Gravitational torque frequency analysis for the Einstein elevator experiment

Abstract

Testing the principle of equivalence with a differential acceleration detector that spins while free falling requires a reliable extraction of a very small violation signal from the noise in the output signal frequency spectrum. The experiment is designed such that the violation signal is modulated by the spin of the test bodies. The possible violation signal is mixed with the intrinsic white noise of the detector and the colored noise associated with the modulation of gravitational perturbations, through the spin, and inertial-motion-related noise. In order to avoid false alarms the frequencies of the gravitational disturbances and the violation signal must be separate. This paper presents a model for the perturbative gravitational torque that affects the measurement. The torque is expanded in an asymptotic series to the fourth order and then expressed as a frequency spectrum. A spectral analysis shows the design conditions for frequency separation between the perturbing torque and the violation signal.