This article needs to be updated. The reason given is: it needs to reflect the 2019 redefinition of the SI base units, which came into effect on May 20, 2019.(January 2020)
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 Essen in 1955 at the National Physical Laboratory in the UK.and promoted worldwide by Gernot M. R. Winkler of the United States Naval Observatory.
Caesium atomic clocks are one of the most accurate time and frequency standards, and serve as the primary standard for the definition of the second in the International System of Units (SI) (the modern form of the metric system). By definition, radiation produced by the transition between the two hyperfine ground states of caesium (in the absence of external influences such as the Earth's magnetic field) has a frequency, ΔνCs, of exactly 9192631770 Hz . That value was chosen so that the caesium second equalled, to the limit of human measuring ability in 1960 when it was adopted, the existing standard ephemeris second based on the Earth's orbit around the Sun. Because no other measurement involving time had been as precise, the effect of the change was less than the experimental uncertainty of all existing measurements.
While the second is the only base unit to be explicitly defined in terms of the caesium standard, the majority of SI units have definitions that mention either the second, or other units defined using the second. Consequently, every base unit except the mole and every named derived unit except the coulomb, ohm, siemens, weber, gray, sievert, radian, and steradian have values that are implicitly defined by the properties of the caesium-133 hyperfine transition radiation. And of these, all but the mole, the coulomb, and the dimensionless radian and steradian are implicitly defined by the general properties of electromagnetic radiation.
The official definition of the second was first given by the BIPM at the 13th General Conference on Weights and Measures in 1967 as: "The second 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." At its 1997 meeting the BIPM added to the previous definition the following specification: "This definition refers to a caesium atom at rest at a temperature of 0 K."
The BIPM restated this definition in its 26th conference (2018), "The second is defined by taking the fixed numerical value of the caesium frequency ∆Cs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9 192 631 770 when expressed in the unit Hz, which is equal to s–1."
The meaning of the preceding definition is as follows. The caesium atom has a ground state electron state with configuration [Xe] 6s1 and, consequently, atomic term symbol 2S1/2. This means that there is one unpaired electron and the total electron spin of the atom is 1/2. Moreover, the nucleus of caesium-133 has a nuclear spin equal to 7/2. The simultaneous presence of electron spin and nuclear spin leads, by a mechanism called hyperfine interaction, to a (small) splitting of all energy levels into two sub-levels. One of the sub-levels corresponds to the electron and nuclear spin being parallel (i.e., pointing in the same direction), leading to a total spin F equal to F = 7/2 + 1/2 = 4; the other sub-level corresponds to anti-parallel electron and nuclear spin (i.e., pointing in opposite directions), leading to a total spin F = 7/2 − 1/2 = 3. In the caesium atom it so happens that the sub-level lowest in energy is the one with F = 3, while the F = 4 sub-level lies energetically slightly above. When the atom is irradiated with electromagnetic radiation having an energy corresponding to the energetic difference between the two sub-levels the radiation is absorbed and the atom is excited, going from the F = 3 sub-level to the F = 4 one. After a small fraction of a second the atom will re-emit the radiation and return to its F = 3 ground state. From the definition of the second it follows that the radiation in question has a frequency of exactly 9.19263177 GHz, corresponding to a wavelength of about 3.26 cm and therefore belonging to the microwave range.
This particular cesium resonance was agreed upon under la Convention du Mètre and remains to the present time as the official definition of the second for the world community.
Note that a common confusion involves the conversion from angular frequency () to frequency (), or vice versa. Angular frequencies are conventionally given as s–1 in scientific literature, but here the units implicitly mean radians per second. In contrast, the unit Hz should be interpreted as cycles per second. The conversion formula is , which implies that 1 Hz corresponds to an angular frequency of approximately 6.28 radians per second (or 6.28 s–1 where radians is omitted for brevity by convention).
Suppose the caesium standard has the parameters:
The first set of units defined using the caesium standard were those relating to time, with the second being defined in 1967 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" meaning that:
This also linked the definitions of the derived units relating to force and energy (see below) and of the ampere, whose definition at the time made reference to the newton, to the caesium standard. Before 1967 the SI units of time and frequency were defined using the tropical year and before 1960 by the length of the mean solar day
In 1983, the meter was, indirectly, defined in terms of the caesium standard with the formal definition "The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. This implied:
Between 1960 and 1983, the metre had been defined by the wavelength of a different transition frequency associated with the krypton 86 atom. This had a much higher frequency and shorter wavelength than the caesium standard, falling inside the visible spectrum. And between 1889 and 1960 by the international prototype meter.
Following the 2019 redefinition of the SI base units, electromagnetic radiation, in general, was explicitly defined to have the exact parameters:
And the caesium 133 hyperfine transition radiation was explicitly defined to have frequency:
Though the above values for c and ΔνCs were already obviously implicit in the definitions of the metre and second. Together they imply:
Notably, the wavelength has a fairly human-sized value of about 3.26 centimetres and the photon energy is surprisingly close to the average molecular kinetic energy per degree of freedom per kelvin. From these it follows that:
Prior to the revision, between 1889 and 2019, the family of metric (and later SI) units relating to mass, force, and energy were somewhat notoriously defined by the mass of the International Prototype of the Kilogram (IPK), a specific object stored at the headquarters of the International Bureau of Weights and Measures in Paris, meaning that any change to the mass of that object would have resulted in a change to the size of the kilogram and of the many other units whose value at the time depended on that of the kilogram.
From 1954 to 2019, the SI temperature scales were defined using the triple point of water and absolute zero. 1.380649×10−23 J/K, implying:The 2019 revision replaced these with an assigned value for the Boltzmann constant, k, of
The mole is an extremely large number of "elementary entities" (i.e. atoms, molecules, ions, etc). From 1969 to 2019, this number was 0.012 × the mass ratio between the IPK and a carbon 12 atom. 6.02214076×1023 elementary entities per mole, thus, uniquely among the base units, the mole maintained its independence from the caesium standard:The 2019 revision simplified this by assigning the Avogadro constant the exact value
Prior to the revision, the ampere was defined as the current needed to produce a force between 2 parallel wires 1 m apart of 0.2 μN per meter. The 2019 revision replaced this definition by giving the charge on the electron, e, the exact value 1.602176634×10−19 coulombs. Somewhat incongruously, the coulomb is still considered a derived unit and the amp a base unit, rather than vice versa. In any case, this convention entailed the following exact relationships between the SI electromagnetic units, electron, and the caesium-133 hyperfine transition radiation:
From 1967 to 1979 the SI optical units, lumen, lux, and candela are defined using the Incandescent glow of platinum at its melting point. After 1979, the candela was defined as the luminous intensity of a monochromatic visible light source of frequency 540 Thz (i.e 6000/1.02140353 that of the caesium standard) and radiant intensity 1/683 watts per steradian. This linked the definition of the candela to the caesium standard and, until 2019, to the IPK. Unlike the units relating to mass, energy, temperature, amount of substance, and electromagnetism, the optical units were not massively redefined in 2019, though they were indirectly affected since their values depend on that of the watt, and hence of the kilogram. The frequency used to define the optical units has the parameters:
The parameters of the caesium 133 hyperfine transition radiation expressed exactly in SI units are:
If the 7 base units of the SI are expressed explicitly in terms of the SI defining constants, they are:
With 6 of the 7 base units notably having values that depend on that of ΔνCs. And ΔνCs appearing far more often than any of the other defining constants.
The ampere (, ; symbol: A), often shortened to amp, is the unit of electric current in the International System of Units (SI). One ampere is equal to 6.241509074×1018 electrons worth of charge moving past a point in a second. It is named after French mathematician and physicist André-Marie Ampère (1775–1836), considered the father of electromagnetism along with Danish physicist Hans Christian Ørsted.
The candela 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 to radiant intensity, but instead of simply adding up the contributions of every wavelength of light in the source's spectrum, the contribution of each wavelength is weighted by the standard luminosity function. A common wax candle emits light with a luminous intensity of roughly one candela. If emission in some directions is blocked by an opaque barrier, the emission would still be approximately one candela in the directions that are not obscured.
Caesium 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 28.5 °C (83.3 °F), which makes it one of only five elemental metals that are liquid at or near room temperature. Caesium has physical and chemical properties similar to those of rubidium and potassium. It is pyrophoric and reacts with water even at −116 °C (−177 °F). It is the least electronegative element, with a value of 0.79 on the Pauling scale. It has only one stable isotope, caesium-133. Caesium is mined mostly from pollucite. The element has 40 known isotopes, making it, along with barium and mercury, one of the elements with the most isotopes. Caesium-137, a fission product, is extracted from waste produced by nuclear reactors.
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 one hertz is the reciprocal of one second. It is named after Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves. Hertz are commonly expressed in multiples: kilohertz (103 Hz, kHz), megahertz (106 Hz, MHz), gigahertz (109 Hz, GHz), terahertz (1012 Hz, THz).
The kilogram 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. It means 'one thousand grams'.
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 based on the metre as the unit of length and either the kilogram as the unit of mass or the kilogram-force as the unit of force.</ref> and the world's most widely used system of measurement. Established and maintained by the General Conference on Weights and Measures (CGPM), it is the only system of measurement with an official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce.
The second is the unit of time in the International System of Units (SI), historically defined as 1⁄86400 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.
The mole, symbol mol, is the unit of amount of substance in the International System of Units (SI). The quantity amount of substance is a measure of how many elementary entities of a given substance are in an object or sample. The mole is defined as containing exactly 6.02214076×1023 elementary entities. Depending on what the substance is, an elementary entity may be an atom, a molecule, an ion, an ion pair, or a subatomic particle such as an electron. For example, 10 moles of water (a chemical compound) and 10 moles of mercury (a chemical element), contain equal amounts of substance and the mercury contains exactly one atom for each molecule of the water, despite the two having different volumes and different masses.
In telecommunications, a primary time standard is a time standard that does not require calibration against another time standard.
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.
Caesium (55Cs) has 40 known isotopes, making it, along with barium and mercury, one of the elements with the most isotopes. The atomic masses of these isotopes range from 112 to 151. Only one isotope, 133Cs, is stable. The longest-lived radioisotopes are 135Cs with a half-life of 2.3 million years, 137
with a half-life of 30.1671 years and 134Cs with a half-life of 2.0652 years. All other isotopes have half-lives less than 2 weeks, most under an hour.
A conventional electrical unit is a unit of measurement in the field of electricity which is based on the so-called "conventional values" of the Josephson constant, the von Klitzing constant agreed by the International Committee for Weights and Measures (CIPM) in 1988, as well as ΔνCs used to define the second. These units are very similar in scale to their corresponding SI units, but are not identical because of the different values used for the constants. They are distinguished from the corresponding SI units by setting the symbol in italic typeface and adding a subscript "90" – e.g., the conventional volt has the symbol V90 – as they came into international use on 1 January 1990.
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 physicist William Thomson, 1st Baron Kelvin (1824–1907). The Kelvin scale is an absolute thermodynamic temperature scale, meaning it uses absolute zero as its null (zero) point.
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalence, the relationship between mass and frequency. Specifically, a photon's energy is equal to its frequency multiplied by the Planck constant. The constant is generally denoted by . The reduced Planck constant, or Dirac constant, equal to the constant divided by , is denoted by .
Time in physics is defined by its measurement: time is what a clock reads. In classical, non-relativistic physics, it is a scalar quantity and, like length, mass, and charge, is usually described as a fundamental quantity. Time can be combined mathematically with other physical quantities to derive other concepts such as motion, kinetic energy and time-dependent fields. Timekeeping is a complex of technological and scientific issues, and part of the foundation of recordkeeping.
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 between such states they interact with a very specific frequency of electromagnetic radiation. This phenomenon serves as the basis for the International System of Units' (SI) definition of a second:
The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency, , 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.
Photon energy is the energy carried by a single photon. The amount of energy is directly proportional to the photon's electromagnetic frequency and thus, equivalently, is inversely proportional to the wavelength. The higher the photon's frequency, the higher its energy. Equivalently, the longer the photon's wavelength, the lower its energy.
In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are now defined by setting exact numerical values, when expressed in SI units, for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre, and candela had previously been redefined using physical constants. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.
The scientific community examined several approaches to redefining the kilogram before deciding on a redefinition of the SI base units in November 2018. Each approach had advantages and disadvantages.