马赫原理的实现：时钟和杆-或更基本的东西？
A realization of Mach's Principle: Clocks and rods - or something more fundamental?
摘要：
本文实质上是对马赫原理实现的一种推测，我们通过两个问题的表述来详细分析：（A）全局惯性时空能与非平凡的全局物质分布相联系吗？(B)如果是，这种全球分布的一般性质是什么？这些问题是在一个极其简单的模型宇宙的背景下解决的，模型宇宙由只具有可数性的粒子组成，这些粒子存在于一个无形的连续体中。由于在这个模型宇宙中没有预先指定的时钟和棒的概念，我们被迫对空间和时间测量的性质进行基本的考虑。为了回答最初的两个问题，分析告诉我们，一个全局惯性时空可以与一个非平凡的全局物质分布相关联，并且这个分布必然是分形的，D=2。后者的结果进行了比较与现代调查的星系分布的结果（通常，乔伊斯，Montuori，拉比尼astro-ph/9901290，ApJ Lett 1999和本文中的其他参考文献），发现这种分布是准分形与D约= 2的小到中尺度，与中到大尺度的情况是一个相当大的争论的话题。因此，考虑到所考虑的模型极其简单，观测证据与这样的解释是一致的，即分析的观点以良好的一阶近似捕捉宇宙现实。我们认为这些结果的影响。
英文摘要：
This paper is essentially a speculation on the realization of Mach's Principle, and we came to the details of the present analysis via the formulation of two questions: (A) Can a globally inertial space & time be associated with a non-trivial global matter distribution? (B) If so, what are the general properties of such a global distribution? These questions are addressed within the context of an extremely simple model universe consisting of particles possessing only the property of enumerability existing in a formless continuum. Since there are no pre-specified ideas of clocks and rods in this model universe, we are forced into fundamental considerations about the nature of spatial and temporal measurement. In answer to the original two questions, the analysis tells us that a globally inertial space & time can be associated with a non-trivial global matter distribution, and that this distribution is necessarily fractal with D=2. This latter result is compared with the results of modern surveys of galaxy distributions (typically, Joyce, Montuori, Labini astro-ph/9901290, ApJ Lett 1999 and other references in this paper), which find that such distributions are quasi-fractal with D approx = 2 on the small-to-medium scales, with the situation on the medium-to-large scales being a topic of considerable debate. Accordingly, and bearing in mind the extreme simplicity of the model considered, the observational evidence is consistent with the interpretation that the analysed point-of-view captures the cosmic reality to a good first-order approximation. We consider the implications of these results.
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