100 Years of Relativity Space-Time Structure: Einstein and Beyond ...

260 N. Ashbyflawed technical report 1 was issued as late as 1996 by an apparently authoritativesource–the Aerospace Corporation, where the civilian counterpart ofthe JPO is located. One source of confusion was the Sagnac effect thatmakes it impossible to self-consistently synchronize clocks on the surfaceof the rotating earth by performing operations with electromagnetic signalsor slowly moving portable clocks, like those that could successfully beused to synchronize clocks in an inertial frame. Thus a problem that hadto be solved was effective synchronization of clocks fixed or slowly movingon earth’s surface. Another source of confusion was whether the sun’sgravitational potential would have a significant effect on clocks in GPSsatellites.The GPS is made possible by extremely accurate, stable atomic clocks.Figure 1 gives a plot of the Allan deviation σ y (τ) for a high-performanceCesium clock, as a function of sample time τ. If an ensemble of clocks isinitially synchronized, then when compared to each other after a time τ, theAllan deviation provides a measure of the rms fractional frequency deviationamong the clocks due to intrinsic noise processes in the clocks. Frequencyoffsets and frequency drifts are additional systematic effects which must beaccounted for separately. Also on Figure 1 is an Allan deviation plot for aQuartz oscillator such as is typically found in a GPS receiver. Quartz oscillatorsusually have better short-term stability performance characteristicsthan Cesium clocks, but after 100 seconds or so, Cesium has far betterperformance. In actual clocks there is a wide range of variation around thenominal values plotted in Figure 1. The most stable GPS clocks use Rubidiumatoms and reach maximum stability levels of a few parts in 10 15 afterabout ten days. What this means is that after initializing such a clock, andleaving it alone for ten days, it should be correct to within about 5 partsin 10 15 , or 0.4 nanoseconds. Relativistic effects are huge compared to this.The purpose of this article is to explain how relativistic effects are accountedfor in the GPS. Although clock velocities are small and gravitationalfields are weak near the earth, they give rise to significant relativisticeffects. These effects include first- and second-order Doppler frequencyshifts of clocks due to their relative motion, gravitational frequencyshifts, and the Sagnac effect due to earth’s rotation. If such effects are notaccounted for properly, unacceptably large errors in GPS navigation andtime transfer will result. In the GPS one can find many examples of theapplication of fundamental relativity principles. Also, experimental tests ofrelativity can be performed with GPS, although generally speaking theseare not at a level of precision any better than previously existing tests.