# Second

A pendulum-governed escapement of a clock, ticking every second

The second (symbol: s) (abbreviated s or sec) is the base unit of time in the International System of Units (SI).[1][2] It is qualitatively defined as the second division of the hour by sixty, the first division by sixty being the minute.[3] SI definition of 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".[4] Seconds may be measured using a mechanical, electrical or an atomic clock.

SI prefixes are combined with the word second to denote subdivisions of the second, e.g., the millisecond (one thousandth of a second), the microsecond (one millionth of a second), and the nanosecond (one billionth of a second). Though SI prefixes may also be used to form multiples of the second such as 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 is also the base unit of time in other systems of measurement: the centimetre–gram–second, metre–kilogram–second, metre–tonne–second, and foot–pound–second systems of units.

## International second

Under the International System of Units (via the International Committee for Weights and Measures, or CIPM), since 1967 the second has been defined as the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.[1] In 1997 CIPM added that the periods would be defined for a caesium atom at rest, and approaching the theoretical temperature of absolute zero (0 K), and in 1999, it included corrections from ambient radiation.[1] Absolute zero implies no movement, and therefore zero external radiation effects (i.e., zero local electric and magnetic fields).

The second thus defined is consistent with the ephemeris second, which was based on astronomical measurements. (See History below.) The realization of the standard second is described briefly in a special publication from the National Institute of Standards and Technology,[5] and in detail by the National Research Council of Canada.[6]

## Equivalence to other units

### Time units

Main article: Time

1 international second is equal to:

### Frequency units

Main article: Reciprocal second

## History of definition

### Early civilizations

Early civilizations constructed divisions in the day, but none used the term second, and none was a precursor to the modern second:

• The Egyptians since 2000 BC subdivided daytime and nighttime into twelve hours each, hence the seasonal variation of the length of their hours.
• The Hellenistic astronomers Hipparchus (c. 150 BC) and Ptolemy (c. AD 150) subdivided the day into sixty parts (the sexagesimal system). They also used a mean hour (124 day); simple fractions of an hour (14, 23, etc.); and time-degrees (1360 day, equivalent to four modern minutes).[7]
• The Babylonians after 300 BC also subdivided the day using the sexagesimal system, and divided each subsequent subdivision by sixty: that is, by 160, by 160 of that, by 160 of that, etc., to at least six places after the sexagesimal point - a precision equivalent to better than 2 microseconds.[8] 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 13 modern seconds (the helek of the modern Hebrew calendar),[9] but did not sexagesimally subdivide these smaller units of time. No sexagesimal unit of the day was ever used as an independent unit of time.

### Based on subdivisions of the moon cycle

• Circa 1000, the Persian scholar al-Biruni, writing in Arabic, used the term second, and defined the division of time between new moons of certain specific weeks as a number of days, hours, minutes, seconds, thirds, and fourths after noon Sunday.[10]
• In 1267, the medieval scientist Roger Bacon, writing in Latin, defined the division of time between full moons as a number of hours, minutes, seconds, thirds, and fourths (horae, minuta, secunda, tertia, and quarta) after noon on specified calendar dates.[11]
• The modern second is subdivided using decimals - although the term third (160 of a second) remains in some languages, for example Polish (tercja) and Turkish (salise).

### Based on mechanical clocks

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 keeping mean time, as opposed to the apparent time displayed by sundials. The earliest spring-driven timepiece with a second hand which marked seconds is an unsigned clock depicting Orpheus in the Fremersdorf collection, dated between 1560 and 1570.[12]:417–418[13] During the 3rd quarter of the 16th century, Taqi al-Din built a clock with marks every 1/5 minute.[14] In 1579, Jost Bürgi built a clock for William of Hesse that marked seconds.[12]:105 In 1581, Tycho Brahe redesigned clocks that displayed minutes at his observatory so they also displayed seconds. However, they were not yet accurate enough for seconds. In 1587, Tycho complained that his four clocks disagreed by plus or minus four seconds.[12]:104

In 1644, Marin Mersenne calculated that a pendulum with a length of 39.1 inches (0.994 m) would have a period at one standard gravity of precisely two seconds, one second for a swing forward and one second for the return swing, enabling such a pendulum to tick in precise seconds.[15]

In 1670, London clockmaker William Clement added this seconds pendulum to the original pendulum clock of Christiaan Huygens.[16] From 1670 to 1680, Clement made many improvements to his clock and introduced the longcase or grandfather clock to the public. This clock used an anchor escapement mechanism with a seconds pendulum to display seconds in a small subdial. This mechanism required less power and caused less friction than the older verge escapement and was accurate enough to measure seconds reliably as one-sixtieth of a minute. Within a few years, most British precision clockmakers were producing longcase clocks and other clockmakers soon followed. Thus the second could now be reliably measured.

In 1832, 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."[17] BAAS formally proposed the CGS system in 1874, although this system was gradually replaced over the next 70 years by 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 186,400 of a mean solar day.

### Based on a fraction of a year

In 1956, the second was redefined in terms of a year (the period of the Earth's revolution around the Sun) for a particular 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 provided a formula for estimating the motion of the Sun relative to the epoch 1900 based on astronomical observations made between 1750 and 1892.[18]

The second was thus defined as:

the fraction 131,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.[18]

This definition was ratified by the Eleventh General Conference on Weights and Measures in 1960, which also established the International System of Units.

The tropical year in the 1960 definition was not measured but calculated from a formula describing a mean tropical year that decreased linearly over time, hence the curious reference to a specific instantaneous tropical year. This was in conformity with the ephemeris time scale adopted by the IAU in 1952.[19] This definition brings the observed positions of the celestial bodies into accord with Newtonian dynamical theories of their motion. Specifically, those tables used for most of the 20th century were Newcomb's Tables of the Sun (used from 1900 through 1983) and Brown's Tables of the Moon (used from 1923 through 1983).[18]

Thus, the 1960 SI definition abandoned any explicit relationship between the scientific second and the length of a day, as most people understand the term.

### Based on caesium microwave atomic clock

With the development of the atomic clock in the early 1960s, it was decided to use atomic time 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 (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.[18][20] Using a common-view measurement method based on the received signals from radio station WWV,[21] 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.[20] As a result, in 1967 the Thirteenth General Conference on Weights and Measures defined the SI second of atomic time as:

FOCS 1, a continuous cold caesium fountain atomic clock in Switzerland, started operating in 2004 at an uncertainty of one second in 30 million years.
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.[18]

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.[22] (Nevertheless, this SI second was already, when adopted, a little shorter than the then-current value of the second of mean solar time.[23][24])

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 1×10−10. 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.[25]

The definition of the second was later refined at the 1997 meeting of the BIPM to include the statement

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

The revised definition seems to imply that the ideal atomic clock contains 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 radiation) within which atomic clocks operate, and extrapolate accordingly to the value of the second at a temperature of absolute zero.

### Proposed: based on optical atomic clock

Today, the atomic clock operating in the microwave region is challenged by atomic clocks operating in the optical region. To quote Ludlow et al.,[26] “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 Canadian National Research Council attaches a "relative uncertainty" of 2.5×10−11 (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 2.2×10−15).[27] See magneto-optical trap and "Trapped ion optical frequency standards". National Physical Laboratory. Such uncertainties rival that of the NIST-F1 caesium atomic clock in the microwave region, estimated as a few parts in 1016 averaged over a day.[28][29]

## SI multiples

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

 Submultiples Multiples Value SI symbol Name Value 10−1 s ds decisecond 101 s das decasecond 10−2 s cs centisecond 102 s hs hectosecond 10−3 s ms millisecond 103 s ks kilosecond 10−6 s µs microsecond 106 s Ms megasecond 10−9 s ns nanosecond 109 s Gs gigasecond 10−12 s ps picosecond 1012 s Ts terasecond 10−15 s fs femtosecond 1015 s Ps petasecond 10−18 s as attosecond 1018 s Es exasecond 10−21 s zs zeptosecond 1021 s Zs zettasecond 10−24 s ys yoctosecond 1024 s Ys yottasecond Common prefixes are in bold

Thus a megasecond is 11 days, 13 hours, 46 minutes and 40 seconds, which is roughly of the order of a week. A kilosecond is 16 minutes, 40 seconds, or the length of a short break. A gigasecond is 31.7 years, so typical human lifespans are 2 to 3 gigaseconds.

## Other current definitions

For specialized purposes, a second may be used as a unit of time in time scales where the precise length differs slightly from the SI definition. One such time scale is UT1, a form of universal time. McCarthy and Seidelmann refrain from stating that the SI second is the legal standard for timekeeping throughout the world, saying only that "over the years UTC [which ticks SI seconds] has become either the basis for legal time of many countries, or accepted as the de facto basis for standard civil time".[30]

## Notes and references

1. "Unit of time (second)". SI Brochure. BIPM. Retrieved December 22, 2013.
2. Second. Merriam Webster Learner's Dictionary.
3. "Base unit definitions: Second". physics.nist.gov. Retrieved September 9, 2016.
4. BN Taylor; A Thompson, eds. (2008). "Appendix 2". The International System of Units (SI) (PDF). NIST Special Publication. 330. pp. 53 ff. Retrieved August 25, 2014.
5. "NRC's Cesium Fountain Clock - FCs1". National Research Council of Canada. Retrieved November 29, 2013.
6. Toomer, G. J. (1998). Ptolemy's Almagest. Princeton, New Jersey: Princeton University Press. pp. 6–7, 23, 211–216. ISBN 978-0-691-00260-6.
7. O Neugebauer (1975). A history of ancient mathematical astronomy. Springer-Verlag. ISBN 0-387-06995-X.
8. See page 325 in O Neugebauer (1949). "The astronomy of Maimonides and its sources". Hebrew Union College Annual. 22: 321–360.
9. al-Biruni (1879). The chronology of ancient nations: an English version of the Arabic text of the Athâr-ul-Bâkiya of Albîrûnî, or "Vestiges of the Past". Sachau C Edward. pp. 147–149.
10. R Bacon (2000) [1928]. The Opus Majus of Roger Bacon. BR Belle. University of Pennsylvania Press. table facing page 231. ISBN 978-1-85506-856-8.
11. Landes, David S. (1983). Revolution in Time. Cambridge, Massachusetts: Harvard University Press. ISBN 0-674-76802-7.
12. Willsberger, Johann (1975). Clocks & watches. New York: Dial Press. ISBN 0-8037-4475-7. full page color photo: 4th caption page, 3rd photo thereafter (neither pages nor photos are numbered).
13. Helaine Selin (July 31, 1997). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Westen Cultures. Springer Science & Business Media. p. 934. ISBN 978-0-7923-4066-9.
14. Greg Jenner (January 29, 2015). A Million Years in a Day: A Curious History of Everyday Life. Orion. p. 275. ISBN 978-0-297-86979-5.
15. Jessica Chappell (October 1, 2001). "The Long Case Clock: The Science and Engineering that Goes Into a Grandfather Clock". Illumin. 1: 1.
16. Jenkin, ed. (1873). Reports of the committee on electrical standards. British Association for the Advancement of Science. p. 90.
17. "Leap Seconds". Time Service Department, United States Naval Observatory. Retrieved November 22, 2015.
18. 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 that 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."
19. W Markowitz, RG Hall, L Essen, JVL Parry; Hall; Essen; Parry (1958). "Frequency of cesium in terms of ephemeris time" (PDF). Physical Review Letters. 1 (3): 105–107. Bibcode:1958PhRvL...1..105M. doi:10.1103/PhysRevLett.1.105.
20. S Leschiutta (2005). "The definition of the 'atomic' second". Metrologia. 42 (3): S10–S19. Bibcode:2005Metro..42S..10L. doi:10.1088/0026-1394/42/3/S03.
21. W Markowitz (1988). AK Babcock, GA Wilkins, eds. The Earth's Rotation and Reference Frames for Geodesy and Geophysics. IAU Sumposia #128. pp. 413–418. Bibcode:1988IAUS..128..413M.
22. DD McCarthy, C Hackman, R Nelson; Hackman; Nelson (2008). "The Physical Basis of the Leap Second". Astronomical Journal. 136 (5): 1906–1908. Bibcode:2008AJ....136.1906M. doi:10.1088/0004-6256/136/5/1906. ... the SI second is equivalent to an older measure of the second of UT1, which was too small to start with and further, as the duration of the UT1 second increases, the discrepancy widens.
23. In the late 1950s, the caesium standard was used to measure both the current mean length of the second of mean solar time (UT2) (9192631830 cycles) and also the second of ephemeris time (ET) (9192631770±20 cycles), see L Essen (1968). "Time Scales" (PDF). Metrologia. 4 (4): 161–165. Bibcode:1968Metro...4..161E. doi:10.1088/0026-1394/4/4/003.. As noted in page 162, the 9192631770 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".
24. See page 515 in RA Nelson; et al. (2000). "The leap second: its history and possible future" (PDF). Metrologia. 38 (6): 509–529. Bibcode:2001Metro..38..509N. doi:10.1088/0026-1394/38/6/6.
25. AD Ludlow; et al. (2006). "Systematic study of the 87Sr clock transition in an optical lattice". Physical Review Letters. 96 (3): 033003. arXiv:. Bibcode:2006PhRvL..96c3003L. doi:10.1103/PhysRevLett.96.033003.
26. "Optical Frequency - Research Projects". February 28, 2006. Archived from the original on January 25, 2009.
27. R Wynands, S Weyers; Weyers (2005). "Atomic fountain clocks". Metrologia. 42 (3): S64–S79. Bibcode:2005Metro..42S..64W. doi:10.1088/0026-1394/42/3/S08.
28. "NIST-F1 Cesium Fountain Atomic Clock". NIST. Retrieved August 19, 2009.
29. McCarty, Dennis D.; Seidelmann, Kenneth P. (2009). Time: From Earth Rotation to Atomic Physics. Weinheim: Wiley. pp. 68, 232.
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