Systems consisting of spheres rolling on elastic membranes have been used as educational tools to introduce a core conceptual idea of General Relativity (GR): how curvature guides the movement of matter. However, previous studies have revealed that such schemes cannot accurately represent relativistic dynamics in the laboratory. Dissipative forces cause the initially GR-like dynamics to be transient and consequently restrict experimental study to only the beginnings of trajectories; dominance of Earth's gravity forbids the difference between spatial and temporal spacetime curvatures. Here by developing a mapping between dynamics of a wheeled vehicle on a spandex membrane, we demonstrate that an active object that can prescribe its speed can not only obtain steady-state orbits, but also use the additional parameters such as speed to tune the orbits towards relativistic dynamics. Our mapping demonstrates how activity mixes space and time in a metric, shows how active particles do not necessarily follow geodesics in the real space but instead follow geodesics in a fiducial spacetime. The mapping further reveals how parameters such as the membrane elasticity and instantaneous speed allow programming a desired spacetime such as the Schwarzschild metric near a non-rotating black hole. Our mapping and framework point the way to the possibility to create a robophysical analog gravity system in the laboratory at low cost and provide insights into active matter in deformable environments and robot exploration in complex landscapes.
翻译:由在弹性膜膜上滚动的球体构成的球体系统已经被用作教育工具,以引入一般相对论(GR):如何曲线引导物质移动的核心概念概念概念概念。 但是,先前的研究显示,这种计划无法准确地代表实验室中的相对动态。 分化力量导致最初的GR型动态变换,从而将实验研究仅限于轨道的起点; 地球重力的主宰力禁止空间与时空时空弯曲的差别。 在这里,通过绘制一个在光外膜上的轮式飞行器动态动态之间的映射,我们证明,一个能够规定其速度的主动物体不仅能够获得稳定状态轨道,而且还能够使用其他参数,例如将轨道调整到相对相对动态的速度。 我们的绘图显示,活动如何将空间和时间混在一起,表明活跃的粒子不一定跟随实际空间的地标,而是跟随空间时段的地貌特征。 绘图进一步揭示了在接近深深层线的深度勘测过程中,在接近空间轨迹的轨迹构造中,在接近空间轨迹定的轨道构造中,并且可以将空间定位速度速度编成一个非轨道构造框架。