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The second (symbol: s) is the unit of
time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, ...
in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, 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 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 clock The caesium standard is a primary frequency standard in which the photon absorption by transitions between the two hyperfine ground states of caesium-133 atoms is used to control the output frequency. The first caesium clock was built by Louis ...
s. 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 observ ...
is added at irregular intervals to
civil time In modern usage, civil time refers to statutory time as designated by civilian authorities. Modern civil time is generally national standard time in a time zone at a fixed offset from Coordinated Universal Time (UTC), possibly adjusted by dayligh ...
to keep clocks in sync with Earth's rotation.


Uses

Analog clock A clock or a timepiece is a device used to measure 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 such as the day, the lunar month and the ...
s 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 b ...
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 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 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 observ ...
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 Magnitude may refer to: Mathematics *Euclidean vector, a quantity defined by both its magnitude and its direction *Magnitude (ma ...
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 t ...
in meters per second squared. The metric system unit
becquerel The becquerel (; symbol: Bq) is the unit of radioactivity in the International System of Units (SI). One becquerel is defined as the activity of a quantity of radioactive material in which one nucleus decays per second. For applications relatin ...
, 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 The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all ...
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 prefi ...
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 ...
(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 phy ...
, and
candela The candela ( or ; symbol: cd) is the unit of luminous intensity in the International System of Units (SI). It measures luminous power per unit solid angle emitted by a light source in a particular direction. Luminous intensity is analogous t ...
also depend on the second. The only base unit whose definition does not depend on the second is the
mole Mole (or Molé) may refer to: Animals * Mole (animal) or "true mole", mammals in the family Talpidae, found in Eurasia and North America * Golden moles, southern African mammals in the family Chrysochloridae, similar to but unrelated to Talpida ...
, 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 tha ...
and
steradian The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry, and is analogous to the radian, which quantifies planar angles. Whereas an angle in radian ...
, 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 International Atomic Time (abbreviated TAI, from its French name ) is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid. TAI is a weighted average of the time kept by over 450 ato ...
(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 mean solar time (such as UT1) at 0° longitude (at the IERS Reference Meridian as the currently use ...
(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 observ ...
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 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 Gravitational time dilation is a form of time dilation, an actual difference of elapsed time between two events as measured by observers situated at varying distances from a gravitating mass. The lower the gravitational potential (the closer ...
.


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 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 sundials. 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 Tycho Brahe ( ; born Tyge Ottesen Brahe; generally called Tycho (14 December 154624 October 1601) was a Danish astronomer, known for his comprehensive astronomical observations, generally considered to be the most accurate of his time. He was ...
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 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 revol ...
'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 and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
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 and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Systems of measurement i ...
. 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 The International Astronomical Union (IAU; french: link=yes, Union astronomique internationale, UAI) is a nongovernmental organisation with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach ...
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 f ...
, 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 by ...
. 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 ...
at 12 hours ephemeris time". This definition was adopted as part of the International System of Units 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 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 o ...
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 clocks 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 An optical lattice is formed by the interference of counter-propagating laser beams, creating a spatially periodic polarization pattern. The resulting periodic potential may trap neutral atoms via the Stark shift. Atoms are cooled and congrega ...
with – atoms.


Rydberg constant

A definition based on the
Rydberg constant In spectroscopy, the Rydberg constant, symbol R_\infty for heavy atoms or R_\text for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to the electromagnetic spectra of an atom. The constant first aro ...
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, hours, 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) An order of magnitude of time is usually a decimal prefix or decimal order-of-magnitude quantity together with a base unit of time, like a microsecond or a million years. In some cases, the order of magnitude may be implied (usually 1), like a ...
*
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 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 o ...


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