从第一原理保守的MOND
Conservative MOND from first principles
摘要：
反对Milgrom的MOND的主要论点是，它没有理论支持，尽管已经花费了相当大的努力试图提供它。与这种批评相反，MOND无可辩驳地享有不断扩大的成功组合，因此几乎可以肯定地利用了一些基本的东西。但是什么呢？大约在MOND成为争议话题的同一时期，巴利舍夫、西洛斯·拉比尼和其他人一直声称，至少在中等尺度上，宇宙中的物质是以准分形$D\approx 2$的方式分布的，早些年也有同样的争议。有一个链接：如果一个中等尺度的准分形$D\approx 2$宇宙的想法被认真对待，那么就有一个相关的特征质量表面密度，比如说$Σ_F$，和一个相关的特征加速度尺度$a_F = 4πG \,Σ_F$。MOND的全部成功都是基于一个临界加速度标度$a_0$的概念。这是一个明显的步骤，使协会$a_0 \sim a_F$，然后考虑MOND临界加速度边界简单地作为一个标志的特征质量表面密度边界分离的“星系”的环境特点是$Σ_F$。这为从第一性原理合成保守MOND提供了一条途径。当应用于非对称样本时，保守MOND的径向加速度关系（RAR）是单位线。没有质量差异。
英文摘要：
The primary argument levelled against Milgrom's MOND is that it has no theoretical support, even though considerable effort has been expended in attempting to provide it. Against that criticism, MOND irrefutably enjoys an expanding portfolio of success and so is almost certainly tapping into something fundamental. But what? Over roughly the same period that MOND has been a topic of controversy, Baryshev, Sylos Labini and others have been claiming, with equal controversy in earlier years, that, on medium scales at least, material in the universe is distributed in a quasi-fractal $D\approx 2$ fashion. There is a link: if the idea of a quasi-fractal $D\approx 2$ universe on medium scales is taken seriously, then there is an associated characteristic mass surface density, $Σ_F$ say, and an associated characteristic acceleration scale $a_F = 4πG \,Σ_F$. The whole success of MOND is predicated upon the idea of a critical acceleration scale, $a_0$. It is an obvious step to make the association $a_0 \sim a_F$ and then to consider the MOND critical acceleration boundary simply as a marker for a characteristic mass surface density boundary separating 'galaxy' from an environment characterized by $Σ_F$. This provides a route to the synthesis of conservative MOND from first principles. The radial acceleration relation (RAR) for conservative MOND when applied to the SPARC sample is the unity line. There is no mass discrepancy.
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