Use of the relativistic phase-time equation in absolute ballistic gravimetry

Abstract

The signal recorded in absolute ballistic gravimeters and used to track the trajectory of the free-falling corner-cube was recently studied for the first time in full agreement with relativistic effects. The outcome was an original phase-time equation describing the optical interference as a function of initial position, initial speed, dimensions and refractive index of the corner-cube. This offers the unique possibility to check possible systematic errors affecting data collected using the conventional position-time equation coupled to the debated "speed of light" correction. To this aim, I simulated and processed threshold-crossing times anticipated by the phase-time equation in typical experimental conditions of working gravimeters. In addition, the fictitious condition when a mirror replaces the corner-cube is investigated to probe the significant correction suggested by the developer of the phase-time equation. The results are given in terms of position and gravity acceleration errors.

Comparison of Open and Solid Falling Retroreflector Gravimeters

“…The apparently large effect on g arising from dimensions and refractive index of the cube resulted in several critical comments [2][3][4], and replies [5][6][7], without throwing light on the real issues. D'Agostino [8] simulated dropping of glass and open retroreflectors using only the difference ϕ(t)−ϕ(0) for the interference observations. This subtraction removes nonrelativistic terms responsible for the predicted change [1] in g, as well as some relativistic contributions.…”