The length of the SI unit one second has varied during the last millennium. The variations are not only due to the rotation of the Earth and to the varying length of the day, but most of all the need of a well known and a more stable time keeping.

A special need arose in the middle of the 19th century when different transport systems evolved. When people and goods were transported by horse and cart it was enough with the local time that every larger town had. But when the transports and especially the railway evolved it became possible to pass different local time zones during some days. The passengers’ watches had to be set several times during the journey and the possibility that someone missed a departure because they did not have the correct time was large. It was important to get a common time within the country and later also within the world. The world was gradually separated into 24 different geographical time zones where every zone was 15 degrees in longitude and with a difference of exactly 1 hour for each time zone. The base of the standardised time was placed at the zero meridian through Greenwich in England. For every eastern move of 15 degrees one add one hour and for every western move of 15 degrees one subtract one hour from Greenwich Mean Time.

An even greater need of well-defined and stable time was developed during 20th century when the development of communication systems for radios and computers but also energy systems increased. These systems are dependent on synchronised clocks. If the synchronisation is good enough the capacity will get better and the risk of errors in the systems will get smaller. In the last few years, systems have also been developed for satellite navigation. If these systems shall work the need of atomic clocks with the highest quality is necessary.

Below you will find different definitions of the SI unit one second that has existed during the last century. Further down you will find information about the time scales that the definitions are based on and the official time of the world today.

A time scale must have a beginning and after that a continuous accumulation of time units. To the beginning of the time scale, which we will call the initial phase, a time interval is added. These time intervals are seconds that accumulate to minutes, hours, days, weeks, months, years, centuries, millenniums and so on. One can separate the time scales by the different beginnings or by the different lengths of the second. As mentioned before the definition of one second has changed several times but also the official time of the world has changed, that is to say that different time scales have been used for defining the official time of the world.

The Universal Time UT is based on the rotation of the Earth about its axis. The true solar time - which is the time interval between two instants of time when the sun reaches its highest point in the sky - is varying depending on where on the globe you are located and when during the year the measurements are done. The largest variations are due to the fact that the inclination of the Earth's axis relative the plane the Earth describes through its orbit around the sun is different, as well as the fact that the rotation of the Earth around the sun is not circular but elliptic. If these variations are corrected for, which can be several tens of minutes, one will get something called mean solar time. The time scale UT0 is equal to the mean solar time if one apply the corrections at the Greenwich meridian in England.

The time scale UT0 is also varying due to something called polar motion, which is caused by the fact that Earth's rotational axis relative to the surface of the Earth varies. If one correct for these variations, which can be as large as 50 milliseconds (ms), one obtain the Universal Time UT1. UT1 is calculated during one day with an accuracy of approximately 3 ms.

Upon till 1960 the SI unit 1-second was defined as 1/86400 parts of the mean solar day given in UT1 and calculated at the Greenwich meridian. The initial phase was chosen so that 00:00:00 UT1 coincide, in average, with midnight in Greenwich.

Despite the corrections applied, the stability of UT1 was eventually not enough as a base for the definition of 1-second. The growth of the society needed a more stabile definition.

Ephemeris Time ET is based on the rotation of the Earth around the Sun. This rotation is considerable more stable than the rotation of the Earth about its axis.

Upon till 1967 the SI unit 1-second was defined as 1/31556925,9747 parts of the tropical year, a year that is calculated through observations against the sun. This involves that 1-second was equal to one average second of the Earth's rotation in the beginning of this century. The initial phase is chosen so that ET and UT1 approximately coincided in the year 1900. Due to that the daily rotation of the Earth is irregular and is slowing down, the difference between ET and UT1 was 56 seconds in 1988.

Despite the better stability in the long run of ET it is only possible to calculate its stability with an accuracy of 50 ms over ten years of measurements.

The so-called dynamic time scales described above are calculated through periods of the Earth's rotation. An atomic time scale is on the other hand determined through calculating the amount of periods of an electromagnetically radiation locked to the resonance frequency of an atom. During the 1940's the first atomic clocks was used to build up atomic time scales. By means of these clocks, variations in UT and ET could be measured very accurately. This lead to a new definition of the SI-unit one second.

Since 1967 the definition of the SI unit 1-second is:

The base unit in SI, 1-second, is defined as the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.

The International Atomic Time TAI uses this definition as a time scale unit. The initial phase coincide with UT1 January 1st 1958 00:00:00.

The definition of TAI is:

The International Atomic Time (TAI) is the coordinated reference time established by the International Bureau of Weights and Measures (BIPM) and based on the time from the atomic clocks maintained according to the agreement of the definition of the second, the unit for time in the International System of Units, SI.

In a coordinated time scale the time is one of the coordinates in a system of three coordinates in space (x , y , z) and one time coordinate (t). In addition to this:

TAI is a coordinated time scale defined in a geocentric reference frame (with the origo at the center of the Earth) with the SI second as a realisation of the rotating geoid as a scale unit.

The clocks that are included in TAI must because of this be placed at the sea level or be correlated for the difference in height. This is due to the gravitational effect within the theory of relativity. A clock that is affected of a smaller gravitation is faster compared to a clock with higher gravitation. The effect is rather big: if a clock is located on a height of 1 km it will approximately be 10 nanoseconds faster per day than a clock at the sea level.

The advantage of TAI is that it can be realised in laboratories with a very high accuracy - better than a few nanoseconds if you carry out the measures during one hour - which assumes the access to an atomic clock. TAI is not a physical clock in distinction from UT1 and ET. TAI is a system time or a so-called "paper clock". TAI is calculated as a weighted average of approximately 450 atomic clocks located in approximately 70 laboratories worldwide.

TAI is independent of the variations in the rotation of the Earth - that is, it is independent of the rise and the set of the sun. The length of the new definition of the second unit is approximately the same as the previous definition, the ET-second. The length of the ET-second was in its turn approximated to the length of the UT1-second in 1900. The rotation of the Earth is slowing down and due to this the mean solar day gets on average a couple of milliseconds longer during 100 years. This increment makes TAI and UT1 to drift apart, at present approximately 2 seconds during 3 years.

The official time of the world was based on UT1 until 1972. But the society was in need of an official time scale with as good properties as an atomic time scale. At the same time astronomies, navigators and people in general was dependent on a time scale that followed the rise and the set of the sun. The solution was a new time scale, UTC. UTC was based on atomic clocks but its frequency was regularly adjusted to be in phase with UT1 and the mean solar day. The new time scale had due to this more or less the same stable properties as TAI but was also approximately following the set and the rise of the sun. The problem was that you had to adjust your clocks continually and that UT1 was hard to predict. A new procedure for the calculation of UTC was in need.

The Coordinated Universal Time UTC got a new definition in 1972 and became at the same time the new official time of the world. UTC is composed of a combination of TAI and UT1. The definition is as follows:

UTC - TAI = n seconds (n integer)

| UTC - UT1 | < 0,9 seconds.

Since 1972 UTC is the official time of the world. UTC 00:00:00 coincide with midnight at the zero meridian in Greenwich.

Due to this definition the difference between UTC and TAI is always a whole number of seconds. Instead of continually changing the rate in UTC to be able to follow UT1, whole seconds are added or subtracted to UTC when the difference to UT1 is more than 0.9 seconds. Due to this, UTC has the same good properties as TAI - the time scales are using the same definition for the second - at the same time as UTC is following the rotation of the Earth. The extra seconds that are added or subtracted are called leap seconds.

Local time scales are based on UTC, through adding or subtracting a complete number or half hours depending on the time zone. Time scales are also dependent of the regulations of daylight savings time. Every official transmission or distribution of time signals e.g. via the phone network, the TV broadcasting, the Internet, the ground based or the satellite based radio transmitters is expected to be based on these local time scales and with that UTC.

The official time in Sweden is UTC + 1 hour during standard time and UTC + 2 hours during daylight savings time.