[Paper Review] Incompatibility between the principle of the constancy of the speed of light and the Lorentz contraction in the GPS Experiment

Masanori Sato|ArXiv.org|Mar 12, 2007

Relativity and Gravitational Theory3 references3 citations

TL;DR

This paper argues that the GPS system's precise operation contradicts the expected effects of Lorentz contraction when accounting for Earth's high-speed motion through the cosmic microwave background (700 km/s), despite the constancy of light speed being assumed in the Earth-Centered Inertial (ECI) frame. The absence of observable 54-meter positional deviations implies Lorentz contraction is not occurring in Earth's gravitational field, challenging the compatibility of special relativity's predictions with GPS functionality under general relativistic conditions.

ABSTRACT

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.

Motivation & Objective

• To investigate whether Lorentz contraction should be observable in the GPS system due to Earth's high-velocity motion through the cosmic microwave background (CMB).
• To assess whether the observed precision of GPS contradicts predictions from special relativity, particularly the Lorentz contraction effect at 700 km/s.
• To evaluate whether the constancy of the speed of light in the ECI frame is compatible with the absence of measurable Lorentz contraction in Earth's gravitational field.

Proposed method

• Analyzes the GPS system's operation in the Earth-Centered Inertial (ECI) coordinate system, assuming the speed of light is constant regardless of satellite or Earth motion.
• Estimates the maximum possible deviation due to Lorentz contraction using Earth's velocity of 700 km/s relative to the CMB.
• Calculates a theoretical maximum positional error of 54 meters in car navigation systems if Lorentz contraction were present.
• Compares this theoretical deviation with actual GPS precision, which shows no such error.
• Applies both special and general relativity to the GPS satellite system, considering the Earth's gravitational field.

Experimental results

Research questions

• RQ1 Is Lorentz contraction observable in the GPS system given Earth's 700 km/s motion relative to the CMB?
• RQ2 Does the constancy of the speed of light in the ECI frame remain consistent with the absence of Lorentz contraction in Earth's gravitational field?
• RQ3 Could the lack of observed 54-meter deviation in GPS navigation imply a contradiction between special relativity and observed GPS performance?
• RQ4 To what extent does general relativity modify the predictions of special relativity in the context of GPS satellite operations?
• RQ5 Is the assumption of constant light speed in the ECI frame compatible with the non-observation of Lorentz contraction effects?

Key findings

• The theoretical maximum deviation due to Lorentz contraction at 700 km/s is estimated at 54 meters in car navigation systems.
• No such 54-meter deviation is observed in actual GPS operations, indicating that Lorentz contraction does not occur in Earth's gravitational field.
• The precise functioning of GPS contradicts the expected effects of Lorentz contraction, suggesting an incompatibility with special relativity's predictions.
• The constancy of the speed of light in the ECI frame remains valid, but its compatibility with Lorentz contraction is called into question by the absence of observable effects.
• The results imply that the standard interpretation of special relativity may not fully apply in the presence of Earth's gravitational field, requiring a reevaluation of relativistic effects in GPS systems.