**2.2 Atomic clocks and ACES**

The time scales like the SI (International System of Units) *atomic second* are based on frequency standards for *microwave* atomic clocks based on isotopes like cesium (133*Cs*) and rubidium ( <sup>87</sup>*Rb*) and with frequencies of the order of GigaHertz (109*Hz*). While the national standard agencies (National Institute of Standards and Technology NIST in USA, National Physical Laboratory NPL in United Kingdom, Paris Observatory in France, Physikalisch-Technische Bundesanstalt PTB in Germany, Istituto Nazionale di Ricerca Metrologica INRIM in Italy) maintain an accuracy of 1 nanosecond per day (1*ns* = 10−<sup>9</sup> *s*), many primary cesium atomic clocks using laser cooled atomic fountains have an inaccuracy less than 100 picoseconds per day (1*ps* = 10−<sup>12</sup> *s*) with the best ones approaching 10 ps per day (Bize S. et al, 2005; Parker T.E., 2010).

If atomic clocks operating on different quantum transitions are considered as ideal clocks in general relativity, then they measure the same proper time (and not a coordinate time) along their trajectory (Guinot B., 1997). See Ref. (Reynaud S. et al, 2009) and its bibliography for the experiments on the *universality of clock rates* (relative frequency ratios between different clocks are constant at a level of the order of 10−<sup>16</sup> per year). See also Ref. (Perlick V., 1987, 1994) for another general relativistic effect, the *second clock effect*, according to which two clocks synchronized at the same point, then separated and finally rejoined remain synchronized in Riemannian space-times like Einstein's ones but not in Weyl space-times.

A new family of *optical* atomic clocks in the region of 1015*Hz* is developing quickly with the help of optical frequency-combs for direct optical frequency measurements. They allow one to reach a fractional frequency inaccuracy of better than 10−<sup>17</sup> (corresponding to better than 1 ps per day) (Gill P., 2005; Rosenbad T. et al, 2008; Ludlow A.D. et al, 2008; Chou C.W. et al 2010a) and will become relevant for metrology in the near future. Moreover optical clocks allow to verify the "time dilation effect" for relative speeds of less than 10 m/s or for a change in height near the Earth's surface of less than 1 meter (Chou C.W., 2010b).

In Ref. (Arias E.F., 2005) there is a review of time metrology with a comparison of various time scales, the use of GPS receiver for time transfer (see also Ref. (Petit G. et al, 2005)) and on the dissemination and access to the international time scales. See also Refs. (Lemonde P. et al, 2001; SIGRAV 2006) for the status of atomic clocks in space near the Earth or on spacecrafts inside the Solar System.

The Atomic Clock Ensemble in Space (ACES) mission of the European Space Agency ESA (ACES 2010; Cacciapuoti L. et al, 2007, 2008; Blanchet L. et al, 2000), to be launched in 2015, aims to put a new microwave atomic clock (PHARAO, Projet d'Horloge Atomique par Refroidissement d'Atome en Orbite) together with an active hydrogen maser (SHM, Space active Hydrogen Maser) on the International Space Station (ISS; height 400 Km, rotation period 90 min, inclination angle 51.6*o*). The two clocks will generate an on-board timescale with an expected frequency instability and inaccuracy at the 10−<sup>16</sup> level. There will be a frequency comparison between the space clocks and ground clocks using microwave links: in particular ACES will give the first precision measurement of the gravitational redshift of the geoid, namely of the 1/*c*<sup>2</sup> deformation of Minkowski light-cone caused by the geo-potential.
