  Incompatibility between the principle of the constancy of the speed of light
and the Lorentz contraction in the global positioning system (GPS) is
discussed. The GPS works precisely in the earth-centered locally inertial (ECI)
coordinate system on the condition that the speed of light c is assumed to be
constant regardless of the inertial motion of the GPS satellites and the earth.
The inertial system of the earth travels not only in the solar system at the
velocity 30 km/s but also in the cosmic microwave background (CMB) at the
velocity 700 km/s. The deviation on the car navigation system by the Lorentz
contraction of 700 km/s is maximally estimated as 54 m. However, such a large
deviation is not observed: that is, the Lorentz contraction is not observed in
the gravitational field of the earth. If there is a Lorentz contraction, the
GPS cannot work so precisely. The GPS satellites are in the gravitational field
of the earth, therefore the system should be interpreted by the theory of
general relativity as well as special relativity.
