Measuring the speed of gravity with laser Doppler vibrometers and silicon mechanical resonators

The old question of the speed of propagation of gravitational interactions still needs a laboratory answer. An experimental setup for direct measurement of the propagation delay in the gravitational interaction between resonating gravitationally coupled oscillators is proposed. The oscillators are designed to act like transmitter and receiver in an AM radio communication. The signal, a dynamic Newtonian field, is generated by the precise vibrations of a massive tungsten disc, in resonance with its suspension system like a trampoline oscillator. The disc is driven by a shaker locked to a GPSDO frequency reference, while its movement is tracked with a laser Doppler vibrometer and a lock-in amplifier, locked to the same frequency reference. The gravitational signal is received by an antenna, a gold-coated silicon oscillator with resonance frequency of 2 kHz and a Q of 200 000 in thermal vacuum. The vibrations of the antenna are tracked by a second laser Doppler vibrometer with a noise level of 30 fm/√Hz and a lock-in amplifier using the output of the first lock-in amplifier as reference. High-vacuum chambers and multi-stage vibration and acoustic isolation systems are required for both the generator and the antenna. Cross-correlating the data of the two oscillators, their phase difference is then measured and, using the frequency of the signal and the distance between oscillators, the speed of gravity will be calculated. Numerous measurements at various distances spanning a 300 mm range are collected and used for the determination of other parameters, including G. (paper)