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Second (s)

Definition, realization and practical time measurement in the International System of Units

Time underlies much of science and engineering. Motion, energy, frequency and speed can all be described in terms of time. Its present definition, and how that definition is realized in practice, is less familiar than the quantity itself.

The modern second is not based on astronomical observations, but is defined through an exact frequency of an atomic transition. To understand this it is, as with the meter and the kilogram, necessary to distinguish between definition, realization and practical use.

The definition of the second in the SI system

Since 1967, the second has been defined within the International System of Units (SI) as:

the duration of 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom.

This definition means that the second is directly tied to a frequency, that is, a number of repeated oscillations per unit of time. The hyperfine transition frequency of the cesium-133 atom, often denoted Δν_Cs, thus has an exact numerical value in the SI.

The second is therefore no longer related to the rotation or orbit of the Earth, but to a reproducible atomic process.

Historical background and reasons for the redefinition

Earlier definitions of the second were based on astronomical phenomena, primarily the rotation of the Earth about its own axis. These proved to be irregular over longer periods, partly because of geophysical processes.

The development of atomic physics and microwave technology during the twentieth century made it possible to define time based on atomic transitions with very high stability and reproducibility. The transition to the atomic definition in 1967 therefore marked a decisive step towards a more stable and universal SI system.

Definition, realization and use

For time measurement too, it is important to distinguish between three levels:

  • The definition states what the second is in principle and is tied to the properties of the cesium atom.
  • The realization refers to the experimental methods by which this definition is turned into actual time standards.
  • The use refers to practical time measurement in engineering, science and everyday life.

Realizing the second: atomic clocks

The second is realized in practice through atomic clocks, in which the hyperfine transition of the cesium atom is used as the reference frequency.

In a cesium atomic clock:

  • cesium atoms are excited with microwave radiation
  • the microwave frequency is adjusted until maximum resonance is reached
  • an oscillator is locked to this frequency

Once the oscillator is stabilized against the atomic transition, the result is a time standard directly traceable to the SI definition of the second.

Cesium atomic clocks remain the primary realization of the second and serve as the reference for international time scales.

Primary and secondary frequency standards

Cesium atomic clocks are regarded as primary frequency standards, since they realize the second directly without needing calibration against any other time standard.

In addition, secondary standards are used, for example hydrogen maser clocks and optical atomic clocks. These can exhibit very high short-term stability or extreme accuracy, but are at present formally traceable to the cesium definition.

Optical atomic clocks, based on transitions in, for example, strontium or ytterbium, have already demonstrated better performance than cesium clocks and are expected in time to form the basis for a future redefinition of the second.

The role of the second in other SI units

The second is one of the most central base units in the SI system. Many other units depend directly on time, for example:

  • the meter (via the speed of light)
  • the kilogram (via the Planck constant)
  • the hertz (frequency)
  • the watt (power)

An exact and stable definition of the second therefore matters for the whole SI system, since so many other units depend on it.

Practical time measurement and time scales

In practical use, many atomic clocks are combined into common time scales. International Atomic Time (TAI) is an example of such a scale and is based on a large number of atomic clocks around the world.

Coordinated Universal Time (UTC), used in everyday contexts, is based on TAI but is adjusted with leap seconds to stay close to the rotation of the Earth.

These time scales illustrate the difference between a strictly physical definition of time and practical, socially adapted time systems.

Summary

The second is today defined through an exact frequency of the cesium-133 atom and forms the basis of all modern time measurement. Through atomic clocks, this definition can be realized with very high stability and traceability.

The development of optical atomic clocks shows that time measurement keeps improving. The definition of the second reflects both the precision the SI system reaches today and where metrology is heading next.