自引力系统中测量几何的出现
The Emergence of Measured Geometry in Self-Gravitating Systems
AI总结：
本研究通过分析牛顿N体问题的中心构型数值解，发现最近邻粒子间距随径向距离的系统性变化，论证了自引力系统中的几何是由引力相互作用塑造的涌现有效几何，而非固定背景。
摘要：
这项工作从亨利·庞加莱和阿尔伯特·爱因斯坦关于测量几何的操作性本质的视角出发，研究了自引力$N$体系统的几何性质。利用最近对中心构型（牛顿$N$体问题的特殊平衡解）的数值分析，我们发现了最近邻粒子间距与距系统质心径向距离相关的系统性空间变化。我们认为，这些变化反映了一种由引力相互作用塑造的、依赖于情境的涌现有效几何，这与庞加莱关于测量几何取决于影响测量设备的力的论断，以及爱因斯坦关于杆和钟通过其局部动力学定义物理几何的观点一致。通过在现代计算框架内重新审视这些基础性见解，我们提供了证据表明，自引力牛顿系统中的几何并非固定背景，而是由内部物理相互作用产生的涌现构造。
英文摘要：
This work investigates the geometrical properties of self-gravitating $N$-body systems from the perspective established by Henri Poincaré and Albert Einstein concerning the operational nature of measured geometry. Utilizing recent numerical analyses of central configurations--special equilibrium solutions to the Newtonian $N$-body problem--we uncover systematic spatial variations in nearest-neighbor particle separations correlated with the radial distance from the system's center of mass. We argue that these variations reflect a context-dependent, emergent effective geometry shaped by gravitational interactions, in accordance with Poincaré's assertion that measured geometry depends on the forces influencing measuring devices, and Einstein's view that rods and clocks define physical geometry through their local dynamics. By revisiting these foundational insights within a modern computational framework, we provide evidence that geometry in self-gravitating Newtonian systems is not a fixed background, but an emergent construct arising from internal physical interactions.
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