Time scales and the leap second
Not a unit of measurement but three scales: UTC, TAI and UT1 · quantity: an instant of time
On the thirty-first of December 2016 the clocks of the International Earth Rotation Service read 23 hours 59 minutes 60 seconds — a time that does not occur in an ordinary day. The second was inserted because by that day the Earth had fallen almost six tenths of a second behind the atomic clocks, and had it not been inserted, the divergence would have crossed a threshold set by agreement. There has been no insertion since: the planet unexpectedly sped up, and the reverse operation is now seriously discussed — a second that will have to be struck out rather than added.
This can only be sorted out by telling apart three things that everyday speech calls by one word, «time». TAI is the atomic scale, running evenly and paying no attention to the planet; UT1 is the rotation angle of the Earth itself, an astronomical phenomenon with a temper of its own; and UTC is the compromise scale, which runs in atomic seconds yet now and then receives a whole inserted one, so as not to part from the planet by more than nine tenths of a second. The first cannot be adjusted, the second cannot be predicted, and the third is appointed by a committee's decision and printed in a bulletin.
01 · Definition
International Atomic Time TAI is assembled from the readings of some two hundred and fifty atomic clocks scattered across national laboratories, and runs in SI seconds without a single correction. Universal Time UT1 is set by the rotation angle of the Earth and therefore changes its pace along with the planet. Coordinated Universal Time UTC differs from TAI by a whole number of seconds and is held close to UT1 by insertions announced by the International Earth Rotation Service.
The idea of UTC is to join what will not join: its second is atomic, even, fit for physics and for communication, while its reading is astronomical, tied to day and night. The joining is bought at the price of a break: once in a few years an extra second is added to the scale, the minute then holds sixty-one seconds, and the stamp 23:59:60 becomes lawful. Hence UTC is the only one of the three scales with instants that the ordinary count of days cannot express.
The threshold beyond which an insertion is appointed equals nine tenths of a second in absolute value, and it was chosen not on physical grounds but as a compromise between astronomers and communications engineers, struck in 1972. The service watches the difference UT1 − UTC by radio interferometry and satellite observation, and publishes its decision in Bulletin C — twice a year, half a year before the possible date, which falls at the end of either June or December.
UTC cannot be checked with an instrument, because it has no true value at all: TAI behaves as a unit, UT1 as a phenomenon, and UTC as an agreement, and its reading is announced rather than measured. One's own clock, on the other hand, can be compared with it to the nanosecond, because the bulletins of the service state by how much the reading of each national scale differs from the agreed one.
The upper staircase is the offset TAI − UTC, growing by whole seconds; the lower saw is the difference UT1 − UTC, which creeps down along with the lagging Earth and jumps up by a second at every insertion. The red strokes below mark the threshold of nine tenths: as soon as the saw approaches it, the service appoints a new insertion, and both lines take their step at once.
The dashed line is the atomic scale, where every second equals the one before; the wavy line is the rotation of the Earth, slowed by tidal friction yet wandering because water and air are redistributed and even because of motions in the liquid core. The red strokes are the moments when the service had to intervene. Precisely because the second line cannot be predicted, insertions cannot be announced a decade ahead: they are appointed half a year in advance, from observations.
02 · Conversion
One instant in different scales
Enter an instant in any customary form — a decimal year, a Julian date, a count of seconds from the beginning of the Unix epoch — and the sheet will show how that same instant looks in the other scales and which offsets were in force that day.
Passages between the atomic scales are exact to the nanosecond, being set by constants: TT differs from TAI by 32.184 s, and the GPS scale by exactly 19 s. Only the line with UT1 is approximate: it is taken from Bulletin A, and for the future it is given as a prediction.
The count of seconds in the POSIX standard is arranged so that a day always holds exactly 86 400 of them, and an inserted second has nothing to be expressed by: the system either repeats one and the same reading twice or sets the clock back. Because of this trifle, in June 2012 the servers of half the large services went down, and several companies have since stretched the extra second over a whole day, smearing it in a thin layer across their clocks.
| Value | Note | ||
|---|---|---|---|
| {u} | {name} | {value} | {note} |
03 · Orders of magnitude
logarithmic scale: from a nanosecond to five hours04 · Measuring instruments
What keeps the scales and what checks them
A cloud of cooled atoms is tossed upward and passed twice through one and the same resonator — on the way up and on the way down — which allows the transition frequency to be measured to the sixteenth digit. Such primary standards set the length of the second and keep no reading of time: they are switched on for a few days to verify the rate of the other clocks.
The maser holds its frequency markedly more evenly than the fountain over intervals from an hour to a day, but slowly drifts sideways, and so in laboratories it serves as the keeper of the scale rather than as the standard of frequency: its rate is compared with a primary standard every few days. It is the masers that yield the continuous reading from which TAI is afterwards assembled.
Two antennas on different continents receive the noise of one and the same quasar, and the difference in the arrival time of the signal betrays the orientation of the Earth with respect to distant sources. This is precisely how UT1 is measured, since no clock can tell the rotation angle of the planet — it can only be observed, and the service does so around the clock.
Every satellite carries atomic clocks on board, and a receiver that has caught four signals recovers not only its own place but also the time to within tens of nanoseconds. The scale transmitted, however, is its own: the GPS system has no insertions whatever, it stands exactly nineteen seconds from TAI, and the current difference from UTC travels in a separate field of the satellite message.
05 · Writing rules
A timestamp without its scale is no timestamp
The names of the scales are written in capitals without periods and without spaces inside, and to the reading itself one always adds which scale it was taken in: the letter Z or an offset in the ISO 8601 form, a separate note of TAI or GPS if the time is atomic. Differences of scales are written with a sign and in seconds, putting first the scale from which the subtraction is made.
The first form is impossible because the insertion is made at the end of the day by UTC, while in the Moscow zone that same instant falls at three in the morning, and the stamp then reads 02:59:60. The second sets an equals sign between the scale and the historical mean time of the Greenwich meridian, long out of use in metrology. The third confuses the direction of subtraction: the atomic scale runs ahead, not behind. The fourth cannot occur in a bulletin at all, since the service is bound to insert a second long before the difference reaches such a value.
06 · Neighbouring scales
Nearby stand all the scales that count the same time from other beginnings or in another frame of reference: terrestrial time TT, in which ephemerides are computed, the atomic scale of the satellite systems, and barycentric coordinate time, which takes into account that clocks on the Earth run otherwise than at the centre of mass of the Solar System.
no insertions, no corrections
an observed phenomenon
the ephemeris scale
Of the Simetrium data sheets nearby stand second, which sets the unit for all three scales, day and hour, where the same unevenness of rotation is seen from another side, and year numbering, whose units agree and whose zeros do not.
07 · Historical section
The second first invented and now abolished
Louis Essen and Jack Parry assembled the first caesium clock at the National Physical Laboratory and discovered something unwelcome: the instrument proved steadier than the thing against which they meant to check it. From that moment the Earth ceased to be the standard of time and became an object of observation, and eight years later the second was redefined through the frequency of the caesium transition.
The first version of UTC adjusted itself to the Earth differently: once a year a correction to the frequency itself was announced, so that the second of the scale deliberately differed from the SI second, and in addition the reading was now and then shifted by tenths. This suited navigators but not physicists, and the elastic second was abandoned, it being granted that a rare break is better than a permanently wrong unit.
From the first of January 1972 UTC went in even SI seconds, standing exactly ten behind the atomic scale, and gained the right to insertions. The threshold of nine tenths of a second was chosen as the middle ground between the demands of seamen, who needed an astronomical tie, and those of communications engineers, who needed continuity.
The twenty-seventh General Conference on Weights and Measures resolved to bring the threshold to zero, that is to give up insertions, no later than 2035. The reason is not the convenience of programmers but that the Earth has begun to speed up: since 2020 records for short days have been broken several times, and instead of the customary insertion a removal of a second may be needed for the first time — and for that no system in the world is ready.
A scale whose reading is announced, not measured
Every quantity in this catalogue has an instrument able to say what it equals, and UTC alone has no such instrument and can have none. Atomic clocks measure intervals, interferometers measure the rotation of the Earth, while the question whether to insert a second at the end of June is settled by people and printed in a bulletin, because the threshold of nine tenths of a second is a matter of agreement, not of nature. Hence a strange property: the divergence from UTC of any clock on the planet is known to the nanosecond, whereas the correctness of UTC itself has nothing to be checked against — it is correct by definition.
The agreed nature of the scale was revealed best of all by the preparation of its abolition. Insertions were to be removed not because the rotation of the planet had come to be measured more precisely, but because the price of the break had grown: exchange timestamps, satellite navigation and communication networks suffer from an extra second more than seamen would suffer from a divergence with the sun. When the threshold is brought to zero, UTC will cease to catch up with the Earth and will part from it first by a minute in a century, and afterwards by more — and what to do with that divergence will be for the generations to come to decide.
Catalogue · units of measurement
A data sheet for every quantity
Seven SI base units, twenty-two derived ones with names of their own, and the non-SI quantities that neither science nor daily life does without. Each gets its own sheet: definition, conversion, instruments, writing rules, history. In 36 languages.