To date, there have been few dynamic measurements of gravitation in the laboratory, and fully controlled quantitative experiments have been limited to frequencies in the millihertz regime. Here we introduce a fully characterized experiment at frequencies in the hertz regime, which allows a quantitative determination of the dynamic gravitational interaction between two parallel beams vibrating at 42 Hz in bending motion. A large amplitude vibration of the transmitter beam produces a gravitationally induced motion of the high-quality-factor resonant detector beam with amplitudes up to 10⁻¹¹ m. The sub-picometre-resolution measurement is made possible by a setup that combines acoustical, mechanical and electrical isolation; a temperature-stable environment; heterodyne laser interferometry; and lock-in detection. The interaction is quantitatively modelled based on Newton’s law of gravitation. Amplitude measurements at varying beam distances follow an inverse square law and agree with theoretical predictions to within approximately three percent. Furthermore, we extract the value of the gravitational constant G and near-field gravitational energy flow. We expect our experiment to enable progress in directions where current experimental evidence for dynamic gravitation is limited, such as the dynamic determination of G, inverse square law and gravitational shielding.

迄今为止，实验室中几乎没有对引力的动态测量，并且完全受控的定量实验仅限于毫赫兹范围内的频率。在这里，我们介绍了一个完全表征的赫兹频率下的实验，它允许定量确定在弯曲运动中以 42 Hz 振动的两个平行梁之间的动态引力相互作用。发射器光束的大振幅振动产生高品质因数谐振探测器光束的重力感应运动，振幅高达 10 ^-11 米。亚皮米分辨率测量是通过结合声学、机械和电气隔离的设置实现的；温度稳定的环境；外差激光干涉仪；和锁定检测。相互作用是根据牛顿万有引力定律定量建模的。不同光束距离下的幅度测量遵循平方反比定律，并且与理论预测一致，大约在 3% 以内。此外，我们提取了引力常数G和近场引力能量流的值。我们希望我们的实验能够在当前动态引力实验证据有限的方向上取得进展，例如G的动态确定、平方反比定律和引力屏蔽。