are the transition frequencies of the transitions in rest. with as ion velocity and as speed of light. In the case of saturation spectroscopy the formula changes to with as the transition frequency in rest. In the case that special relativity is valid is equal to zero. Slow moving clocks Meanwhile, the measurement of time dilation at everyday speeds has been accomplished as well. Chou et al. (2010) created two clocks each holding a single 27Al+ ion in a Paul trap. In one clock, the Al+ ion was accompanied by a 9Be+ ion as a "logic" ion, while in the other, it was accompanied by a 25Mg+ ion. The two clocks were situated in separate laboratories and connected with a 75 m long, phase-stabilized optical fiber for exchange of clock signals. These optical atomic clocks emitted frequencies in the petahertz (1 PHz = 1015 Hz) range and had frequency uncertainties in the 10−17 range. With these clocks, it was possible to measure a frequency shift due to time dilation of ∼10−16 at speeds below 36 km/h (< 10 m/s, the speed of a fast runner) by comparing the rates of moving and resting aluminum ions. It was also possible to detect gravitational time dilation from a difference in elevation between the two clocks of 33 cm. See also Experimental testing of time dilation Tests of special relativity References Further reading Doppler effects Tests of special relativity 1938 in science