Satellite test of special relativity using the global positioning system

Abstract

A test of special relativity has been carried out using data of clock comparisons between hydrogen maser clocks on the ground and cesium and rubidium clocks on board 25 global positioning system (GPS) satellites. The clocks were compared via carrier phase measurements of the GPS signal using geodetic receivers at a number of stations of the International GPS Service for Geodynamics (IGS) spread worldwide. In special relativity, synchronization of distant clocks by slow clock transport and by Einstein synchrony (using the transmission of light signals) is equivalent in any inertial frame. A violation of this equivalence can be modeled using the parameter $\ensuremath{\delta}c/c,$ where $c$ is the round-trip speed of light ($c=299792458\mathrm{m}/\mathrm{s}$ in vacuum) and $\ensuremath{\delta}c$ is the deviation from $c$ of the observed velocity of a light signal traveling one way along a particular spatial direction with the measuring clocks synchronized using slow clock transport. In special relativity $\ensuremath{\delta}c/c=0.$ Experiments can set a limit on the value of $\ensuremath{\delta}c/c$ along a particular spatial direction (henceforth referred to as ``direction of $\ensuremath{\delta}c$''). Within this model our experiment is sensitive to a possible violation of special relativity in any direction of $\ensuremath{\delta}c,$ and on a nonlaboratory scale (baselines $>~20000\mathrm{km}$). The results presented here set an upper limit on the value of $\ensuremath{\delta}c/c<5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ when considering all spatial directions of $\ensuremath{\delta}c$ and $\ensuremath{\delta}c/c<2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ for the component in the equatorial plane.