Testing special relativity with geodetic VLBI

TL;DR

This paper explores the use of geodetic VLBI to test special relativity by detecting second-order relativistic effects in Earth's orbit, developing a generalized model to estimate parameters related to Lorentz invariance.

Contribution

It introduces a modified RMS formalism for geodetic VLBI data to test Lorentz invariance and estimates related parameters, expanding the theoretical framework for relativity tests.

Findings

Second order relativistic effects reach up to 300 ps in VLBI measurements.

The generalized model includes three parameters for testing Lorentz invariance.

Equations can be used to test VLBI group delay model itself.

Abstract

Geodetic Very Long Baseline Interferometry (VLBI) measures the group delay in the barycentric reference frame. As the Earth is orbiting around the Solar system barycentre with the velocity $V$ of 30 km/s, VLBI proves to be a handy tool to detect the subtle effects of the special and general relativity theory with a magnitude of $(V/\textrm{c})^2$. The theoretical correction for the second order terms reaches up to 300~ps, and it is implemented in the geodetic VLBI group delay model. The total contribution of the second order terms splits into two effects - the variation of the Earth scale, and the deflection of the apparent position of the radio source. The Robertson-Mansouri-Sexl (RMS) generalization of the Lorenz transformation is used for many modern tests of the special relativity theory. We develop an alteration of the RMS formalism to probe the Lorenz invariance with the geodetic VLBI data. The kinematic approach implies three parameters (as a function of the moving reference frame velocity) and the standard Einstein synchronisation. A generalised relativistic model of geodetic VLBI data includes all three parameters that could be estimated. Though, since the modern laboratory Michelson-Morley and Kennedy-Thorndike experiments are more accurate than VLBI technique, the presented equations may be used to test the VLBI group delay model itself.