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The second (symbol: s) is the 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 pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
(SI), historically defined as of a day – this factor derived from the division of the day first into 24
hour An hour (symbol: h; also abbreviated hr) is a unit of time conventionally reckoned as of a day and scientifically reckoned between 3,599 and 3,601 seconds, depending on the speed of Earth's rotation. There are 60 minutes in an hour, and 24 ...
s, then to 60 minutes and finally to 60 seconds each (24 × 60 × 60 = 86400). The current and formal definition in the International System of Units ( SI) is more precise:
The second ..is defined by taking the fixed numerical value of the caesium frequency, Δ''ν''Cs, the unperturbed ground-state
hyperfine In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate energy levels and the resulting splittings in those energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the ...
transition frequency of the caesium 133 atom, to be when expressed in the unit Hz, which is equal to s−1.
This current definition was adopted in 1967 when it became feasible to define the second based on fundamental properties of nature with caesium clocks. Because the speed of Earth's rotation varies and is slowing ever so 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 obser ...
is added at irregular intervals to civil time to keep clocks in sync with Earth's rotation.


Uses

Analog clocks and
watch A watch is a portable 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, attached ...
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. SI prefixes are frequently combined with the word ''second'' to denote subdivisions of the second: milliseconds (thousandths), microseconds (millionths), nanoseconds (billionths), and sometimes smaller units of a second. Multiples of seconds are usually counted in hours and minutes. Though SI prefixes may also be used to form multiples of the second such as kiloseconds (thousands of seconds), such units are rarely used in practice. An everyday experience with small fractions of a second is a 1-gigahertz microprocessor which has a cycle time of 1 nanosecond. Camera shutter speeds 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 with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form ...
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 that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions betwe ...
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 (referred to as civil time in modern usage) when direct sunlight shines by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a f ...
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 object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as ...
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 A metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or submultiple of the unit. All metric prefixes used today are decadic. Each prefix has a unique symbol that is prepended to any unit symbol. The pre ...
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 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 astronomical year or ...
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 obser ...
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 directly part of other units, such as
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
measured in
hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that o ...
(inverse seconds or second−1),
speed In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quant ...
in meters per second, and
acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by ...
in meters per second squared. The metric system unit becquerel, a measure of radioactive decay, is measured in inverse seconds. Though many derivative units for everyday things are reported in terms of larger units of time, not seconds, they are ultimately defined in terms of the SI second; this includes time expressed 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. Moreover, most other SI base units are defined by their relationship to the second: the
metre The metre ( British spelling) or meter ( American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pre ...
is defined by setting the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...
(in a vacuum) to be 299 792 458 m/s, exactly; definitions of the SI base units kilogram, ampere,
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and ...
, and candela also depend on the second. The only base unit whose definition does not depend on the second is the mole, and only two of the 22 named derived units,
radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that ...
and steradian, do not depend on the second either.


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 (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 by which the world regulates clocks and time. It is within about one second of Solar time#Mean solar time, mean solar time (such as Universal Time, UT1) at 0° longitude (at the I ...
(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 obser ...
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 Universal Time (UT or UT1) is a time standard based on Earth's rotation. While originally it was mean solar time at 0° longitude, precise measurements of the Sun are difficult. Therefore, UT1 is computed from a measure of the Earth's angle wit ...
. 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 with the symbol Sr and atomic number 38. An alkaline earth metal, strontium is a soft silver-white yellowish metallic element that is highly chemically reactive. The metal forms a dark oxide layer when it is e ...
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) (or cesium in American English) is a chemical element with the symbol Cs and atomic number 55. It is a soft, silvery-golden alkali metal with a melting point of , which makes it one of only five elemental metals that a ...
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=), 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 (referred to as civil time in modern usage) when direct sunlight shines by the apparent position of the Sun in the sky. In the narrowest sense of the word, it consists of a f ...
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: Ὀρφεύς, classical pronunciation: ; french: Orphée) is a Thracian bard, legendary musician and prophet in ancient Greek religion. He was also a renowned poet and, according to the legend, travelled with J ...
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 and Prague, was a Swiss clockmaker, a maker of astronomical instruments and a ma ...
built a clock for William of Hesse that marked seconds. 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. In 1656, Dutch scientist
Christiaan Huygens Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists o ...
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 and clockmaker who invented the marine chronometer, a long-sought-after device for solving the problem of calculating longitude while at sea. Harrison's solution revo ...
's maritime chronometers could keep time accurate to within one second in 100 days. 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 of a mean solar day.


Fraction of an ephemeris year

Sometime 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 scale expressed in units of the sidereal year at that epoch by the IAU 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 or solar year (or tropical period) is the time that the Sun takes to return to the same position in the sky of a celestial body of the Solar System such as the Earth, completing a full cycle of seasons; for example, the time ...
, 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 and periodization, an epoch or reference epoch is an instant in time chosen as the origin of a particular calendar era. The "epoch" serves as a reference point from which time is measured. The moment of epoch is usually decided ...
. The second was thus defined as "the fraction of the tropical year for 1900 January 0 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 pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
in 1960.


"Atomic" second

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 periods of the radiation corresponding to the transition between the two 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.Draft resolutions
of the 27. General Conference on Weights and Measures in November 2022, Section E, p. 25
Atomic clocks now set the length of a second and the time standard for the world.


Table


Future redefinition

In 2022, the best realisation of the second is done with caesium primary standard clocks such as IT-CsF2, NIST-F2, NPL-CsF2, PTB-CSF2, SU–CsFO2 or SYRTE-FO2. These clocks work by laser-cooling a cloud of Cs atoms to a microkelvin in a magneto-optic trap. These cold atoms are then launched vertically by laser light. The atoms then undergo Ramsey excitation in a microwave cavity. The fraction of excited atoms are then detected by laser beams. These clocks have systematic uncertainty, which is equivalent to 50 picoseconds per day. A system of several fountains worldwide contribute to International Atomic Time. These caesium clocks also underpin optical frequency measurements.
Optical clock An atomic clock is a clock that measures time by monitoring the resonant frequency of atoms. It is based on atoms having different energy levels. Electron states in an atom are associated with different energy levels, and in transitions betwee ...
s are based on forbidden optical transitions in ions or atoms. They have frequencies around , with a natural linewidth \Delta f of typically 1 Hz, so the Q-factor is about , or even higher. They have better stabilities than microwave clocks, which means that they can facilitate evaluation of lower uncertainties. They also have better time resolution, which means the clock "ticks" faster. Optical clocks use either a single ion, or an optical lattice with – atoms.


Rydberg constant

A definition based on the Rydberg constant would involve fixing the value to a certain value: R_=\frac=\frac. The Rydberg constant describes the energy levels in a hydrogen atom with the nonrelativistic approximation E_n \approx -\frac. The only viable way to fix the Rydberg constant involves trapping and cooling hydrogen. Unfortunately, this is difficult because it is very light and the atoms move very fast, causing Doppler shifts. The radiation needed to cool the hydrogen –– is also difficult. Another hurdle involves improving the uncertainty in QED calculations.


Requirements

A redefinition must include improved optical clock reliability. TAI must be contributed to by optical clocks before the BIPM affirms a redefinition. A consistent method of sending signals must be developed before the second is redefined, such as fiber-optics.


SI multiples

SI prefixes 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: minutes,
hour An hour (symbol: h; also abbreviated hr) is a unit of time conventionally reckoned as of a day and scientifically reckoned between 3,599 and 3,601 seconds, depending on the speed of Earth's rotation. There are 60 minutes in an hour, and 24 ...
s, days, and in astronomy Julian years. Reprinted from the "IAU Style Manual" by G.A. Wilkinson, Comm. 5, in IAU Transactions XXB (1987).


See also

* Caesium standard * Orders of magnitude (time) *
Seconds pendulum A seconds pendulum is a pendulum whose period is precisely two seconds; one second for a swing in one direction and one second for the return swing, a frequency of 0.5 Hz. Pendulum A pendulum is a weight suspended from a pivot so that ...
* Time standard


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 Units of time