Editing Second (section)

==History of definition==
{{see also|History of timekeeping devices}}

There have only ever been three definitions of the second: as a fraction of the day, as a fraction of an extrapolated year, and as the microwave frequency of a [[caesium]] atomic clock, which have each realized a sexagesimal division of the day from ancient astronomical calendars.

===Sexagesimal divisions of calendar time and day===
Civilizations in the classic period and earlier created divisions of the calendar as well as arcs using a sexagesimal system of counting, so at that time the second was a sexagesimal subdivision of the day (ancient second{{nbsp}}={{nbsp}}{{sfrac|day|60×60}}), not of the hour like the modern second (={{nbsp}}{{sfrac|hour|60×60}}).{{cn|date=November 2024}}  Sundials and water clocks were among the earliest timekeeping devices, and units of time were measured in degrees of arc.  Conceptual units of time smaller than realisable on sundials were also used.

There are references to "second" as part of a lunar month in the writings of natural philosophers of the Middle Ages, which were mathematical subdivisions that could not be measured mechanically.{{refn 
|In 1000, the [[Persian people|Persian]] scholar [[al-Biruni]], writing in Arabic, used the term ''second'', and defined the division of time between [[new moon]]s of certain specific weeks as a number of days, hours, minutes, seconds, thirds, and fourths after noon Sunday.<ref name="al-Biruni">{{cite book
 |author=Al-Biruni
 |year=1879
 |orig-year=1000
 |title=The chronology of ancient nations
 |url=https://books.google.com/books?id=pFIEAAAAIAAJ&pg=PA148
 |pages=147–149
 |translator-last=Sachau
 |translator-first=C. Edward
 |author-link=Al-Biruni
 |access-date=February 23, 2016
 |archive-url=https://web.archive.org/web/20190916000857/https://books.google.com/books?id=pFIEAAAAIAAJ&pg=PA148&hl=en#v=onepage&q=
 |archive-date=September 16, 2019
 |url-status=live
 }}</ref>|group=nb}}{{refn |In 1267, the medieval English scientist [[Roger Bacon]], writing in Latin, defined the division of time between [[full moon]]s 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
 |first=Roger |last=Bacon
 |year=2000 |orig-year=1267
 |title=The Opus Majus of Roger Bacon
 |publisher=[[University of Pennsylvania Press]]
 |page=table facing page 231
 |isbn=1-85506-856-7
 |no-pp=true
 |others=translated by Robert Belle Burke
}}</ref>|group=nb}}

===Fraction of solar day===
{{see also|Seconds_pendulum#Defining_the_second}}

The earliest mechanical clocks, which appeared starting in the 14th century, had displays that divided the hour into halves, thirds, quarters and sometimes even 12 parts, but never by 60. In fact, the hour was not commonly divided in 60 minutes as it was not uniform in duration. It was not practical for timekeepers to consider minutes until the first mechanical clocks that displayed minutes appeared near the end of the 16th century. Mechanical clocks kept the ''mean time'', as opposed to the ''apparent time'' displayed by [[sundial]]s. 
By that time, sexagesimal divisions of time were well established in Europe.{{#tag:ref|It may be noted that 60 is the smallest multiple of the first 6 counting numbers. So a clock with 60 divisions would have a mark for thirds, fourths, fifths, sixths and twelfths (the hours); whatever units the clock would likely keep time in, would have marks.|group=nb}}

The earliest clocks to display seconds appeared during the last half of the 16th century. The second became accurately measurable with the development of mechanical clocks. The earliest spring-driven timepiece with a second hand that marked seconds is an unsigned clock depicting [[Orpheus]] in the Fremersdorf collection, dated between 1560 and {{nowrap|1570.<ref name="Landes">{{cite book | first1=David S. |last1=Landes |author-link1=David S. Landes |title=[[Revolution in Time]] | location=Cambridge, Massachusetts| publisher= Harvard University Press |year= 1983 | isbn = 0-674-76802-7 }}</ref>{{rp|417–418}}<ref>{{cite book |first1=Johann |last1=Willsberger |title=Clocks & watches |location=New York |publisher=Dial Press |year=1975 |isbn=0-8037-4475-7 |url-access=registration |url=https://archive.org/details/clockswatchessix0000will }} full page color photo: 4th caption page, 3rd photo thereafter (neither pages nor photos are numbered).</ref>}} During the 3rd quarter of the 16th century, [[Taqi al-Din Muhammad ibn Ma'ruf|Taqi al-Din]] built a clock with marks every 1/5 minute.<ref name="Selin1997">{{cite book |first=Helaine |last=Selin |author-link=Helaine Selin |title=Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures |url=https://books.google.com/books?id=raKRY3KQspsC&pg=PA934 |date=July 31, 1997 |publisher=Springer Science & Business Media |isbn=0-7923-4066-3 |page=934 |access-date=February 23, 2016 |archive-url=https://web.archive.org/web/20161120013247/https://books.google.com/books?id=raKRY3KQspsC&pg=PA934 |archive-date=November 20, 2016 |url-status=live }}</ref>
In 1579, [[Jost Bürgi]] built a clock for [[William IV, Landgrave of Hesse-Kassel|William of Hesse]] that marked seconds.<ref name="Landes" />{{rp|105}} In 1581, [[Tycho Brahe]] redesigned clocks that had displayed only minutes at his observatory so they also displayed seconds, even though those seconds were not accurate. In 1587, Tycho complained that his four clocks disagreed by plus or minus four seconds.<ref name="Landes" />{{rp|104}}

In 1656, Dutch scientist [[Christiaan Huygens]] invented the first pendulum clock. It had a pendulum length of just under a meter, giving it a swing of one second, and an escapement that ticked every second. It was the first clock that could accurately keep time in seconds. By the 1730s, 80 years later, [[John Harrison]]'s maritime chronometers could keep time accurate to within one second in 100 days.

In 1832, [[Carl Friedrich Gauss|Gauss]] proposed using the second as the base unit of time in his millimeter–milligram–second [[system of units]]. The [[British Association for the Advancement of Science]] (BAAS) in 1862 stated that "All men of science are agreed to use the second of mean solar time as the unit of time."<ref>{{cite book |url=https://books.google.com/books?id=540DAAAAQAAJ&pg=PR1 |title=Reports of the committee on electrical standards |year=1873 |publisher=British Association for the Advancement of Science |editor-first=Henry Charles Fleeming |editor-last=Jenkin |editor-link=Henry Charles Fleeming Jenkin |page=90 |access-date=February 23, 2016 |archive-url=https://web.archive.org/web/20161120015337/https://books.google.com/books?id=540DAAAAQAAJ&pg=PR1#v=onepage&q&f=true |archive-date=November 20, 2016 |url-status=live }}</ref> BAAS formally proposed the [[CGS|CGS system]] in 1874, although this system was gradually replaced over the next 70 years by [[MKS system of units|MKS]] units. Both the CGS and MKS systems used the same second as their base unit of time. MKS was adopted internationally during the 1940s, defining the second as {{frac|86,400}} of a mean solar day.

===Fraction of an ephemeris year===
{{see also|Ephemeris time}}

Sometime in the late 1940s, quartz crystal oscillator clocks with an operating frequency of ~100&nbsp;kHz advanced to keep time with accuracy better than 1 part in 10<sup>8</sup> over an operating period of a day. It became apparent that a consensus of such clocks kept better time than the rotation of the Earth. [[Time metrology|Metrologists]] also knew that Earth's orbit around the Sun (a year) was much more stable than Earth's rotation. This led to proposals as early as 1950 to define the second as a fraction of a year.

The Earth's motion was described in [[Newcomb's Tables of the Sun|Newcomb's ''Tables of the Sun'']] (1895), which provided a formula for estimating the motion of the Sun relative to the epoch 1900 based on astronomical observations made between 1750 and 1892.<ref name="USNO">{{cite web
 | title=Leap Seconds
 | publisher=Precise Time Department, [[United States Naval Observatory]]
 | url=https://www.cnmoc.usff.navy.mil/Our-Commands/United-States-Naval-Observatory/Precise-Time-Department/Global-Positioning-System/USNO-GPS-Time-Transfer/Leap-Seconds/
 | access-date=May 13, 2025
 }}</ref> This resulted in adoption of an [[ephemeris time]] scale expressed in units of the [[sidereal year]] at that epoch by the [[International Astronomical Union|IAU]] in 1952.<ref>
{{citation
 |author=Nautical Almanac Offices of the United Kingdom and the United States of America 
 |url=https://archive.org/details/explanatorysupplement/page/n19
 |title=Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac
 |year=1961
 |page=9
 |quote=... defined ephemeris time ... [was] adopted by the [[International Astronomical Union]] in Sept. 1952.}}
</ref> This extrapolated timescale brings the observed positions of the celestial bodies into accord with Newtonian dynamical theories of their motion.<ref name="USNO" /> In 1955, the [[tropical year]], considered more fundamental than the sidereal year, was chosen by the IAU as the unit of time. The tropical year in the definition was not measured but calculated from a formula describing a mean tropical year that decreased linearly over time.

In 1956, the second was redefined in terms of a year relative to that [[epoch (astronomy)|epoch]]. The second was thus defined as "the fraction {{frac|31,556,925.9747}} of the tropical year for 1900 [[January 0]] at 12 hours ephemeris time".<ref name="USNO" /> This definition was adopted as part of the [[International System of Units]] in 1960.<ref>{{cite web
 |title=SI Brochure (2006)
 |work=SI Brochure 8th Edition
 |url=https://www.bipm.org/utils/common/pdf/si_brochure_8.pdf
 |page=112
 |publisher=[[BIPM]]
 |access-date=May 23, 2019
 |archive-url=https://web.archive.org/web/20190503133741/https://www1.bipm.org/utils/common/pdf/si_brochure_8.pdf
 |archive-date=May 3, 2019
 |url-status=live
 }}</ref>

===Atomic definition ===
Even the best mechanical, electric motorized and quartz crystal-based clocks develop discrepancies from environmental conditions; far better for timekeeping is the natural and exact "vibration" in an energized atom. The frequency of vibration (i.e., radiation) is very specific depending on the type of atom and how it is excited.<ref>{{cite book |last1=McCarthy |first1=Dennis D. |author-link1=Dennis McCarthy (scientist) |last2=Seidelmann |first2=P. Kenneth |title=Time: From Earth Rotation to Atomic Physics |chapter = Definition and Role of a Second |year=2009 |location=Weinheim |publisher=Wiley}}</ref> Since 1967, the second has been defined as exactly "the duration of 9,192,631,770 [[frequency|periods]] of the radiation corresponding to the transition between the two [[Hyperfine structure|hyperfine levels]] of the ground state of the [[caesium-133]] atom". This length of a second was selected to correspond exactly to the length of the ephemeris second previously defined. Atomic clocks use such a frequency to measure seconds by counting cycles per second at that frequency. Radiation of this kind is one of the most stable and reproducible phenomena of nature. The current generation of atomic clocks is accurate to within one second in a few hundred million years. Since 1967, atomic clocks based on atoms other than caesium-133 have been developed with increased precision by a factor of 100. Therefore a new definition of the second is planned.<ref name="CGPM2022-Draft">[https://www.bipm.org/documents/20126/64811571/Draft-Resolutions-2022.pdf/2e8e53df-7a14-3fc8-8a04-42dd47df1a04?t=1644502962693 Draft resolutions] of the 27. [[General Conference on Weights and Measures]] in November 2022, Section&nbsp;E, p.&nbsp;25</ref>

Atomic clocks now set the length of a second and the [[time standard]] for the world.<ref name="McCarthy 2009" />{{Rp|231–232}}

===Table===
{| class="wikitable" 
! colspan="3" |Evolution of the Second
|-
! style="width: 40%;" | Decisions of the CIPM
! style="width: 40%;" | Resolution of the CGPM
! style="width: 20%;" | Information
|-style="vertical-align: top;"
|That according to the decisions of the 8th General Assembly of the International Astronomical Union (Rome, 1952), the second of ephemeris time (ET) is the fraction

<math>\frac{12960276813}{408986496}\times10^{-9}</math> of the tropical year for 1900 January 0 at 12 h ET.  
|The second is the fraction <math>\frac{1}{31556925.9747}</math> of the tropical year for 1900 January 0 at 12 hours ephemeris time.
|1956 CIPM
11th CGPM 1960 Resolution 9
|-style="vertical-align: top;"
|The standard to be employed is the transition between the hyperfine levels F=4, M=0 and F=3, M=0 of the ground state <math>^2S_{1/2}</math> of the caesium 133 atom, unperturbed by external fields, and that the frequency of this transition is assigned the value 9192631770 hertz.
|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
|13th CGPM Resolution 1
CIPM 1967
|-style="vertical-align: top;"
|This definition implies that the caesium atom is at rest and unperturbed. In consequence, in its practical realization, measurements must be corrected for velocity of the atoms with respect to the clock reference frame, for magnetic and electric fields including ambient black-body radiation, for spin-exchange effects and for other possible perturbations.
|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 Cs atom unperturbed by black-body radiation, that is, in an environment whose temperature is 0 K, and that the frequencies of primary frequency standards should therefore be corrected for the shift due to ambient radiation, as stated at the meeting of the CCTF in 1999.
|footnote added by the 14th meeting of the Consultative Committee for Time and Frequency in 1999
the footnote was added at the 86th (1997) meeting of the CIPM
GCPM 1998 7th Edition SI Brochure
|-style="vertical-align: top;"
|The definition of a unit refers to an idealized situation that can be reached in the practical realization with some uncertainty only. In this spirit, the definition of the second has to be understood as referring to atoms free of any perturbation, at rest and in the absence of electric and magnetic fields.
A future re-definition of the second would be justified if these idealized conditions can be achieved much easier than with the current definition.

The definition of the second should be understood as the definition of the unit of proper time: it applies in a small spatial domain that shares the motion of the caesium atom used to realize the definition.

In a laboratory sufficiently small to allow the effects of the non-uniformity of the gravitational field to be neglected when compared to the uncertainties of the realization of the second, the proper second is obtained after application of the special relativistic correction for the velocity of the atom in the laboratory. It is wrong to correct for the local gravitational field.
|'''The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency, Δ''ν''<sub>Cs</sub>, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s<sup>−1</sup>.'''

The reference to an unperturbed atom is intended to make it clear that the definition of the SI second is based on an isolated caesium atom that is unperturbed by any external field, such as ambient black-body radiation.

The second, so defined, is the unit of proper time in the sense of the general theory of relativity. To allow the provision of a coordinated time scale, the signals of different primary clocks in different locations are combined, which have to be corrected for relativistic caesium frequency shifts (see section 2.3.6).

The CIPM has adopted various secondary representations of the second, based on a selected number of spectral lines of atoms, ions or molecules. The unperturbed frequencies of these lines can be determined with a relative uncertainty not lower than that of the realization of the second based on the <sup>133</sup>Cs hyperfine transition frequency, but some can be reproduced with superior stability.
|'''Current Definition''' resolved in 2018 effective after the 26th GCPM approved the redefinition May 20, 2019.
SI Brochure 9
|}