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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.

[[SI prefix]]es 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) and [[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]],” or one thousand seconds), such units are rarely used in practice.  More commonly encountered, non-SI units of time such as the [[minute]], [[hour]], and [[day]] increase by multiples of 60 and 24 (rather than by powers of ten as in the SI system).

== International second ==
Under the International System of Units, the second is currently defined as {{cquote|the duration of 9&nbsp;192&nbsp;631&nbsp;770 [[Period (physics)|periods]] of the radiation corresponding to the transition between the two [[Hyperfine structure|hyperfine levels]] of the [[ground state]] of the [[caesium]]&nbsp;133 atom.<ref name="BIPM21">[http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.html Official BIPM definition]</ref>}} This definition refers to a caesium atom at rest at a temperature of 0 [[Kelvin|K]] ([[absolute zero]]). The ground state is defined at zero [[magnetic field]].  The second thus defined is equivalent to the ephemeris second, which was based on astronomical measurements.  (See [[#History|History]] below.)

The international standard symbol for a second is '''s'''<ref>ISO 31-1</ref> (see [[ISO 31-1]])

The realization of the standard second is described briefly in [http://physics.nist.gov/Pubs/SP330/sp330.pdf NIST Special Publication 330; Appendix 2, pp. 53 ff], and in detail by [http://inms-ienm.nrc-cnrc.gc.ca/research/cesium_clock_e.html National Research Council of Canada].

== Equivalence to other units of time ==
1 international second is equal to:

* 1/60 [[minute]]
* 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 ==
The Egyptians had subdivided daytime and nighttime into twelve hours each since at least 2000 BC, hence their hours varied seasonally. The [[Hellenistic]] astronomers [[Hipparchus]] (''c.'' 150 BC) and [[Ptolemy]] (''c.'' AD 150) subdivided the day [[sexagesimal]]ly and also used a mean hour ({{frac|1|24}} day), 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 {{frac|1|60}}, by {{frac|1|60}} of that, by {{frac|1|60}} of that, etc., to at least six places after the sexagesimal point by the [[Babylonia]]ns 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).<ref>{{cite book |author=Neugebauer Otto |title=A history of ancient mathematical astronomy |location=Berlin |publisher=Springer |year=1975 |isbn=}}</ref> They did not use the hour, but did use a double-hour, a time-degree lasting four of our minutes, and a barleycorn lasting 3⅓ of our seconds (the ''helek'' of the modern Hebrew calendar).<ref>{{cite journal |author=Neugebauer Otto |title=The astronomy of Maimonides and its sources |journal=Hebrew Union College Annual |volume=22 |year=1949 |pages=321-360 |page=325}}</ref>

In 1000, the [[Muslim]] 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.<ref>{{cite book |author=[[al-Biruni]]  |title=The chronology of ancient nations: an English version of the Arabic text of the Athâr-ul-Bâkiya of Albîrûnî, or "Vestiges of the Past"|translator=Sachau C Edward |location=London |publisher=W.H. Allen |year=1879 |pages=147-149 |url=http://books.google.com/books?id=pFIEAAAAIAAJ&pg=PA376&lr=#PPA148,M1 |oclc=9986841}}</ref> 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.<ref>{{cite book |author=Bacon Roger |title=The Opus Majus of Roger Bacon |translator=Burke Robert Belle |location=Philadelphia |publisher=University of Pennsylvania Press |originalyear=1928 |year=2000 |page=table facing page 231 |isbn=9781855068568}}</ref> Although a ''third'' for {{frac|1|60}} of a second remains in some languages, for example [[Polish language|Polish]] (''tercja'') and [[Arabic language|Arabic]] (ثالثة), the modern second is subdivided decimally.

The second first became measurable with the development of [[pendulum clock]]s 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]].<ref>[http://illumin.usc.edu/article.php?articleID=64&page=2 Long Case Clock: Pendulum]</ref> 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 face]]s of precision clocks.

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]], which provides a formula for the motion of the Sun at the epoch 1900 based on astronomical observations made between 1750 and 1892.<ref name="USNO">{{cite web | title=Leap Seconds | publisher=Time Service Department, [[United States Naval Observatory]] | url=http://tycho.usno.navy.mil/leapsec.html | accessdate=2006-12-31 }}</ref>  The second thus defined is

:''the fraction 1/31,556,925.9747 of the [[tropical year]] for 1900 January 0 at 12 hours [[ephemeris time]].''<ref name="USNO"/>

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. Because this second was the independent variable of time used in [[ephemeris|ephemerides]] of the Sun and Moon during most of the twentieth century (Newcomb's ''Tables of the Sun'' were used from 1900 through 1983, and [[Ernest William Brown|Brown]]'s ''Tables of the Moon'' were used from 1920 through 1983), it was called the ''ephemeris second''.<ref name="USNO"/>

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.<ref name="USNO"/>  Using a common-view measurement method based on the received signals from [[radio station]] [[WWV (radio station)|WWV]],<ref>{{cite journal |title=The definition of the 'atomic' second |journal=Metrologia |date=2005-06-07 |author=Leschiutta Sigfrido |coauthors= |volume=42 |issue=3 |pages=S10–S19 |doi=10.1088/0026-1394/42/3/S03 |url=http://stacks.iop.org/0026-1394/42/S10 |format= |accessdate= }}</ref> 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.  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

:''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.''<ref name="USNO"/>

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{{E|−10}}. 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.<ref>{{cite journal|author=Nelson RA ''et al.'', |url=http://www.cl.cam.ac.uk/~mgk25/time/metrologia-leapsecond.pdf |format=PDF 381KB |title=The leap second: its history and possible future |journal=Metrologia |volume=38 |year=2000 |pages=509-529 |page=515 |issn= |doi=}}</ref>

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

:''This definition refers to a caesium atom at rest at a temperature of 0'' K.

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 as defined above.

For approximately twenty years, it has been possible to confine an ion to a region of space smaller than one cubic micron (10<sup>-6</sup> m)<sup>3</sup>. Such an ion is almost completely isolated from the surrounding environment and suggests a frequency or time standard with a reproducibility and stability several orders of magnitude superior to the best caesium time standards. Such standards are under development. See [[magneto-optical trap]] and {{cite web |url=http://www.npl.co.uk/server.php?show=ConWebDoc.1086 |publisher=National Physical Laboratory |title=Trapped ion optical frequency standards}}

==Approximations==
It is a common belief that saying one one thousand, two one thousand three one thousand...... can be used to time events in seconds (one mississippi, two mississippi is another common sequence)

== 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]] and [[days]] are used.
<div style="float:center; margin-left: 1em;">
{{SI multiples
|unit=second
|symbol=s
|note=Common prefixes are in bold
| n= | µ= | m=
}}
</div>

==See also==
{{wiktionarypar|second}}
*[[Hertz]]
*[[Becquerel]]
*[[Leap second]]
*[[Magneto-optical trap]]
*[[Time standard]]
*[[Atomic clock]]
*[[International System of Units]]
*[[International Atomic Time]]

==References==
<references/>

==External links==
*[http://physics.nist.gov/cuu/Units/second.html NIST: ''Definition of the second''; notice the cesium atom must be in its ground state at 0 K]
*[http://www.bipm.org/en/si/si_brochure/chapter2/2-1/second.html Official BIPM definition of the second]
*[http://www.npl.co.uk/server.php?show=ConWebDoc.1086 National Physical Laboratory: ''Trapped ion optical frequency standards'' ]
*[http://inms-ienm.nrc-cnrc.gc.ca/research/optical_frequency_projects_e.html#optical National Research Council of Canada: ''Optical frequency standard based on a single trapped ion'']
*[http://inms-ienm.nrc-cnrc.gc.ca/faq_time_e.html#10 ''What is a Cesium atom clock?'']
*[http://tycho.usno.navy.mil/leapsec.html Seconds and leap seconds by the USNO]
*[http://www.cl.cam.ac.uk/~mgk25/time/metrologia-leapsecond.pdf The leap second: its history and possible future]

{{Time Topics}}
{{Time measurement and standards}}

[[Category:SI base units]]
[[Category:Units of time]]
[[Category:Centimetre gram second system of units]]

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