TIME SCALES: the making of time

Time... from astronomers to physicists

As soon as the dawn of mankind, search has been made to measure time for predicting the return of cold and hot seasons so, for facilitating living. The alternation of day and night, the apparent motion of the Sun in the sky, have been used for that purpose. Practical considerations have guided the first researchs for making time, but the concept of time is also a scientific and philosophical question of the utmost importance. This fundamental quest for knowledge now led scientists to research in physics of very high level.
During the long history of mankind, time is mainly an astronomical subject. Time will become the business of physicists only during the XX^th century.

1- Time in astronomy

All the periodic phenomena may be used to define a time scale. The first idea is then to use the alternating day and night, i.e. the apparent motion of the Sun as the fundamental phenomenon. Sundials were based on the apparent motion of the Sun. One of the first sundial came from Egypt in 1500 B.C. but the best sundials will be made during the XVI^th and XVII^th centuries.

1-1 Solar time and the second of mean time

The time given by sundials is what is known in astronomy as the true local time. This time is local and not uniform due to the non-uniformity of the apparent motion of the Sun on the celestial sphere. This is because the real Sun moves on an elliptical orbit following Kepler's laws, in the plane of the ecliptic. This time was a very common use until the eighteenth century. However, the rapid development of communications made necessary the adoption of a mean solar time as a legal time, uniform and no more local. The mean solar time is given by a mean Sun (fictional) moving on a circular orbit at a constant speed in the plane of the celestial equator. The mean solar time is at the origin of the first astronomical definition of the second until 1960: it was the 86400^th part of the mean solar day. The difference between mean solar time and true solar time is called the equation of time.

Variations in true solar time versus mean solar time are essentially geometrical nature. Newton is probably the first to have thought of the non-uniformity of motion of the Earth as explicitly mentions in his book Principles (1686) that astromomers must correct the true time provided by the observation of the Sun's equation of time. He adds: "It may be that it is no uniform motion by which time can be measured with precision." Kant in 1754 and Lalande in 1771 emit doubts about the uniformity of the rotation of the Earth, and consequently that of the Sun in the sky. We now know that the rotation of the Earth is not uniform: the friction of ocean tides on the Earth's crust, seasonal weather-related variations are now well known causes of non-uniformity of the Earth's rotation.

1-2 Ephemeris time and the second of the Ephemeris

This has led astronomers to build another time scale based on the orbital motion (revolution) of the Earth around the Sun. This new time scale legally in use between 1960 and 1967 is called Ephemeris time. It is based on the observation of the longitude of the Sun in the sky during the year. The equation numerically defining the longitude of the Sun was given by Newcomb and was officially adopted in 1952 by the International Astronomical Union. It is a second degree polynomial of time. So if the longitude of the Sun is observed, it is easy deducing the corresponding time in the ephemeris time scale. In 1960 the Eleventh General Conference on Weights and Measures decided that the second is 1/31556925.9747 fraction of the tropical year for January 0, 1900 at 12 hours Ephemeris time.

The definition of the Ephemeris time is difficult to achieve in practice. It is also difficult to be understood by non-astronomers; accessibility and universality are expected timescales properties. This has led to the abandon of this time scale in favor of the atomic time scale which is at present our best reference.

2- Time in physics

It was in 1955 that the first frequency standard was built by L. Essen and J. Parry who worked at the National Physical Laboratory in London. This early work paved the way for a new definition of the second which was born in 1967 at the Thirteenth General Conference on Weights and Measures. The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine 2 levels F = 3 and F = 4 of the ground state 6S1 / of the cesium 133 atom. Despite the apparent complexity at least as great as that of the definition of the second of Ephemeris time, this definition has the advantage of a much better accessibility.

2-1 Principle of a primary frequency standard, second of atomic time

Quantum mechanics tells us that the atoms can be in different states or energy levels that are quantified . That is to say that the values of the energy of atoms are discrete and not continuous values. The lowest energy level is called the fundamental state. The basic level of energy is divided itself into two hyperfine levels respectively denoted F = 3 and F = 4. We also know, from Max Planck, that to get an atom from an energy level to another , you must give him energy under the form of electromagnetic radiation, matching the energy difference of the two levels considered . Measurements made between 1955 and 1958 showed that the cesium-133 atom could go from hyperfine level denoted F = 3 to hyperfine level F = 4 when subjected to microwave radiation of frequency 9192631770 Hz. It is this value that is the basis of the definition of the atomic second. An electronic device , a cycle counter , will therefore rely 9192631770 cycles for a period of one second. The apparatus that performs the making of the atomic second is called a primary frequency standard . There are currently different types: primary frequency standard with magnetic deflection , optical pumping and atomic fountains. The device that counts the seconds and accumulates over time is an atomic clock.

2-2Primary frequency standard with magnetic deflection

Cesium is an alkali metal with a melting temperature of about 27 Celsius degree. The cesium is enclosed in an oven and heated to a temperature of about 100 Celsius degree. Cesium vapors exit the furnace and are collimated by the diaphragm so as to obtain a constant velocity cesium . Cesium is then passed through the gap of a magnet whose field is made inhomogeneous . Cesium atoms , which are naturally in two hyperfine levels F = 3 and F = 4 , will then be deflected differently by the magnetic field . This deflection is different due to the fact that atoms have different magnetic moments after they are in the states F = 3 or F = 4. Suppose that only the atoms are in the state F = 3 are used that is to say, they only fit in the microwave cavity of the standard (Ramsey cavity) . If the frequency sent to the atoms is exactly equal to 9192631770 Hz all the atoms will move from level F=3 to level F=4. Actually the frequency sent to the cavity is never exactly equal to the frequency definition . This translates into the fact that a greater or lesser amount of atoms will undergo the atomic transition. The number of atoms in the state F = 4 will be even greater than the frequency is close to the frequency definition . It is therefore necessary to measure the proportion of atoms in the state F = 4. This is achieved through a magnet selector with inhomogeneous field which will sort the atoms since they have different magnetic moments . Atoms in the state F = 3 are deflected out of the etalon and the atoms in the state F = 4 are ionized to create a current which is readily detectable . The greater the intensity of the current is strong , the number of atoms in the state F = 4 will be bigger and the frequency sent in the cavity will be close to the desired frequency . A frequency control device allows it to be modified in real time , based on the measured current value . With this device the frequency delivered by the standard is always locked to the resonant frequency . Primary frequency standards with magnetic deflection , PTB- and PTB- CSIII CsIV , are at the Physikalisch - Technische Bundesanstalt in Germany.

2-3 The optical pumping standards

The optical pumping standards are another type of primary standards , which are very similar to the previous . The essential difference lies in the fact that the magnets are replaced by lasers which must create a "population inversion". In principle, the idea is to provide the energy needed by the cesium atom in the form of light energy , so that it passes from the state F = 3 to F = 4 state . The frequency of the laser used is of course as the corresponding energy calculated by Planck's law , is equal to the energy it takes for the atom to change its state . In reality the cesium atom does not go directly from the state F = 3 to F = 4 state . The atoms which are in the state F = 4 will be excited by the laser so that they pass into a higher energy level . A key property of this level is that its life is very short, ie the atoms will be back very soon either in the state F = 3 or in the state F = 4. The initial population of the state F = 4 is found to be half in the state F = 3 and half in state F = 4. It is then the recovery of the previous mechanism until the level F = 4 is completely depopulated in favor of level F = 3. Atoms can then enter the microwave cavity as in the case of the standard with deflection . Similarly as for the population inversion , the detection of the atoms having their transition made into the cavity is made using a laser. These atoms are now overwhelmingly if the microwave frequency has the correct value in the F = 4 state. In passing through the beam of the second laser they will be excited to higher energy levels . When falling back to the ground state , F = 3 or F = 4 , they will release energy in a form of light called fluorescence . It is therefore necessary to detect the fluorescence light and make its maximum intensity by varying the microwave frequency so that it is as close as possible to the frequency of the definition of ther second. Several standards with optical pumping are currently in operation in the world : JPO at the primary laboratory time and frequency, laboratory of the National Bureau of Metrology in the Paris Observatory , NIST7 at the National Institute of Standards and Technology (USA).

2-4 Atomic fountains

Atomic fountains are the latest developments in the technique of frequency standards. They use the technique of cooling atoms which won the Nobel Prize to C. Cohen- Tannoudji in 1997. Indeed, and whatever the standard considered , the number of atoms undergoing the microwave interaction is even more determined that the interaction time of the latter in the cavity is larger. To increase the interaction time, the atoms are trapped and confined in six intersecting laser beams to minimize their thermal velocity. Statistical physics teach us that the temperature of a gas is proportional to the speed of agitation of the particles that compose it. If the speed is very low the corresponding temperature is very low , hence the name of the technique used. Once the atoms confined, they will be launched in the direction of the microwave cavity, as in conventional standards , the only difference being that this cavity is vertical. The verticality of the cavity is necessary because of the low speed of the atoms: they are on a horizontal ballistic flight and will then fall down. For technical reasons (homogeneity of the magnetic field...) the microwave cavity is not made of a single piece of length D within which would take place continuously the interaction. In the case of the use of standards with deflection or with optical pumping with Ramsey cavity Ramsey in which the interaction takes place at each of its ends which are separated by a distance D. In the case of the atomic fountain cavity, it is a little different: there is one area in which the microwave interaction, but twice , once when the atoms are going up and once when they go down . Preparation and detection of cesium atoms are as in the case of a conventional standard optical pumping. The best atomic fountain currently in operation in the world, FO1 , is at the primary laboratory time and frequency, laboratory of the National Bureau of Metrology at the Paris Observatory.

2-5 Determination of the "Temps atomique international" TAI (International Atomic Time)

The cesium atomic clocks are very peculiar primary standards frequency. They generate the second of the international system as in the case of a conventional standard but also accumulate to produce the minutes and hours. The purpose of these instruments is different from the standards . While they must have a very good accuracy, a smallest possible difference between the definition of the SI second and the second produced by the instrument, the clocks must have excellent long-term stability is to say that changes in the second produced must be as low as possible around an average value (which is not necessarily very close to the SI second ) . The main commercial cesium atomic clocks are of the first type studied : they are instruments with magnetic deflection. Other atomic clocks exist that do not use the cesium atom . There are rubidium clocks , quartz clocks , hydrogen masers ... It is this latter type of clock with cesium clocks , which is the most used in the calculation of the international atomic time . The 14^th General Conference on Weights and Measures (CGPM ) has decided that the International Atomic Time (TAI) will be the time reference coordinate established on the basis of indications of atomic clocks operating in various establishments in accordance with the definition of the second unit of time of the international System of Units . It is currently the International Bureau of Weights and Measures which is responsible for calculating the TAI. This organization collects data from about 230 clocks (in 2000), in 65 laboratories (in 2000). The calculation of TAI is performed using an algorithm ALGOS , which performs a weighted average of the readings of the clocks , the purpose is to obtain a good long-term stability . The accuracy of the time scale is provided by regular comparisons between the unit interval and the unit interval obtained by different primary frequency standards around the world . This calculation provides another expected timescales properties : the durability . A clock that stops working can easily be replaced by another without the overall behavior of the TAI is affected. Currently, the instability of TAI is estimated at about 4.0 10^-15 at 10 days, 4.3 10^-15 at 40 days, 4.5 10^-15 at 160 days and 10^-14 over 3 years. These estimates are made using a statistical estimator called Allan variance.

2-6 Remote comparison of clocks

There are many organizations around the world that have atomic clocks or primary frequency standards. Of course each of these organizations wish to compare their own instruments to others, for the purpose of evaluating and improving their metrological qualities , or simply to participate in the calculation of the International Atomic Time TAI . The most common method to compare remote clocks is to use the satellites of the Global Positioning System, GPS.

The GPS is a military radio-navigation system consisting in a set of satellites orbiting at 20 000 km around the Earth. Each station equipped with a clock to be compared receives signals from a GPS satellite . The arrival times of signals are dated by the clock of the receiving station while the transmission time of these signals by any satellite are dated in the time scale of the clock embedded in the satellite. An algorithm allows to make the correspondence between the time scale of the satellite and the GPS time. By doing a simple difference between the observations made at the same times in both stations, GPS time disappears and it is thus possible to obtain the difference in reading clocks of the two stations.

3- Applications of the metrology of time

All studies undertaken in time metrology have applications. In the field of basic research, it includes attempts to connect the SI units to the definition of the second because it is the unit we know , by far, the best (the relative uncertainty is of the order of 10^-15) . Some physical constants can be determined only by the measurement of the frequency of physical phenomena, then we can get the value with very little uncertainty : the Rydberg constant , the Lande factor of the electron and the fine structure constant are some examples . The metrology of time also has an impact on atomic physics through checking the linearity of quantum mechanics (Schrodinger equation) and its contribution to the knowledge of some atomic and molecular properties . The measurement of time is also involved in testing models of the structure of space-time and gravitation by direct or indirect use of atomic time standards. The purpose of these tests is the discrimination of the different theories of gravitation, Einstein's general relativity being a theory among others. Time metrology also finds its place in many applications of positioning, geodesy and navigation: GPS system is one example, GLObal NAvigation Satellite System (GLONASS) and DORIS system (Doppler orbit radio-positioning integrated by satellite) and PRARE (Precise Range Rate Equipment) are others . The technique of radio interferometry with a very long baseline called VLBI (Very Long Baseline Interferometry ) has applications in the study of the rotation of the Earth and the formation of celestial and terrestrial reference systems .

VLBI measurements rely on the frequency stability of hydrogen masers present in the observing stations : it is the domain of the metrology of time. Millisecond pulsars are objects whose observation showed that their frequency stability could possibly compete with the best stability scales Atomic Time (TAI, TT(BIPM),...). Long-term studies are underway to know the answer to this question. Time metrology is doubly present in this research. First, because the arrival time of the radio pulses emitted by these stars are dated compared to an atomic clock present in the observing station. Secondly because it is necessary to connect this clock to the best atomic time scales for purpose of comparison.

4- Bibliography

Calendriers et chronologie
J. P. Parisot, F. Suagher
Ed. Masson

Les fondements de la mesure du temps. Comment les fréquences atomiques règlent le monde
C. Audoin, B. Guinot
Ed. Masson

Gnomonique moderne
D. Savoie
Ed. Société astronomique de France

Introduction aux éphémérides astronomiques. Supplément explicatif à la connaissance des temps
J. L. Simon, M. Chapront-Touzé, B. Morando, W. Thuillot
EDP Sciences

Echelles de temps atomiques
M. Granveaud
Ed. Chiron

Credit : F. Taris/Observatoire de Paris