting manually updated and maintained tables of when leap seconds have occurred. Moreover, it is not possible even in theory to compute such time intervals for instants more than about six months in the future. This is not a matter of computer programmers being "lazy"; rather, the uncertainty of leap seconds introduces to those applications needing accurate notions of elapsed time intervals either fundamentally new (and often untenable) operational burdens for computer systems (the need to be online and do lookups) or unsurmountable theoretical concerns (the inability in a UTC-based computer to accurately schedule any event more than six months in the future).

A counter to this argument is that computers need not use UTC. They could use either TAI or GPS time and convert to UTC or local civil time as necessary for output. GPS time is an especially convenient choice as inexpensive GPS timing receivers are readily available and the satellite broadcasts include the necessary information to convert GPS time to UTC. It is also easy to convert GPS time to TAI as TAI is always exactly 19 seconds ahead of GPS time.

Examples of systems based on GPS time include the CDMA digital cellular systems IS-95 and CDMA2000.

Should UTC be redefined and/or should leap seconds go away?
Category:Timekeeping
 * Why the US wants to end link between time and sun - Wall Street Journal article
 * The leap second: its history and possible future - R A Nelson et al, Metrologia, 2001
 * UTC might be redefined without Leap Seconds - extensive references by Steve Allen at Lick Observatory
 * Summary of the US Working Group proposal and brief responses
 * Opposition to the change from Kenneth Seidelmann - a member of the US Working Party 7A (USWP7A)
 * Efforts to abolish leap seconds from Markus Kuhn
 * the LEAPSECS mailing list - archive and joining info

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