Time probably is the most under-appreciated concept by many that use it. Everyone experiences it but explaining is a difficult job. The perception of time is usually associated with change and for that one needs a unit and a starting point, moreover some sort of uniformity is also required for the unit. Defining a unit for time is not that hard as many of the changes that we relate to time are periodic. If the changing phenomenon varies with uniform period, then the associated time scale is uniform. Clearly, a desirable property of a description and realization of time is that its scale should be uniform at least in the local frame. In the past, Earth’s rotation provided the most suitable and evident phenomenon to represent the time scale, with the unit being a (solar) day, however, Earth’s rotation is not uniform (it is varying at many different scales: daily, bi-weekly, monthly, etc. In addition to scale or units, an origin must be defined for a time system, that is, a zero-point, or an epoch, at which a value of time is specified. Finally, whatever system of time is defined, it should be accessible and, thereby, realizable, thus creating a time frame [1].
Definition for the unit time, i.e., the second, was the first thing to be agreed upon for progressing with common time. Prior to 1960, a second of time was defined as 1/86400 of a mean solar day. Today, a fundamental time scale is defined by the natural oscillation of the cesium atom and all time, systems can be referred or transformed to this scale. Specifically, the SI (Système International) second is defined as follows [2]:
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 cesium 133 atom.
This definition has been refined to specify that the atom should be at rest and at mean sea level then corrections are applied to actual measurements to comply with these requirements. The value of the SI second was set to the previously (in 1956) adopted value of a second of ephemeris time (ET), defined as 1/31.556.925,9747 of a mean tropical (solar) year, being computed for the epoch, 1 January 1900, on the basis of Newcomb’s theory of motion of the Earth around the Sun [3].
Although the SI second now defines the fundamental time unit, one still distinguishes between systems of time that have different origins and even different scales depending on the application. Dynamic time is the independent variable in the most complete theory of the dynamics of the solar system. It is uniform by definition. Mean solar time, or universal time (UT), is the time scale based on Earth’s rotation with respect to the Sun and is used for general civilian time keeping. Finally, sidereal time is defined by Earth’s rotation with respect to the celestial sphere.
Dynamic Time
Dynamic time generally refers to the time variable in the equations of motion describing the dynamical behavior of the massive bodies of our solar system. The dynamic time scale refers to a coordinate system and thus represent a coordinate time. Common choices include the barycentric reference system (origin at the center of mass of the solar system) or the geocentric reference system. On the other hand, dynamic time has also been defined as a proper time, the time associated with the frame of the observer that a uniformly running clock would keep and that describes observed motions in that frame.
Atomic Time
Atomic time refers to the time scale defined and realized by the oscillations in energy states of the cesium-133 atom. The SI second thus is the unit that defines the atomic time scale. Atomic time was not realized until 1955 with the development of standardized atomic clocks. From 1958 through 1968, the Bureau International de l’Heure (BIH) in Paris maintained the atomic time scale. The origin, or zero point, for atomic time has been chosen officially as 0h 0m 0s, January 1, 1958. International Atomic Time was officially introduced in January 1972. It was determined and subsequently defined that on 0h 0m 0s, January 1, 1977 (TAI), the ET epoch was 0h 0m 32:184s, January 1, 1977 (ET);
TAI is realized today by the Bureau International des Poids et Mesures (BIPM), which combines data from over 400 high-precision atomic clocks around the world in order to maintain the SI-second scale as accurately as possible. TAI is published and accessible as a correction to each time-center clock. In the United States, the official atomic time clocks are maintained by the US Naval Observatory (USNO) in Washington, DC, and by the National Institute of Standards and Technology (NIST) in Boulder, CO, USA. Within each such center several cesium beam clocks are running simultaneously and averaged. Other centers participating in the realization of TAI include observatories in Paris, Greenwich, Moscow, Tokyo, Ottawa, Wettzell, Beijing, and Sydney, among over 70 others. The comparison and amalgamation of the clocks of participating centers around the world are accomplished by LORAN-C, satellite transfers, and actual clock visits. Time offsets of individual laboratories and their uncertainties are reported in the monthly issues of the BIPM Circular T [4].
Sidereal and Universal Time
Sidereal time represents the rotation of the Earth with respect to the celestial sphere and reflects the actual rotation rate of the Earth, plus effects due to the small motion of the spin axis relative to space. Reader is referred to [1, pp 28-29] for more detailed explanation.
Universal Time (UT) is the time scale used for general civilian time keeping and is based approximately on the diurnal motion of the Sun. However, the Sun, as viewed by a terrestrial observer does not move uniformly on the celestial sphere. To create a uniform time scale requires the notion of a fictitious, or mean Sun, and the corresponding time is known as mean solar time (MT). UT is defined as mean solar time on the Greenwich meridian. The basic unit of UT is the mean solar day, being the time interval between two consecutive transits of the mean Sun across the meridian. The mean solar day has 24 mean solar hours and 86400 mean solar seconds. In comparison to sidereal time, the following approximate relations hold
| 1 mean solar day = 24h 03m 56.5554s in sidereal time | (2.1) |
| 1 mean sidereal day = 23h 56m 04.0905s in solar time | (2.2) |
A mean solar day is longer than a sidereal day because in order for the Sun to return to the observer’s meridian, the Earth must rotate an additional amount due to its orbital advance. Universal time as a scale derived from Earth’s rotation has thus been separated into:
UT1: Universal Time determined with respect to the meridian attached to the spin axis;
UT2: Universal Time UT1 corrected for seasonal variations
UT2 is the best approximation of UT to a uniform time, although it is still affected by small secular variations. However, as a matter of practical utilization it has now been replaced by an atomic time scale. All civilian clocks in the world are now set with respect to an atomic time standard since atomic time is much more uniform than solar time and more easily realized through time transfer by satellite signals. Yet, there is still a desire (particularly, in the astronomic community) that civil time should correspond to solar time; therefore, a new atomic time was defined that approximates UT. This atomic time is called Coordinated Universal Time (UTC) and implemented in accord with Recommendation TF.460 of the International Telecommunication Union (ITU) [5]:
UTC is the time scale maintained by the BIPM, with assistance from the IERS, which forms the basis of a coordinated dissemination of standard frequencies and time signals. It corresponds exactly in rate with TAI but differs from it by an integral number of seconds. The UTC scale is adjusted by the insertion or deletion of seconds (positive or negative leap seconds) to ensure approximate agreement with UT1.
Initially, UTC was adjusted so that |UT2 – UTC| < 0.1s. As of 1972, the requirement for the correspondence between UTC and UT was relaxed to |UT1 – UTC| < 0.9s. The adjustments, called leap seconds, are introduced either January 1 or July 1 of any particular year.
The international standard for Universal Time Coordinated is maintained by the Bureau des Poids et Mesures (BIPM) in Sevres, France. This UTC (BIPM) is the result of a weighted average of about 200 clocks distributed worldwide. The U. S. Naval Observatory (USNO) maintains a Master Clock (MC) that represents the time standard UTC(USNO-MC) that is kept within 100 nanoseconds of UTC(BIPM).
REFERENCES
- Teunissen, Peter JG, and Oliver Montenbruck, eds. Springer Handbook of Global Navigation Satellite Systems. Vol. 10. Cham, Switzerland: Springer International Publishing, 2017.
- Thompson, Ambler, and Barry N. Taylor. “Use of the international system of units (SI).” NIST Special Publication, Gaithersburg (2008).
- Seidelmann, P. Kenneth, ed. Explanatory supplement to the astronomical almanac. University Science Books, 1992.
- Bureau International des Poids et Mesures: BIPM Circular T, ftp://ftp2.bipm.org/pub/tai/publication/cirt:
- Standard-Frequency and Time-Signal Emissions, ITU-R Recommendation TF.460-6 (International Telecommunication Union, Radio-communication Bureau, Geneva, Feb. 2002)
