Seconds, how they leap, and universal time measures.
The Slashdot.org article about the Terran Calendar generated much discussion about the poor definitions in some cases, and the lack of a resolutions of time-keeping on the level of seconds. Often, comments referred to the SI second maintained by the International Bureau for Weights and Measures. This is their definition:
The unit of time, the second, was at one time considered to be the fraction
1/86 400 of the mean solar day. The exact definition of “mean solar day” was left to the astronomers. However measurements showed that irregularities in the rotation of the Earth made this an unsatisfactory definition. In order to define the unit of time more precisely, the 11th CGPM (1960, Resolution 9) adopted a definition given by the International Astronomical Union based on the tropical year 1900. Experimental work, however, had already shown that an atomic standard of time, based on a transition between two energy levels of an atom or a molecule, could be realized and reproduced much more accurately. Considering that a very precise definition of the unit of time is indispensable for science and technology, the 13th CGPM (1967/68, Resolution 1) replaced the definition of the second by the following:
The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.
It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly 9 192 631 770 hertz, (hfs Cs) = 9 192 631 770 Hz.
At its 1997 meeting the CIPM affirmed that:
This definition refers to a caesium atom at rest at a temperature of 0 K.
This note was intended to make it clear that the definition of the SI second is based on a caesium atom unperturbed by black body radiation, that is, in an environment whose thermodynamic temperature is 0 K. The frequencies of all primary frequency standards should therefore be corrected for the shift due to ambient radiation, as stated at the meeting of the Consultative Committee for Time and Frequency in 1999.
The standards for counting seconds include Coordinated Universal Time:
Coordinated Universal Time (UTC), maintained by the BIPM, is the time scale that forms the basis for the coordinated dissemination of standard frequencies and time signals. The UTC scale is adjusted by the insertion of leap seconds to ensure approximate agreement with the time derived from the rotation of the Earth. These leap seconds are inserted on the advice of the International Earth Rotation and Reference Systems Service (IERS).
Compare to the International Atomic Time (TAI):
A practical scale of time for world-wide use has two essential elements: a realization of the unit of time and a continuous temporal reference. The reference used is International Atomic Time (TAI), a time scale calculated at the BIPM using data from some two hundred atomic clocks in over fifty national laboratories.
The long-term stability of TAI is assured by a judicious way of weighting the participating clocks. The scale unit of TAI is kept as close as possible to the SI second by using data from those national laboratories which maintain the best primary caesium standards.
TAI is a uniform and stable scale which does not, therefore, keep in step with the slightly irregular rotation of the Earth. For public and practical purposes it is necessary to have a scale that, in the long term, does. Such a scale is Coordinated Universal Time (UTC), which is identical with TAI except that from time to time a leap second is added to ensure that, when averaged over a year, the Sun crosses the Greenwich meridian at noon UTC to within 0.9 s. The dates of application of the leap second are decided by the International Earth Rotation Service (IERS).
Now, the IERS has this to say about leap seconds:
The Coordinated Universal Time (UTC, replacing GMT) is the reference time scale derived from The Temps Atomique International (TAI) calculated by the Bureau International des Poids et Mesures (BIPM) using a worldwide network of atomic clocks. UTC differs from TAI by an integer number of seconds; it is the basis of all activities in the world. UT1 is the time scale based on the observation of the Earth’s rotation. It is now derived from Very Long Baseline Interferometry (VLBI). The various irregular fluctuations progressively detected in the rotation rate of the Earth lead in 1972 to the replacement of UT1 as the reference time scale . However, it was desired by the scientific community to maintain the difference UT1-UTC smaller than 0.9 second to ensure agreement between the physical and astronomical time scales.
Since the adoption of this system in 1972, firstly due to the initial choice of the value of the second (1/86400 mean solar day of the year 1820) and secondly to the general slowing down of the Earth’s rotation, it has been necessary to add 25 s to UTC. The last additional second has been introduced on 1 July 2012, at 0hUTC.
The decision to introduce a leap second in UTC is the responsibility of the Earth Orientation Center of the International Earth Rotation and reference System Service (IERS). This center is located at paris observatory. According to international agreements, first preference is given to the opportunities at the end of December and June, and second preference to those at the end of March and September. Since the system was introduced in 1972, only dates in June and December have been used.
and in an earlier Bulletin:
INFORMATION ON UTC - TAI NO leap second will be introduced at the end of June 2014. The difference between Coordinated Universal Time UTC and the International Atomic Time TAI is : from 2012 July 1, 0h UTC, until further notice : UTC-TAI = -35 s Leap seconds can be introduced in UTC at the end of the months of December or June, depending on the evolution of UT1-TAI. Bulletin C is mailed every six months, either to announce a time step in UTC, or to confirm that there will be no time step at the next possible date.
UT1 is the principal form of Universal Time. While conceptually it is mean solar time at 0° longitude, precise measurements of the Sun are difficult. Hence, it is computed from observations of distant quasars using long baseline interferometry, laser ranging of the Moon and artificial satellites, as well as the determination of GPS satellite orbits. UT1 is the same everywhere on Earth, and is proportional to the rotation angle of the Earth with respect to distant quasars, specifically, the International Celestial Reference Frame (ICRF), neglecting some small adjustments. The observations allow the determination of a measure of the Earth’s angle with respect to the ICRF, called the Earth Rotation Angle (ERA, which serves as a modern replacement for Greenwich Mean Sidereal Time). UT1 is required to follow the relationship
ERA = 2π(0.7790572732640 + 1.00273781191135448Tu) radians
where Tu = (Julian UT1 date – 2451545.0)
Okay, that’s enough of that, because it does overwhelm.
One thought occurred to me (prior to reading through all this material, some supplementary stuff, giving it all a good shake, and see what ferments): theAbysmal Calendar would be able to use TAI for the perpetual calendar, and UT1 would be able to apply to the lunar calendar, as it counts every second, every day, every lunar month, every year, as most accurately described within our current means.
The other convenience as regards leap seconds (or minutes, or whatever all else might befall us) is that they can be inserted between any two days. It simply wouldn’t count towards the 364 x 24 x 60 x 60 + 24 x 60 x 60 seconds of the year. It will fall outside of them in June, or as part of the New Year day, or Leap Year day should the leap second be inserted in December.
I may be oversimplifying the case (may, ha!), however, I’ll leave the more complicated task of figuring out how to define the second, the day, the year as accurately as is possible, that I might benefit from those findings to base my system of time-reckoning.
Still a work in progress.