Second

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second
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A pendulum-governed escapement of a clock, ticking every second
General information
Unit system SI base unit
Unit of Time
Symbols

The second (symbol: s, abbreviation: sec) is the base unit of time in the International System of Units (SI) (French: Système International d’unités), commonly understood and historically defined as 186400 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. 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. The second is also part of several other units of measurement like meters per second for velocity, meters per second per second for acceleration, and cycles per second for frequency.

Contents

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) is a much steadier timekeeper: it is defined by taking the fixed numerical value of the caesium frequency ∆νCs, the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s−1. [1] [2] Because the Earth's rotation varies and is also slowing ever so slightly, a leap second is periodically added to clock time [nb 1] 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 speeds are often expressed in fractions of a second, such as 130 second or 11000 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[ citation needed ]. 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 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 representing 10−24 to 1024 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 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 (TAI). TAI "ticks" atomic seconds. [3]

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. [4]

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. [5] 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. [6]

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, 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 = day/60×60), not of the hour like the modern second (= hour/60×60). 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 realizable 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. [nb 2] [nb 3]

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. [nb 4]

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 1570. [9] :417–418 [10] During the 3rd quarter of the 16th century, Taqi al-Din built a clock with marks every 1/5 minute. [11] In 1579, Jost Bürgi built a clock for William of Hesse that marked seconds. [9] :105 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. [9] :104

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'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." [12] 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 186,400 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. [13] This resulted in adoption of an ephemeris time scale expressed in units of the sidereal year at that epoch by the IAU in 1952. [14] This extrapolated timescale brings the observed positions of the celestial bodies into accord with Newtonian dynamical theories of their motion. [13] In 1955, the tropical year, 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. The second was thus defined as "the fraction 131,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time". [13] This definition was adopted as part of the International System of Units in 1960. [15]

"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. [16] 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" (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 for the world. [17]

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. [18]

SI multiples for second (s)
SubmultiplesMultiples
ValueSI symbolNameValueSI symbolNameHuman-readable
10−1 sdsdecisecond101 sdasdecasecond10 seconds
10−2 scscentisecond102 shshectosecond1 minute 40 seconds
10−3 smsmillisecond103 skskilosecond16 minutes 40 seconds
10−6 sµsmicrosecond106 sMsmegasecond11.6 days
10−9 snsnanosecond109 sGsgigasecond31.7 years
10−12 spspicosecond1012 sTsterasecond31,700 years
10−15 sfsfemtosecond1015 sPspetasecond31.7 million years
10−18 sasattosecond1018 sEsexasecond31.7 billion years
10−21 szszeptosecond1021 sZszettasecond31.7 trillion years
10−24 sysyoctosecond1024 sYsyottasecond31.7 quadrillion years

See also

Notes

  1. Clock time (that is, civil time) is set, directly or indirectly, to Coordinated Universal Time, which includes leap seconds. Other time scales are used in scientific and technical fields which do not contain leap seconds.
  2. In 1000, the Persian scholar al-Biruni, writing in Arabic, used the term second, and defined the division of time between new moons of certain specific weeks as a number of days, hours, minutes, seconds, thirds, and fourths after noon Sunday. [7]
  3. In 1267, the medieval English scientist Roger Bacon, writing in Latin, defined the division of time between full moons as a number of hours, minutes, seconds, thirds, and fourths (horae, minuta, secunda, tertia, and quarta) after noon on specified calendar dates. [8]
  4. It may be noted that 60 is the smallest multiple of the first 6 counting numbers. So a clock with 60 divisions would have a mark for thirds, fourths, fifths, sixths and twelfths (the hours); whatever units the clock would likely keep time in, would have marks.

Related Research Articles

International Atomic Time is a high-precision atomic coordinate time standard based on the notional passage of proper time on Earth's geoid. It is the principal realisation of Terrestrial Time. It is also the basis for Coordinated Universal Time (UTC), which is used for civil timekeeping all over the Earth's surface. As of 1 January 2017, when another leap second was added, TAI is exactly 37 seconds ahead of UTC. The 37 seconds results from the initial difference of 10 seconds at the start of 1972, plus 27 leap seconds in UTC since 1972.

Clock Instrument for measuring, keeping or indicating time.

A clock is a device used to measure, 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, the lunar month, and the year. Devices operating on several physical processes have been used over the millennia.

Day Unit of time

A day is approximately the period of time during which the Earth completes one rotation around its axis. A solar day is the length of time which elapses between the Sun reaching its highest point in the sky two consecutive times. Days on other planets are defined similarly and vary in length due to differing rotation periods, that of Mars being slightly longer and sometimes called a sol.

Δ<i>T</i> (timekeeping) Measure of variation of solar time from atomic time

In precise timekeeping, ΔT is a measure of the cumulative effect of the departure of the Earth's rotation period from the fixed-length day of atomic time. Formally it is the time difference obtained by subtracting Universal Time from Terrestrial Time : ΔT = TT − UT. The value of ΔT for the start of 1902 was approximately zero; for 2002 it was about 64 seconds. So the Earth's rotations over that century took about 64 seconds longer than would be required for days of atomic time. As well as this long-term drift in the length of the day there are short-term fluctuations in the length of day which are dealt with separately.

The term ephemeris time can in principle refer to time in connection with any astronomical ephemeris. In practice it has been used more specifically to refer to:

  1. a former standard astronomical time scale adopted in 1952 by the IAU, and superseded in the 1970s. This time scale was proposed in 1948, to overcome the drawbacks of irregularly fluctuating mean solar time. The intent was to define a uniform time based on Newtonian theory. Ephemeris time was a first application of the concept of a dynamical time scale, in which the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via the dynamical theory of its motion.
  2. a modern relativistic coordinate time scale, implemented by the JPL ephemeris time argument Teph, in a series of numerically integrated Development Ephemerides. Among them is the DE405 ephemeris in widespread current use. The time scale represented by Teph is closely related to, but distinct from, the TCB time scale currently adopted as a standard by the IAU.
Leap second Extra second inserted to keep civil time in sync with the Earths rotation

A leap second is a one-second adjustment that is occasionally applied to Coordinated Universal Time (UTC), to accommodate the difference between precise time and imprecise observed solar time. The UTC time standard, widely used for international timekeeping and as the reference for civil time in most countries, uses precise atomic time and consequently would run ahead of observed solar time unless it is reset to UT1 as needed. The leap second facility exists to provide this adjustment.

The minute is a unit of time usually equal to ​160 of an hour, or 60 seconds. In the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds. Although not an SI unit, the minute is accepted for use with SI units. The SI symbol for minute or minutes is min. The prime symbol is also sometimes used informally to denote minutes of time.

Terrestrial Time (TT) is a modern astronomical time standard defined by the International Astronomical Union, primarily for time-measurements of astronomical observations made from the surface of Earth. For example, the Astronomical Almanac uses TT for its tables of positions (ephemerides) of the Sun, Moon and planets as seen from Earth. In this role, TT continues Terrestrial Dynamical Time, which in turn succeeded ephemeris time (ET). TT shares the original purpose for which ET was designed, to be free of the irregularities in the rotation of Earth.

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 custom and practice. An example of a kind of time standard can be a time scale, specifying a method for measuring divisions of time. A standard for civil time can specify both time intervals and time-of-day.

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. All of these versions of UT, except for UTC, are based on Earth's rotation relative to distant celestial objects, but with a scaling factor and other adjustments to make them closer to solar time. UTC is based on International Atomic Time, with leap seconds added to keep it within 0.9 second of UT1.

Metric time is the measure of time intervals using the metric system. The modern SI system defines the second as the base unit of time, and forms multiples and submultiples with metric prefixes such as kiloseconds and milliseconds. Other units of time: minute, hour, and day, are accepted for use with SI, but are not part of it. Metric time is a measure of time intervals, while decimal time is a means of recording time of day.

Sidereal time

Sidereal time is a timekeeping system that astronomers use to locate celestial objects. Using sidereal time, it is possible to easily point a telescope to the proper coordinates in the night sky. Briefly, sidereal time is a "time scale that is based on Earth's rate of rotation measured relative to the fixed stars".

Solar time calculation of elapsed time by the apparent position of the sun

Solar time is a calculation of the passage of time based on the position of the Sun in the sky. The fundamental unit of solar time is the day. Two types of solar times are apparent solar time and mean solar time.

Unit of time Measurement unit for time

A unit of time or midst unit is any particular time interval, used as a standard way of measuring or expressing duration. The base unit of time in the International System of Units (SI) and by extension most of the Western world, is the second, defined as about 9 billion oscillations of the caesium atom. The exact modern definition, from the National Institute of Standards and Technology is: "The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom."

In time standards, dynamical time is the time-like argument of a dynamical theory; and a dynamical time scale in this sense is the realization of a time-like argument based on a dynamical theory: that is, the time and time scale are defined implicitly, inferred from the observed position of an astronomical object via a theory of its motion. A first application of this concept of dynamical time was the definition of the ephemeris time scale (ET).

Seconds pendulum Pendulum whose period is precisely two seconds

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.

Shortt–Synchronome clock Precision pendulum clock invented by William Hamilton Shortt and Frank Hope-Jones

The Shortt–Synchronome free pendulum clock was a complex precision electromechanical pendulum clock invented in 1921 by British railway engineer William Hamilton Shortt in collaboration with horologist Frank Hope-Jones, and manufactured by the Synchronome Co., Ltd. of London, UK. They were the most accurate pendulum clocks ever commercially produced, and became the highest standard for timekeeping between the 1920s and the 1940s, after which mechanical clocks were superseded by quartz time standards. They were used worldwide in astronomical observatories, naval observatories, in scientific research, and as a primary standard for national time dissemination services. The Shortt was the first clock to be a more accurate timekeeper than the Earth itself; it was used in 1926 to detect tiny seasonal changes in the Earth's rotation rate. Shortt clocks achieved accuracy of around a second per year, although a recent measurement indicated they were even more accurate. About 100 were produced between 1922 and 1956.

A tropical year is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice. This differs from the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars by about 20 minutes because of the precession of the equinoxes.

Coordinated Universal Time Primary time standard

Coordinated Universal Time or UTC is the primary time standard by which the world regulates clocks and time. It is within about 1 second of mean solar time at 0° longitude, and is not adjusted for daylight saving time. It is effectively a successor to Greenwich Mean Time (GMT).

Atomic clock Extremely accurate reference clock used as a standard for timekeeping

An atomic clock is a clock device that uses a hyperfine transition frequency in the microwave, or electron transition frequency in the optical or ultraviolet region of the electromagnetic spectrum of atoms as a frequency standard for its timekeeping element. Atomic clocks are the most accurate time and frequency standards known, and are used as primary standards for international time distribution services, to control the wave frequency of television broadcasts, and in global navigation satellite systems such as GPS.

References

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  14. Nautical Almanac Offices of the United Kingdom and the United States of America (1961), Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac, p. 9, ... defined ephemeris time ... [was] adopted by the International Astronomical Union in Sept. 1952.
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