The SECOND (symbol: S) (abbreviated S or SEC) is the base unit of
time in the
International System of Units
International System of Units / Système International
d'Unités (SI). It is qualitatively defined as the second division
of the hour by sixty, the first division by sixty being the minute .
The 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 caesium 133 atom".
Seconds may be measured using a mechanical, electrical or an atomic
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.
* 1 International second
* 2 Equivalence to other units
History of definition
* 3.1 Early civilizations
* 3.2 Based on subdivisions of the moon cycle
* 3.3 Based on mechanical clocks
* 3.4 Based on a fraction of a year
* 3.5 Based on caesium microwave atomic clock
* 3.6 Proposed: based on optical atomic clock
* 3.7 Modern folklore
* 4 SI multiples
* 5 Other current definitions
* 6 See also
* 7 Notes and references
* 8 External links
International System of Units
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 7009919263177000000♠9192631770
periods of the radiation corresponding to the transition between the
two hyperfine levels of the ground state of the caesium 133 atom. 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.
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
National Institute of Standards and Technology ,
and in detail by the
National Research Council of Canada .
EQUIVALENCE TO OTHER UNITS
1 international second is equal to:
* 1⁄60 minute (but see also leap second )
* 1⁄3,600 hour
* 1⁄86,400 day (IAU system of units)
* 1⁄31,557,600 Julian year (IAU system of units)
* 1⁄(1 hertz ); more generally, (period of wave in seconds) =
1⁄(frequency of wave in hertz), where (period of
wave)×(wavenumber ) = 1⁄(velocity of wave) in seconds per metre
(SI ) or in kayser -seconds (
* 1⁄(1 becquerel ).
HISTORY OF DEFINITION
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, and the differences in length between daytime and nighttime
hours in any given day.
Hipparchus (c. 150 BC) and
AD 150) subdivided the day into sixty parts (the sexagesimal system).
They also used a mean hour ( 1⁄24 day); simple fractions of an
hour ( 1⁄4, 2⁄3, etc.); and time-degrees ( 1⁄360 day,
equivalent to four modern minutes).
* The Babylonians after 300 BC also subdivided the day using the
sexagesimal system, and divided each subsequent subdivision by sixty:
that is, by 1⁄60, by 1⁄60 of that, by 1⁄60 of that,
etc., to at least six places after the sexagesimal point - a precision
equivalent to better than 2 microseconds. 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
1⁄3 modern seconds (the helek of the modern Hebrew calendar), but
did not sexagesimally subdivide these smaller units of time. No
sexagesimal unit of the day was ever used as an independent unit of
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.
* 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.
* The modern second is subdivided using decimals - although the term
third ( 1⁄60 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
Orpheus in the Fremersdorf collection, dated between 1560
and 1570. :417–418 During the 3rd quarter of the 16th century, Taqi
al-Din built a clock with marks every 1/5 minute. In 1579, Jost
Bürgi built a clock for William of Hesse that marked seconds. :105 In
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. :104
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
London clockmaker William Clement added this seconds
pendulum to the original pendulum clock of
Christiaan Huygens . 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." 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 1⁄86,400 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
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.
The second was thus defined as:
the fraction 1⁄31,556,925.9747 of the tropical year for 1900
January 0 at 12 hours ephemeris time.
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. 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).
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
United States Naval Observatory
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 , 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 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.
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. )
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
The definition of the second was later refined at the 1997 meeting of
BIPM to include the statement
This definition refers to a caesium atom at rest at a temperature of
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., “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
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). 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.
* The phrase "One Mississippi, Two Mississippi" is one of several
similar phrases used to measure time verbally.
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.
SI multiples for second (s)
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 has become either the basis for legal time of
many countries, or accepted as the de facto basis for standard civil
Orders of magnitude (time)
* Coordinated Universal
* International Atomic
International System of Units
International System of Units
NOTES AND REFERENCES
* ^ A B C D "
Unit of time (second)". SI Brochure.
BIPM . Retrieved
December 22, 2013.
* ^ Second. Merriam Webster Learner's Dictionary.
* ^ "Online Etymology Dictionary".
* ^ "Base unit definitions: Second". physics.nist.gov. Retrieved
September 9, 2016.
* ^ BN Taylor; A Thompson, eds. (2008). "Appendix 2". The
International System of Units
International System of Units (SI) (PDF).
330. pp. 53 ff. Retrieved August 25, 2014.
* ^ "NRC\'s Cesium Fountain
Clock - FCs1". National Research
Council of Canada . Retrieved November 29, 2013.
* ^ Toomer, G. J. (1998). Ptolemy's Almagest. Princeton, New
Jersey: Princeton University Press. pp. 6–7, 23, 211–216. ISBN
* ^ O Neugebauer (1975). A history of ancient mathematical
Springer-Verlag . ISBN 0-387-06995-X .
* ^ See page 325 in O Neugebauer (1949). "The astronomy of
Maimonides and its sources".
Hebrew Union College Annual . 22:
* ^ 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.
* ^ R Bacon (2000) . The Opus Majus of Roger Bacon. BR Belle.
University of Pennsylvania Press
University of Pennsylvania Press . table facing page 231. ISBN
* ^ A B C Landes, David S. (1983). Revolution in
Time . Cambridge,
Massachusetts: Harvard University Press. ISBN 0-674-76802-7 .
* ^ 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).
* ^ Helaine Selin (July 31, 1997). Encyclopaedia of the
Science, Technology, and Medicine in Non-Westen Cultures. Springer
Science & Business Media. p. 934. ISBN 978-0-7923-4066-9 .
* ^ Greg Jenner (January 29, 2015). A Million Years in a Day: A
History of Everyday Life. Orion. p. 275. ISBN
* ^ Jessica Chappell (October 1, 2001). "The Long Case Clock: The
Science and Engineering that Goes Into a Grandfather Clock". Illumin .
* ^ Jenkin, ed. (1873). Reports of the committee on electrical
standards. British Association for the Advancement of Science. p. 90.
* ^ A B C D E "Leap Seconds".
Time Service Department, United
States Naval Observatory . Retrieved November 22, 2015.
* ^ 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
International Astronomical Union and were formally adopted by
Commission 4 and the General Assembly of the Union in Rome in
* ^ A B 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 . CS1 maint:
Multiple names: authors list (link )
* ^ S Leschiutta (2005). "The definition of the 'atomic' second".
Metrologia . 42 (3): S10–S19.
Bibcode :2005Metro..42S..10L. doi
* ^ 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. CS1 maint: Uses
editors parameter (link )
* ^ DD McCarthy, C Hackman, R Nelson; Hackman; Nelson (2008). "The
Physical Basis of the Leap Second".
Astronomical Journal . 136 (5):
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. CS1 maint: Multiple names: authors list (link )
* ^ In the late 1950s, the caesium standard was used to measure
both the current mean length of the second of mean solar time (UT2)
(7009919263183000000♠9192631830 cycles) and also the second of
ephemeris time (ET) (7009919263177000000♠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 7009919263177000000♠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".
* ^ 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 .
* ^ AD Ludlow; et al. (2006). "Systematic study of the 87Sr clock
transition in an optical lattice".
Physical Review Letters . 96 (3):
Bibcode :2006PhRvL..96c3003L. arXiv :physics/0508041 . doi
:10.1103/PhysRevLett.96.033003 . CS1 maint: Explicit use of et al.
* ^ "Optical
Frequency - Research Projects". February 28, 2006.
Archived from the original on January 25, 2009.
* ^ R Wynands, S Weyers; Weyers (2005). "Atomic fountain clocks".
Metrologia . 42 (3): S64–S79.
Bibcode :2005Metro..42S..64W. doi
* ^ "
NIST-F1 Cesium Fountain Atomic Clock".
NIST . Retrieved August
* ^ McCarty, Dennis D. ; Seidelmann, Kenneth P. (2009). Time: From
Earth Rotation to Atomic Physics. Weinheim: Wiley. pp. 68, 232.
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* National Physical Laboratory: Trapped ion