AI 中文总结
研究通过两个球形质量体在不同外部引力场中的动力学，推导其内部动力学解，确定区分不同配置所需的灵敏度，评估相关效应，如检测简单MOND插值函数预测对亚毫米质量体需0.1飞米空间灵敏度，为修正引力理论实验测试提供依据。
AI 中文摘要
尽管有确凿证据，但尚未证实暗物质粒子的存在，这使得修正引力作为观测现象的另一种解释备受关注。一个突出例子是修正牛顿动力学（MOND），它预测系统的内部动力学取决于其所处的外部引力场。这种所谓的外场效应违反了强等效原理（SEP），在经典力学中不存在，是修正引力实验测试的一个有前景的途径。受此启发，我们研究了两个球形质量体的动力学，其对称轴与局部引力场平行或正交。我们推导了在强均匀和径向外部场中此类系统内部动力学的解。特别是对于径向外部场，如果非相对论引力场的旋度可以不为零，我们发现垂直配置中质量体的相互吸引力并不严格与对称轴对齐，即使外部引力场处处由非引力力平衡时也会获得一个小的横向分量。利用这些解，我们确定了区分两种配置所需的空间和时间灵敏度，并系统地评估了包括空气阻力、物体大小和表面相互作用等与实验相关的效应。例如，对于在大约30分钟内演化的亚毫米质量体，检测简单MOND插值函数的预测需要0.1飞米量级的空间灵敏度。这样的时间在悬浮粒子或太空环境中可能实现。较低分辨率的实验作为SEP的独立测试也很有趣，并对修正引力理论施加了限制。
英文摘要
Despite compelling evidence, the absence of a confirmed dark matter particle has sustained interest in modified gravity as an alternative explanation for the observed phenomenology. One prominent example is Modified Newtonian Dynamics (MOND), which predicts that the internal dynamics of a system depends on the external gravitational field in which it is embedded. This so-called External Field Effect violates the strong equivalence principle (SEP) and is absent in canonical mechanics, making it a promising avenue for experimental tests of modified gravity. Motivated by this, we investigate the dynamics of two spherical masses arranged such that their symmetry axis is either parallel or orthogonal to the local gravitational field. We derive solutions describing the internal dynamics of such systems in both strong uniform and radial external fields. In particular, for a radial external field, if the non-relativistic gravitational field is free to have non-vanishing curl, we find that the mutual attraction of the masses in the perpendicular configuration is not strictly aligned with their symmetry axis. It acquires a small transverse component, even when the external gravitational field is everywhere balanced by non-gravitational forces. Using these solutions, we determine the spatial and temporal sensitivities required to distinguish the two configurations and systematically assess experimentally relevant effects, including air drag, object size, and surface interactions. As an example, detecting the prediction of the simple MOND interpolating function requires a spatial sensitivity of order 0.1 fm for sub-millimeter masses evolving over approximately 30 minutes. Such times may be achievable with levitated particles or in space-based environments. Experiments operating at lower resolutions are also interesting as independent tests of SEP and place constraints on modified-gravity theories.
Comments11 pages, 5 figures
