The second (SI symbol: s), sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units (SI) base unit of time. It may be measured using a clock.

SI prefixes are frequently combined with the word second to denote subdivisions of the second, e.g., the millisecond (one thousandth of a second) and nanosecond (one billionth of a second). Though SI prefixes may also be used to form multiples of the second (such as “kilosecond,” or one thousand seconds), such units are rarely used in practice. More commonly encountered, non-SI units of time such as the minute, hour, and day increase by multiples of 60 and 24 (rather than by powers of ten as in the SI system).

The second was also the base unit of time in the centimetre-gram-second, metre-kilogram-second, metre-tonne-second, and foot-pound-second systems of units.

International second

Under the International System of Units, the second is currently defined as

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.^[1]

This definition refers to a caesium atom at rest at a temperature of 0 K (absolute zero). The ground state is defined at zero magnetic field. The second thus defined is consistent with the ephemeris second, which was based on astronomical measurements. (See History below.)

The international standard symbol for a second is s^[2] (see ISO 31-1)

The realization of the standard second is described briefly in NIST Special Publication 330; Appendix 2, pp. 53 ff, and in detail by National Research Council of Canada.

The standard does not mention whether the transition should be measured in free space (a theoretical reference state that cannot be attained in practice) or in the quantum vacuum. The transitions may not have the same frequencies in these two situations due to vacuum fluctuations, which can lead, for example, to a Lamb shift of the energy levels in vacuum relative to their values in free space.^[3]

Equivalence to other units of time

1 international second is equal to:

• 1/60 minute
• 1/3,600 hour
• 1/86,400 day (IAU system of units)
• 1/31,557,600 Julian year (IAU system of units)

History

The Egyptians subdivided daytime and nighttime into twelve hours each since at least 2000 BC, hence their hours varied seasonally. The Hellenistic astronomers Hipparchus (c. 150 BC) and Ptolemy (c. AD 150) subdivided the day sexagesimally and also used a mean hour (1⁄24 day), but did not use distinctly named smaller units of time. Instead they used simple fractions of an hour.

The day was subdivided sexagesimally, that is by 1⁄60, by 1⁄60 of that, by 1⁄60 of that, etc., to at least six places after the sexagesimal point (a precision of less than 2 microseconds) by the Babylonians after 300 BC, but they did not sexagesimally subdivide smaller units of time. For example, six fractional sexagesimal places of a day was used in their specification of the length of the year, although they were unable to measure such a small fraction of a day in real time. As another example, they specified that the mean synodic month was 29;31,50,8,20 days (four fractional sexagesimal positions), which was repeated by Hipparchus and Ptolemy sexagesimally, and is currently the mean synodic month of the Hebrew calendar, though restated as 29 days 12 hours 793 halakim (where 1 hour = 1080 halakim).^[4] The Babylonians did not use the hour, but did use a double-hour, a time-degree lasting four of our minutes, and a barleycorn lasting 3⅓ of our seconds (the helek of the modern Hebrew calendar).^[5]

In 1000, the Persian scholar al-Biruni gave the times of the new moons of specific weeks as a number of days, hours, minutes, seconds, thirds, and fourths after noon Sunday.^[6] In 1267, the medieval scientist Roger Bacon stated the times of full moons as a number of hours, minutes, seconds, thirds, and fourths (horae, minuta, secunda, tertia, and quarta) after noon on specified calendar dates.^[7] Although a third for 1⁄60 of a second remains in some languages, for example Polish (tercja) and Arabic (ثالثة), the modern second is subdivided decimally.

The first attempt at creating a clock that could measure time in seconds was created by Taqi al-Din at the Istanbul observatory of al-Din between 1577-1580. He called it the "observational clock" in his In the Nabik Tree of the Extremity of Thoughts, where he described it as "a mechanical clock with three dials which show the hours, the minutes, and the seconds." He used it as an astronomical clock, particularly for measuring the right ascension of the stars.^[8]

The second first became accurately measurable with the development of pendulum clocks keeping mean time (as opposed to the apparent time displayed by sundials), specifically in 1670 when William Clement added a seconds pendulum to the original pendulum clock of Christian Huygens.^[9] The seconds pendulum has a period of two seconds, one second for a swing forward and one second for a swing back, enabling the longcase clock incorporating it to tick seconds. From this time, a second hand that rotated once per minute in a small subdial began to be added to the clock faces of precision clocks.

In 1956 the second was defined in terms of the period of revolution of the Earth around the Sun for a particular epoch, because by then it had become recognized that the Earth's rotation on its own axis was not sufficiently uniform as a standard of time. The Earth's motion was described in Newcomb's Tables of the Sun, which provides a formula for the motion of the Sun at the epoch 1900 based on astronomical observations made between 1750 and 1892.^[10] The second thus defined is

the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.^[10]

This definition was ratified by the Eleventh General Conference on Weights and Measures in 1960. The tropical year in the definition was not measured, but calculated from a formula describing a mean tropical year which decreased linearly over time, hence the curious reference to a specific instantaneous tropical year. Because this second was the independent variable of time used in ephemerides of the Sun and Moon during most of the twentieth century (Newcomb's Tables of the Sun were used from 1900 through 1983, and Brown's Tables of the Moon were used from 1920 through 1983), it was called the ephemeris second.^[10]

With the development of the atomic clock, it was decided to use atomic clocks as the basis of the definition of the second, rather than the revolution of the Earth around the Sun.

Following several years of work, Louis Essen from the National Physical Laboratory (Teddington, England) and William Markowitz from the United States Naval Observatory (USNO) determined the relationship between the hyperfine transition frequency of the caesium atom and the ephemeris second.^[10] Using a common-view measurement method based on the received signals from radio station WWV,^[11] they determined the orbital motion of the Moon about the Earth, from which the apparent motion of the Sun could be inferred, in terms of time as measured by an atomic clock. As a result, in 1967 the Thirteenth General Conference on Weights and Measures defined the second of atomic time in the International System of Units as

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.^[10]

During the 1970s it was realized that gravitational time dilation caused the second produced by each atomic clock to differ depending on its altitude. A uniform second was produced by correcting the output of each atomic clock to mean sea level (the rotating geoid), lengthening the second by about 1×10⁻¹⁰. This correction was applied at the beginning of 1977 and formalized in 1980. In relativistic terms, the SI second is defined as the proper time on the rotating geoid.^[12]

The definition of the second was later refined at the 1997 meeting of the BIPM to include the statement

This definition refers to a caesium atom at rest at a temperature of 0 K.

The revised definition would seem to imply that the ideal atomic clock would contain a single caesium atom at rest emitting a single frequency. In practice, however, the definition means that high-precision realizations of the second should compensate for the effects of the ambient temperature (black-body radiation) within which atomic clocks operate and extrapolate accordingly to the value of the second as defined above.

For approximately twenty years, it has been possible to confine an ion to a region of space smaller than one cubic micrometre (10^-6 m)³. Such an ion is almost completely isolated from the surrounding environment and suggests a frequency or time standard with a reproducibility and stability several orders of magnitude superior to the best caesium time standards. Such standards are under development. See magneto-optical trap and "Trapped ion optical frequency standards". National Physical Laboratory.

SI multiples

SI prefixes are commonly used to measure time less than a second, but rarely for multiples of a second. Instead, the non-SI units minutes, hours, days, Julian years, Julian centuries, and Julian millennia are used.

See also

• Atomic clock
• Becquerel
• Hertz
• International Atomic Time
• International System of Units
• Leap second
• Magneto-optical trap
• Orders of magnitude (time)
• Time standard

References

External links

• National Physical Laboratory: Trapped ion optical frequency standards
• National Research Council of Canada: Optical frequency standard based on a single trapped ion
• NIST: Definition of the second; notice the cesium atom must be in its ground state at 0 K
• Official BIPM definition of the second
• Seconds and leap seconds by the USNO* The leap second: its history and possible future
• What is a Cesium atom clock?