Internationale Basiseinheit für Zeit

Zur technischen Erzeugung von regelmässigen Zeitpunkten benötigt man eine Uhr $u$ mit einer bestimmten Granularität $1/f_{u} = g_{u}$. Um aber bei verschiedenen Uhren zu einheitlichen Aussagen bzgl. der Zuordnung eines bestimmten vergleichbaren Zeitpunktes zu kommen, benötigt man eine Referenzuhr und eine Referenzzeitdauer, um jede beliebige Uhr in Beziehung zu dieser Referenzuhr setzen zu können.

Weltweit zuständig für den gültigen Zeitstandard und dessen Messung ist das Bureau International des Poids et Mesures (BIPM)(URL: http://www.bipm.org/), das im Park de Saint-Cloud von Sèvres liegt, einem Vorort süd-westlich von Paris. Das BIPM beschreibt seine Aufgabe wie folgt:

The task of the BIPM is to ensure world-wide uniformity of measurements and their traceability to the International System of Units (SI). It does this with the authority of the Convention of the Metre, a diplomatic treaty between fifty-one nations, and it operates through a series of Consultative Committees, whose members are the national metrology laboratories of the Member States of the Convention, and through its own laboratory work.

The BIPM carries out measurement-related research. It takes part in, and organizes, international comparisons of national measurement standards, and it carries out calibrations for Member States.

Die Existenz des BIPM geht zurück auf eine lange historische Entwicklung, deren Inhalt die immer klarere Herausarbeitung der heute benutzten internationalen Standards zur Bescheibung physikalischer Grössen ist. Hier eine kurze Geschichte der Entwicklung der internationalen Standards aus der Sicht des BIPM:

1. The creation of the decimal Metric System at the time of the French Revolution and the subsequent deposition of two platinum standards representing the metre and the kilogram, on 22 June 1799, in the Archives de la République in Paris can be seen as the first step in the development of the present International System of Units.
2. In 1832, Gauss strongly promoted the application of this Metric System, together with the second defined in astronomy, as a coherent system of units for the physical sciences. Gauss was the first to make absolute measurements of the earth's magnetic force in terms of a decimal system based on the three mechanical units millimetre, gram and second for, respectively, the quantities length, mass and time. In later years Gauss and Weber extended these measurements to include electrical phenomena.
3. These applications in the field of electricity and magnetism were further developed in the 1860s under the active leadership of Maxwell and Thomson through the British Association for the Advancement of Science (BAAS). They formulated the requirement for a coherent system of units with base units and derived units. In 1874 the BAAS introduced the CGS system, a three-dimensional coherent unit system based on the three mechanical units centimetre, gram and second, using prefixes ranging from micro to mega to express decimal submultiples and multiples. The following development of physics as an experimental science was largely based on this system.
4. The sizes of the coherent CGS units in the fields of electricity and magnetism, proved to be inconvenient so, in the 1880s, the BAAS and the International Electrical Congress, predecessor of the International Electrotechnical Commission (IEC), approved a mutually coherent set of practical units. Among them were the ohm for electrical resistance, the volt for electromotive force, and the ampere for electric current.
5. After the establishment of the Metre Convention on 20 May 1875 the CIPM concentrated on the construction of new prototypes taking the metre and kilogram as the base units of length and mass. In 1889 the 1st CGPM sanctioned the international prototypes for the metre and the kilogram. Together with the astronomical second as unit of time, these units constituted a three-dimensional mechanical unit system similar to the CGS system, but with the base units metre, kilogram and second.
6. In 1901 Giorgi showed that it is possible to combine the mechanical units of this metre-kilogram-second system with the practical electric units to form a single coherent four-dimensional system by adding to the three base units, a fourth base unit of electrical nature, such as the ampere or the ohm, and rewriting the equations occurring in electro-magnetism in the so-called rationalized form. Giorgi's proposal opened the path to a number of new developments.
7. After the revision of the Metre Convention by the 6th CGPM in 1921, which extended the scope and responsibilities of the BIPM to other fields in physics, and the subsequent creation of the CCE (now CCEM) by the 7th CGPM in 1927, the Giorgi proposal was thoroughly discussed by the IEC and the IUPAP and other international organizations. This led the CCE to recommend, in 1939, the adoption of a four-dimensional system based on the metre, kilogram, second and ampere, a proposal approved by the ClPM in 1946.
8. Following an international inquiry by the BIPM, which began in 1948, the 10th CGPM, in 1954, approved the introduction of the ampere, the kelvin and the candela as base units, respectively, for electric current, thermodynamic temperature and luminous intensity. The name International System of Units (SI) was given to the system by the 11th CGPM in 1960. At the 14th CGPM in 1971 the current version of the SI was completed by adding the mole as base unit for amount of substance, bringing the total number of base units to seven.

Wichtig ist, dass das internatinale System der Standards kein statisches System ist, sondern sich entsprechend den technischen Bedürfnissen dynamisch weiterentwickelt.

Die aktuelle Tafel der Basiseinheit nach der Darstellung des BIPM lautet wie folgt:

The 11th General Conference on Weights and Measures (1960) adopted the name Système International d'Unités (International System of Units, international abbreviation SI), for the recommended practical system of units of measurement.

The 11th CGPM laid down rules for the prefixes, the derived units, and other matters. The base units are a choice of seven well-defined units which by convention are regarded as dimensionally independent: the metre, the kilogram, the second, the ampere, the kelvin, the mole, and the candela. Derived units are those formed by combining base units according to the algebraic relations linking the corresponding quantities. The names and symbols of some of the units thus formed can be replaced by special names and symbols which can themselves be used to form expressions and symbols of other derived units.

The SI is not static but evolves to match the world's increasingly demanding requirements for measurement.

There are seven base units of the SI:

1. metre ( m): 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.
2. kilogram (kg): The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.

3. second (s): The second is 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.

4. ampere (A): The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2 x 10?7 newton per metre of length.
5. kelvin (K): The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
6. mole (mol): (1) The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. (2) When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.
7. candela (cd): The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

Insbesondere schreibt das BIPM zur Definition der Sekunde:

The unit of time, the second, was at one time considered to be the fraction 1/86 400 of the mean solar day. The exact definition of "mean solar day" was left to the astronomers. However measurements showed that irregularities in the rotation of the Earth made this an unsatisfactory definition. In order to define the unit of time more precisely, the 11th CGPM (1960, Resolution 9) adopted a definition given by the International Astronomical Union based on the tropical year 1900. Experimental work, however, had already shown that an atomic standard of time, based on a transition between two energy levels of an atom or a molecule, could be realized and reproduced much more accurately. Considering that a very precise definition of the unit of time is indispensable for science and technology, the 13th CGPM (1967/68, Resolution 1) replaced the definition of the second by the following:

The second is 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.

It follows that the hyperfine splitting in the ground state of the caesium 133 atom is exactly 9 192 631 770 hertz, nu(hfs Cs) = 9 192 631 770 Hz. At its 1997 meeting the CIPM affirmed that: This definition refers to a caesium atom at rest at a temperature of 0 K. This note was intended to make it clear that the definition of the SI second is based on a caesium atom unperturbed by black body radiation, that is, in an environment whose thermodynamic temperature is 0 K. The frequencies of all primary frequency standards should therefore be corrected for the shift due to ambient radiation, as stated at the meeting of the Consultative Committee for Time and Frequency in 1999.

Damit ergeben sich für die Frequenz und Granularität von Cäsium-basierten Atomuhren:

Frequenz einer Cäsium-basierten Atomuhr: fcs = 9.192.631.770 pro sec

Granularität einer Cäsium-basierten Atomuhr: gcs = 1/9.192.631.770 sec

Eine gute prinzipielle Beschreibung einer Cäsium-basierten Atomuhr findet sich auf der Seite von Herget (URL: http://www.heret.de/radioclock/ptb.htm#K2):

Atomic clocks work on the following principle: Atoms occur in different energy states one of which is identified by the symbol (+) and one by the symbol (-). The transition of an atom from the (+) to the (-) state can be stimulated and is connected with the emission of electromagnetic radiation of a characteristic frequency. In the case of the caesium atom, this frequency, fcs has a value of 9.192.631.770 Hz, corresponding to an oscillation period of ( $1 / 9.192.631.770$) seconds. According to the laws of atomic physics, fcs is equal to the energy difference between the (+) and (-) states divided by the Planck constant h. For the caesium atom in particular, the constancy in time of fcs much better than that of, for example, the oscillation period of a pendulum, the oscillation frequency of a quartz or the rotation period of the earth.

Caesium atoms are evaporated in the vacuum chamber of an atomic clock. The magnet arranged behind the oven separates the atoms such that only atoms in the (+) state enter the cavity resonator. Here exposure to a microwave field stimulates the atoms to pass into the (-) state. The second magnet then directs to the detector only these atoms. The number of atoms at the collector reaches a maximum when the frequency of the irradiation field has the value fcs. A feedback circuit ensures that the microwave oscillator Q is kept at the frequency fcs. By the counting of 9.192.631.770 periods, the time interval of one second is obtained from the oscillator signal.