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The second (symbol: s, also abbreviated: sec) is the
base unit
base unit
of
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
in the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms_and_initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wi ...
(SI) (french: Système International d’unités), commonly understood and historically defined as of a
day A day is approximately the period during which the Earth completes one rotation around its axis, which takes around 24 hours. A solar day is the length of time which elapses between the Sun reaching its highest point in the sky two consecutive t ...

day
– this factor derived from the division of the day first into 24
hour An hour (metric symbol, symbol: h; also abbreviated hr) is a unit of measurement, unit of time conventionally reckoned as of a day and scientifically reckoned as 3,599–3,601 seconds, depending on conditions. There are 60 minutes in an hour, a ...
s, then to 60
minute The minute is a unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation ...
s and finally to 60 seconds each.
Analog clock Analog or analogue may refer to: Computing and electronics * Analog signal An analog signal is any continuous signal for which the time-varying feature of the signal is a representation of some other time-varying quantity, i.e., ''analogous' ...
s and
watch A watch is a portable Clock, timepiece intended to be carried or worn by a person. It is designed to keep a consistent movement despite the motions caused by the person's activities. A wristwatch is designed to be worn around the wrist, attach ...

watch
es often have sixty tick marks on their faces, representing seconds (and minutes), and a "second hand" to mark the passage of time in seconds. Digital clocks and watches often have a two-digit seconds counter. The second is also part of several other units of measurement like meters per second for
speed In everyday use and in kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, bodies (objects), and systems of bodies (groups of objects) without considerin ...

speed
, meters per second per second for
acceleration In mechanics Mechanics (Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approx ...

acceleration
, and cycles per second for
frequency Frequency is the number of occurrences of a repeating event per unit of time A unit of time is any particular time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparen ...

frequency
. Although the historical definition of the unit was based on this division of the Earth's rotation cycle, the formal definition in the International System of Units (
SI
SI
) is a much steadier timekeeper:
''The second is defined as being equal to the time duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the fundamental unperturbed ground-state of the
caesium-133 Caesium Caesium (IUPAC spelling) (American and British English spelling differences, also spelled cesium in American English) is a chemical element with the Symbol (chemistry), symbol Cs and atomic number 55. It is a soft, silvery-golde ...

caesium-133
atom.''
Because the Earth's rotation varies and is also slowing very slightly, a
leap second A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC), to accommodate the difference between precise time (International Atomic Time (TAI), as measured by atomic clocks) and imprecise solar tim ...

leap second
is added at irregular intervals to clock time to keep clocks in sync with Earth's rotation. Multiples of seconds are usually counted in hours and minutes. Fractions of a second are usually counted in tenths or hundredths. In scientific work, small fractions of a second are counted in milliseconds (thousandths), microseconds (millionths), nanoseconds (billionths), and sometimes smaller units of a second. An everyday experience with small fractions of a second is a 1-gigahertz microprocessor which has a cycle time of 1 nanosecond. Camera
shutter speed In photography Photography is the art Art is a diverse range of (products of) human activities involving creative imagination to express technical proficiency, beauty, emotional power, or conceptual ideas. There is no generall ...

shutter speed
s are often expressed in fractions of a second, such as second or second.
Sexagesimal Sexagesimal, also known as base 60 or sexagenary, is a numeral system A numeral system (or system of numeration) is a writing system A writing system is a method of visually representing verbal communication Communication (from Latin ...
divisions of the day from a calendar based on astronomical observation have existed since the third millennium BC, though they were not seconds as we know them today. Small divisions of time could not be measured back then, so such divisions were mathematically derived. The first timekeepers that could count seconds accurately were pendulum clocks invented in the 17th century. Starting in the 1950s,
atomic clock An atomic clock is a clock A clock is a device used to measure, verify, keep, and indicate time. The clock is one of the oldest human inventions, meeting the need to measure intervals of time shorter than the natural units: the day, t ...

atomic clock
s became better timekeepers than Earth's rotation, and they continue to set the standard today.


Clocks and solar time

A mechanical clock, one which does not depend on measuring the relative rotational position of the Earth, keeps uniform time called ''mean time'', within whatever accuracy is intrinsic to it. That means that every second, minute and every other division of time counted by the clock will be the same duration as any other identical division of time. But a
sundial A sundial is a horological device that tells the time of day (in modern usage referred to as civil time In modern usage, civil time refers to statutory time scales designated by civilian authorities, or to local time indicated by clocks. Mo ...

sundial
which measures the relative position of the sun in the sky called ''apparent time'', does not keep uniform time. The time kept by a sundial varies by time of year, meaning that seconds, minutes and every other division of time is a different duration at different times of the year. The time of day measured with mean time versus apparent time may differ by as much as 15 minutes, but a single day will differ from the next by only a small amount; 15 minutes is a cumulative difference over a part of the year. The effect is due chiefly to the obliqueness of Earth's axis with respect to its
orbit In celestial mechanics, an orbit is the curved trajectory of an physical body, object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an satellite, artificial satellite around an object or po ...

orbit
around the sun. The difference between apparent solar time and mean time was recognized by astronomers since antiquity, but prior to the invention of accurate mechanical clocks in the mid-17th century, sundials were the only reliable timepieces, and apparent solar time was the only generally accepted standard.


Events and units of time in seconds

Fractions of a second are usually denoted in decimal notation, for example 2.01 seconds, or two and one hundredth seconds. Multiples of seconds are usually expressed as minutes and seconds, or hours, minutes and seconds of clock time, separated by colons, such as 11:23:24, or 45:23 (the latter notation can give rise to ambiguity, because the same notation is used to denote hours and minutes). It rarely makes sense to express longer periods of time like hours or days in seconds, because they are awkwardly large numbers. For the metric unit of second, there are decimal prefixes representing 10 to 10 seconds. Some common units of time in seconds are: a minute is 60 seconds; an hour is 3,600 seconds; a day is 86,400 seconds; a week is 604,800 seconds; a year (other than
leap year A leap year (also known as an intercalary year or wikt:bissextile, bissextile year) is a calendar year that contains an additional day (or, in the case of a lunisolar calendar, a month) added to keep the calendar year synchronized with the astron ...

leap year
s) is 31,536,000 seconds; and a ( Gregorian) century averages 3,155,695,200 seconds; with all of the above excluding any possible
leap second A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC), to accommodate the difference between precise time (International Atomic Time (TAI), as measured by atomic clocks) and imprecise solar tim ...

leap second
s. Some common events in seconds are: a stone falls about 4.9 meters from rest in one second; a pendulum of length about one meter has a swing of one second, so pendulum clocks have pendulums about a meter long; the fastest human sprinters run 10 meters in a second; an ocean wave in deep water travels about 23 meters in one second; sound travels about 343 meters in one second in air; light takes 1.3 seconds to reach Earth from the surface of the Moon, a distance of 384,400 kilometers.


Other units incorporating seconds

A second is part of other units, such as frequency measured in hertz (inverse seconds or second−1), speed (meters per second) and acceleration (meters per second squared). The metric system unit becquerel, a measure of radioactive decay, is measured in inverse seconds. The meter is defined in terms of the speed of light and the second; definitions of the metric base units kilogram, ampere, kelvin, and candela also depend on the second. The only base unit whose definition does not depend on the second is the mole. Of the 22 named derived units of the SI, only two (radian and steradian), do not depend on the second. Many derivative units for everyday things are reported in terms of larger units of time, not seconds, such as clock time in hours and minutes, velocity of a car in kilometers per hour or miles per hour, kilowatt hours of electricity usage, and speed of a turntable in rotations per minute.


Timekeeping standards

A set of atomic clocks throughout the world keeps time by consensus: the clocks "vote" on the correct time, and all voting clocks are steered to agree with the consensus, which is called
International Atomic Time International Atomic Time (TAI, from the French name ) is a high-precision atomic coordinate In geometry Geometry (from the grc, γεωμετρία; ''wikt:γῆ, geo-'' "earth", ''wikt:μέτρον, -metron'' "measurement") is, with a ...
(TAI). TAI "ticks" atomic seconds. Civil time is defined to agree with the rotation of the Earth. The international standard for timekeeping is
Coordinated Universal Time Coordinated Universal Time or UTC is the primary time standard A time standard is a specification for measuring time: either the rate at which time passes; or points in time; or both. In modern times, several time specifications have been o ...
(UTC). This time scale "ticks" the same atomic seconds as TAI, but inserts or omits
leap second A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC), to accommodate the difference between precise time (International Atomic Time (TAI), as measured by atomic clocks) and imprecise solar tim ...

leap second
s as necessary to correct for variations in the rate of rotation of the Earth. A time scale in which the seconds are not exactly equal to atomic seconds is UT1, a form of
universal time#REDIRECT Universal Time Universal Time (UT) is a time standard based on Earth's rotation. There are several versions of Universal Time, which differ by up to a few seconds. The most commonly used are Coordinated Universal Time (UTC) and UT1 (see ...

universal time
. UT1 is defined by the rotation of the Earth with respect to the sun, and does not contain any leap seconds. UT1 always differs from UTC by less than a second.


Optical lattice clock

While they are not yet part of any timekeeping standard, optical lattice clocks with frequencies in the visible light spectrum now exist and are the most accurate timekeepers of all. A
strontium Strontium is the chemical element upright=1.0, 500px, The chemical elements ordered by link=Periodic table In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science ...

strontium
clock with frequency 430  THz, in the red range of visible light, now holds the accuracy record: it will gain or lose less than a second in 15 billion years, which is longer than the estimated age of the universe. Such a clock can measure a change in its elevation of as little as 2 cm by the change in its rate due to gravitational time dilation.


History of definition

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 Caesium (IUPAC spelling) (American and British English spelling differences, also spelled cesium in American English) is a chemical element with the Symbol (chemistry), symbol Cs and atomic number 55. It is a soft, silvery-golden alkali ...

caesium
atomic clock, and they have 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=), not of the hour like the modern second (=). 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.


Fraction of solar day

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 A sundial is a horological device that tells the time of day (in modern usage referred to as civil time In modern usage, civil time refers to statutory time scales designated by civilian authorities, or to local time indicated by clocks. Mo ...

sundial
s. By that time, sexagesimal divisions of time were well established in Europe. 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 which marked seconds is an unsigned clock depicting
Orpheus Orpheus (; Ancient Greek Ancient Greek includes the forms of the used in and the from around 1500 BC to 300 BC. It is often roughly divided into the following periods: (), Dark Ages (), the period (), and the period (). Ancie ...

Orpheus
in the Fremersdorf collection, dated between 1560 and During the 3rd quarter of the 16th century, Taqi al-Din built a clock with marks every 1/5 minute. In 1579,
Jost Bürgi Jost Bürgi (also ''Joost, Jobst''; Latinized surname ''Burgius'' or ''Byrgius''; 28 February 1552 – 31 January 1632), active primarily at the courts in Kassel Kassel (; in Germany, spelled Cassel until 1926) is a city on the Fulda River in ...
built a clock for William of Hesse that marked seconds. In 1581,
Tycho Brahe Tycho Brahe ( ; born Tyge Ottesen Brahe; 14 December 154624 October 1601) was a Danish , known for his accurate and comprehensive astronomical observations. He was born in , which became part of Sweden in the next century. Tycho was well known ...

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. In 1656, Dutch scientist
Christiaan Huygens Christiaan Huygens ( , also , ; la, Hugenius; 14 April 1629 – 8 July 1695), also spelled Huyghens, was a Dutch mathematician, physicist, astronomer and inventor, who is regarded as one of the greatest scientists of all time and a major fig ...

Christiaan Huygens
invented the first pendulum clock. It had a pendulum length of just under a meter which gave 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 John Harrison ( – 24 March 1776) was a self-educated English carpenter Carpenters in an Indian village Carpentry is a skilled trade and a craft in which the primary work performed is the cutting, shaping and installation of building mate ...

John Harrison
's maritime chronometers could keep time accurate to within one second in 100 days. In 1832,
Gauss Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician This is a List of German mathematician A mathematician is someone who uses an extensive knowledge of m ...

Gauss
proposed using the second as the base unit of time in his millimeter-milligram-second
system of units A system of measurement is a collection of units of measurement A unit of measurement is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of ...
. The
British Association for the Advancement of Science The British Science Association (BSA) is a charity Charity may refer to: Giving * Charitable organization or charity, a non-profit organization whose primary objectives are philanthropy and social well-being * Charity (practice), the practice ...
(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 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 of a mean solar day.


Fraction of an ephemeris year

Some time in the late 1940s, quartz crystal oscillator clocks with an operating frequency of ~100 kHz advanced to keep time with accuracy better than 1 part in 108 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. 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'' (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. This resulted in adoption of an
ephemeris time The term ephemeris time (often abbreviated ET) can in principle refer to time in association with any ephemeris (itinerary of the trajectory of an astronomical object). In practice it has been used more specifically to refer to: # a former stand ...
scale expressed in units of the
sidereal year A sidereal year (, ; from Latin "asterism, star") is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. Hence, it is also the time taken for the Sun to return to the same position with respect to the fixed stars af ...
at that epoch by the
IAU The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a Non-governmental organization, nongovernmental organisation with the objective of advancing astronomy in all aspects, including promoting ...
in 1952. This extrapolated timescale brings the observed positions of the celestial bodies into accord with Newtonian dynamical theories of their motion. In 1955, the
tropical year A tropical year (also known as a solar year or tropical period) is the time Time is the continued of and that occurs in an apparently succession from the , through the , into the . It is a component quantity of various s used to event ...
, 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 In chronology 222px, Joseph Scaliger's ''De emendatione temporum'' (1583) began the modern science of chronology Chronology (from Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-E ...
. The second was thus defined as "the fraction of the tropical year for 1900
January 0 Several non-standard dates are used in calendars. Some are used sarcastically, some for scientific or mathematical purposes, and some for exceptional or fictional calendars. January 0 January 0 or 0 January is an alternative name for December 31. ...
at 12 hours ephemeris time". This definition was adopted as part of the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms_and_initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wi ...
in 1960.


"Atomic" second

But 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. Since 1967, the second has been defined as exactly "the duration of 9,192,631,770 of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the
caesium-133 Caesium Caesium (IUPAC spelling) (American and British English spelling differences, also spelled cesium in American English) is a chemical element with the Symbol (chemistry), symbol Cs and atomic number 55. It is a soft, silvery-golde ...

caesium-133
atom" (at a temperature of 0 K). 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. Atomic clocks now set the length of a second and the
time standard A time standard is a specification for measuring time: either the rate at which time passes; or points in time; or both. In modern times, several time specifications have been officially recognized as standards, where formerly they were matters of ...
for the world.


SI multiples

SI prefix The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms_and_initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wi ...
es are commonly used for times shorter than one second, but rarely for multiples of a second. Instead, certain non-SI units are permitted for use in SI:
minute The minute is a unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatrical presentation ...
s,
hour An hour (metric symbol, symbol: h; also abbreviated hr) is a unit of measurement, unit of time conventionally reckoned as of a day and scientifically reckoned as 3,599–3,601 seconds, depending on conditions. There are 60 minutes in an hour, a ...
s,
day A day is approximately the period during which the Earth completes one rotation around its axis, which takes around 24 hours. A solar day is the length of time which elapses between the Sun reaching its highest point in the sky two consecutive t ...

day
s, and in astronomy Julian years. Reprinted from the "IAU Style Manual" by G.A. Wilkinson, Comm. 5, in IAU Transactions XXB (1987).


See also

*
Orders of magnitude (time) An order of magnitude An order of magnitude is an approximation of the logarithm In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure ...
*
Seconds pendulum A seconds pendulum is a pendulum A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity ...
*
Time standard A time standard is a specification for measuring time: either the rate at which time passes; or points in time; or both. In modern times, several time specifications have been officially recognized as standards, where formerly they were matters of ...


Notes


References


External links


National Physical Laboratory: ''Trapped ion optical frequency standards''

''High-accuracy strontium ion optical clock''; National Physical Laboratory (2005)


* ttp://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
Official BIPM definition of the second

The leap second: its history and possible future




{{Authority control Centimetre–gram–second system of units Orders of magnitude (time) SI base units UCUM base units Units of time