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Second

The '''second''' (International System of Units|SI symbol: '''s'''), sometimes abbreviated '''sec.''', is the name of a units of measurement|unit of time, and is the International System of Units (SI) SI base unit|base unit of time. It may be measured using a clock. Early definitions of the second were based on the motion of the earth: 24 hours in a day meant that the second could be defined as of the average time required for the earth to complete one rotation about its axis. However, nineteenth- and twentieth-century astronomical observations revealed that this average time is lengthening, and thus the motion of the earth is no longer considered a suitable standard for definition. With the advent of atomic clocks, it became feasible to define the second based on fundamental properties of nature. Since 1967, the second has been defined to be SI prefixes are frequently combined with the word ''second'' to denote subdivisions of the second, ''e.g.'', the 1 E-3 s|millisecond (one thousandth of a second), the 1 E-6 s|microsecond (one millionth of a second), and the 1 E-9 s|nanosecond (one billionth of a second). Though SI prefixes may also be used to form multiples of the second such as 1 E3 s|kilosecond (one thousand seconds), such units are rarely used in practice. The more common larger non-SI units of time are not formed by powers of ten; instead, the second is multiplied by 60 to form a minute, which is multiplied by 60 to form an hour, which is multiplied by 24 to form a day. The second was also the base unit of time in the Centimetre gram second system of units|centimetre-gram-second, Mks system of units|metre-kilogram-second, Metre-tonne-second system of units|metre-tonne-second, and Imperial units|foot-pound-second systems of units.

International second

Under the International System of Units, the second is currently defined as This definition refers to a caesium atom at rest at a temperature of 0 Kelvin|K (absolute zero), and with appropriate corrections for gravitational time dilation. The ground state is defined at zero electric field|electric and magnetic fields. The second thus defined is consistent with the ephemeris second, which was based on astronomical measurements. (See #History|History below.) The international standard symbol for a second is '''s''' (see ISO 31-1). The realization of the standard second is described briefly in a special publication from the National Institute of Science and Technology, and in detail by the National Research Council of Canada.

Equivalence to other units of time

1 international second is equal to:
- 1/60 minute (but see also leap second)
- 1/3,600 hour
- 1/86,400 day (International Astronomical Union|IAU system of units)
- 1/31,557,600 Julian year (astronomy)|Julian year (IAU system of units)

History

Before mechanical clocks

The Egyptians subdivided daytime and nighttime into twelve hours each since at least 2000 BC, hence the seasonal variation of their hours. The Hellenistic astronomers Hipparchus (''c.'' 150 BC) and Ptolemy (''c.'' AD 150) subdivided the day sexagesimally and also used a mean hour , but did not use distinctly named smaller units of time. Instead they used simple fractions of an hour. The day was subdivided sexagesimally, that is by , by of that, by of that, etc, to at least six places after the sexagesimal point (a precision of less than 2 microseconds) by the Babylonians after 300 BC, but they did not sexagesimally subdivide smaller units of time. For example, six fractional sexagesimal places of a day was used in their specification of the length of the year, although they were unable to measure such a small fraction of a day in real time. As another example, they specified that the mean synodic month was 29;31,50,8,20 days (four fractional sexagesimal positions), which was repeated by Hipparchus and Ptolemy sexagesimally, and is currently the mean synodic month of the Hebrew calendar, though restated as 29 days 12 hours 793 helek|halakim (where 1 hour = 1080 halakim). The Babylonians did not use the hour, but did use a double-hour lasting 120 modern minutes, a time-degree lasting four modern minutes, and a barleycorn lasting 3 modern seconds (the ''helek'' of the modern Hebrew calendar).See page 325 in In 1000, the Persian people|Persian scholar al-Biruni gave the times of the new moons of specific weeks as a number of days, hours, minutes, seconds, thirds, and fourths after noon Sunday. In 1267, the medieval scientist Roger Bacon stated the times of full moons as a number of hours, minutes, seconds, thirds, and fourths (''horae'', ''minuta'', ''secunda'', ''tertia'', and ''quarta'') after noon on specified calendar dates. Although a ''third'' for of a second remains in some languages, for example Polish language|Polish (''tercja'') and Turkish language|Turkish (''salise''), the modern second is subdivided decimally.

Seconds measured by mechanical clocks

The first clock that could show time in seconds was created by Taqi al-Din Muhammad ibn Ma'ruf|Taqi al-Din at the Istanbul observatory of Taqi al-Din between 1577-1580. He called it the "observational clock" in his ''In the Nabik Tree of the Extremity of Thoughts'', where he described it as "a mechanical clock with three Clock face|dials which show the hours, the minutes, and the seconds." He used it as an astronomical clock, particularly for measuring the right ascension of the stars. The first mechanical clock displaying seconds in Western Europe was constructed in Switzerland at the beginning of the 17th century. The second first became accurately measurable with the development of pendulum clocks keeping ''mean time'' (as opposed to the ''apparent time'' displayed by sundials), specifically in 1670 when William Clement added a seconds pendulum to the original pendulum clock of Christian Huygens.See page 2 in The seconds pendulum has a period of two seconds, one second for a swing forward and one second for a swing back, enabling the longcase clock incorporating it to tick seconds. From this time, a second hand that rotated once per minute in a small subdial began to be added to the clock faces of precision clocks.

Modern measurements

In 1956 the second was defined in terms of the period of revolution of the Earth around the Sun for a particular epoch (astronomy)|epoch, because by then it had become recognized that the Earth's rotation on its own axis was not sufficiently uniform as a standard of time. The Earth's motion was described in Newcomb's Tables of the Sun (1895), which provide a formula estimating the motion of the Sun relative to the epoch 1900 based on astronomical observations made between 1750 and 1892. The second thus defined is This definition was ratified by the ''Eleventh General Conference on Weights and Measures'' in 1960. The ''tropical year'' in the definition was not measured, but calculated from a formula describing a mean tropical year which decreased linearly over time, hence the curious reference to a specific ''instantaneous'' tropical year. This definition of the second was in conformity with the ephemeris time scale adopted by the International Astronomical Union|IAU in 1952,''Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac'' (prepared jointly by the Nautical Almanac Offices of the United Kingdom and the United States of America, HMSO, London, 1961), at Sect. 1C, p.9), stating that at a conference "in March 1950 to discuss the fundamental constants of astronomy ... the recommendations with the most far-reaching consequences were those which defined ephemeris time and brought the lunar ephemeris into accordance with the solar ephemeris in terms of ephemeris time. These recommendations were addressed to the International Astronomical Union and were formally adopted by Commission 4 and the General Assembly of the Union in Rome in September 1952." defined as the measure of time that brings the observed positions of the celestial bodies into accord with the Newtonian dynamical theories of their motion (those accepted for use during most of the twentieth century being Newcomb's Tables of the Sun, used from 1900 through 1983, and Ernest William Brown#Work on the motion of the Moon|Brown's Tables of the Moon, used from 1923 through 1983). With the development of the atomic clock, it was decided to use atomic clocks as the basis of the definition of the second, rather than the revolution of the Earth around the Sun. Following several years of work, Louis Essen from the National Physical Laboratory, UK|National Physical Laboratory (Teddington, England) and William Markowitz from the United States Naval Observatory (USNO) determined the relationship between the hyperfine transition frequency of the caesium atom and the ephemeris second. Using a common-view measurement method based on the received signals from radio station WWV (radio station)|WWV, they determined the orbital motion of the Moon about the Earth, from which the apparent motion of the Sun could be inferred, in terms of time as measured by an atomic clock. They found that the second of ephemeris time (ET) had the duration of 9,192,631,770 ± 20 cycles of the chosen caesium frequency. As a result, in 1967 the Thirteenth Conférence Générale des Poids et Mesures|General Conference on Weights and Measures defined the second of International Atomic Time|atomic time in the International System of Units as This SI second, referred to atomic time, was later verified to be in agreement, within 1 part in 10¹⁰, with the second of ephemeris time as determined from lunar observations. (Nevertheless, this SI second was already, when adopted, a little shorter than the then-current value of the second of mean solar time. In the late 1950s, the caesium standard was used to measure both the current mean length of the second of mean solar time (UT2) () and also the second of ephemeris time (ET) (), see . As noted in page 162, the figure was chosen for the SI second. L Essen in the same 1968 article stated that this value "seemed reasonable in view of the variations in UT2".) During the 1970s it was realized that gravitational time dilation caused the second produced by each atomic clock to differ depending on its altitude. A uniform second was produced by correcting the output of each atomic clock to mean sea level (the rotating geoid), lengthening the second by about 1. This correction was applied at the beginning of 1977 and formalized in 1980. In relativistic terms, the SI second is defined as the proper time on the rotating geoid.See page 515 in The definition of the second was later refined at the 1997 meeting of the Bureau International des Poids et Mesures|BIPM to include the statement The revised definition would seem to imply that the ideal atomic clock would contain a single caesium atom at rest emitting a single frequency. In practice, however, the definition means that high-precision realizations of the second should compensate for the effects of the ambient temperature (black body|black-body radiation) within which atomic clocks operate, and extrapolate accordingly to the value of the second at a temperature of absolute zero. Today, the atomic clock operating in the microwave region is challenged by atomic clocks operating in the optical region. To quote Ludlow ''et al.'' “In recent years, optical atomic clocks have become increasingly competitive in performance with their microwave counterparts. The overall accuracy of single trapped ion based optical standards closely approaches that of the state-of-the-art caesium fountain standards. Large ensembles of ultracold alkaline earth atoms have provided impressive clock stability for short averaging times, surpassing that of single-ion based systems. So far, interrogation of neutral atom based optical standards has been carried out primarily in free space, unavoidably including atomic motional effects that typically limit the overall system accuracy. An alternative approach is to explore the ultranarrow optical transitions of atoms held in an optical lattice. The atoms are tightly localized so that Doppler and photon-recoil related effects on the transition frequency are eliminated.” The NRC attaches a "relative uncertainty" of 2.5 (limited by day-to-day and device-to-device reproducibility) to their atomic clock based upon the ¹²⁷I₂ molecule, and is advocating use of an ⁸⁸Sr ion trap instead (relative uncertainty due to linewidth of 2.2). See magneto-optical trap and Such uncertainties rival that of the NIST F-1 caesium atomic clock in the microwave region, estimated as a few parts in 10¹⁶ averaged over a day.

SI multiples

SI prefixes are commonly used to measure time less than a second, but rarely for multiples of a second. Instead, the non-SI units minutes, hours, days, Julian year (astronomy)|Julian years, Julian centuries, and Julian millennia are used.