Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544.
Proc Natl Acad Sci U S A. 2014 Feb 18;111(7):2409-16. doi: 10.1073/pnas.1318003111. Epub 2014 Jan 29.
Using basic physical arguments, we derive by dimensional and physical analysis the characteristic masses and sizes of important objects in the universe in terms of just a few fundamental constants. This exercise illustrates the unifying power of physics and the profound connections between the small and the large in the cosmos we inhabit. We focus on the minimum and maximum masses of normal stars, the corresponding quantities for neutron stars, the maximum mass of a rocky planet, the maximum mass of a white dwarf, and the mass of a typical galaxy. To zeroth order, we show that all these masses can be expressed in terms of either the Planck mass or the Chandrasekar mass, in combination with various dimensionless quantities. With these examples, we expose the deep interrelationships imposed by nature between disparate realms of the universe and the amazing consequences of the unifying character of physical law.
我们运用基本的物理论证，通过量纲和物理分析，仅用少数几个基本常数，推导出宇宙中重要物体的特征质量和尺寸。这一练习说明了物理学的统一力量，以及我们所居住的宇宙中微观世界和宏观世界之间的深刻联系。我们专注于正常恒星的最小和最大质量、相应的中子星数量、岩石行星的最大质量、白矮星的最大质量以及典型星系的质量。在零阶近似下，我们表明所有这些质量都可以用普朗克质量或钱德拉塞卡质量来表示，同时结合各种无量纲量。通过这些例子，我们揭示了自然界在宇宙不同领域之间强加的深刻相互关系，以及物理定律的统一性质所带来的惊人后果。
