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The second (symbol: s) is the unit of time 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. E ...
(SI), historically defined as of a
day A day is the time period of a full rotation of the Earth with respect to the Sun. On average, this is 24 hours, 1440 minutes, or 86,400 seconds. In everyday life, the word "day" often refers to a solar day, which is the length between two so ...
– 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 ho ...
s, then to 60
minute The minute is a unit of time usually equal to (the first sexagesimal fraction) of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds (there is a provision to insert a nega ...
s 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 The ground state of a quantum mechanics, quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than t ...
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 nuc ...
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 is added at irregular intervals to civil time to keep clocks in sync with Earth's rotation.


Uses

Analog clocks and watches 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 prefix 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. E ...
es 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 speed In photography, shutter speed or exposure time is the length of time that the film or digital sensor inside the camera is exposed to light (that is, when the camera's shutter (photography), shutter is open) when taking a photograph. The am ...
s are often expressed in fractions of a second, such as second or second. Sexagesimal 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 clocks 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 flat ...
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 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 (mathematics), multiple or submultiple of the unit. All metric prefixes used today are decimal, decadic. Each prefix has a unique symbol that is prepen ...
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 years) is 31,536,000 seconds; and a ( Gregorian) century averages 3,155,695,200 seconds; with all of the above excluding any possible leap seconds. 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 measured in hertz (inverse seconds or second−1), speed in meters per second, and acceleration 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 is defined by setting the speed of light (in a vacuum) to be 299 792 458 m/s, exactly; definitions of the SI base units
kilogram The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce worldwide, and is often simply called a kilo colloquially ...
,
ampere The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to elect ...
, kelvin, 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 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 (UTC). This time scale "ticks" the same atomic seconds as TAI, but inserts or omits leap seconds 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. 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 ex ...
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 flat ...
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 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''; Latinisation of names, Latinized surname ''Burgius'' or ''Byrgius''; 28 February 1552 – 31 January 1632), active primarily at the courts