# 大数假说

## 维基百科，自由的百科全书

• 重力常数反比于宇宙的年龄：${\displaystyle G\propto 1/t\,}$
• 宇宙带有的质量正比于宇宙年龄的平方：${\displaystyle M\propto t^{2))$

## 发展背景

${\displaystyle {\frac {r_{H)){r_{e))}\approx 10^{42}\approx {\frac {R_{U)){r_{e))))$
${\displaystyle r_{e}={\frac {e^{2)){4\pi \epsilon _{0}m_{e}c^{2))))$
${\displaystyle r_{H}={\frac {e^{2)){4\pi \epsilon _{0}m_{H}c^{2))))$
${\displaystyle m_{H}c^{2}={\frac {Gm_{e}^{2)){r_{e))))$

${\displaystyle {\frac {e^{2)){4\pi \epsilon _{0}Gm_{e}^{2))}\approx {\sqrt {N))\approx 10^{42))$.

${\displaystyle G=\left({\frac {c^{3)){M_{U))}\right)t}$

## 狄拉克对大数巧合的诠释

${\displaystyle {\frac {ct}{r_{e))}\approx 10^{40))$

${\displaystyle {\frac {4\pi \epsilon _{0}Gm_{p}m_{e)){e^{2))}\approx 10^{-40))$

• 附加生成：新的物质从空间中均匀产生。
• 倍数生成：新的物质伴随原有的物质产生。

## 参考资料

1. S. Ray; U. Mukhopadhyay; P. P. Ghosh. Large Number Hypothesis: A Review. 2007. arXiv:0705.1836 [gr-qc].
2. ^ H. Weyl. Zur Gravitationstheorie. Annalen der Physik. 1917, 359 (18): 117. Bibcode:1917AnP...359..117W. doi:10.1002/andp.19173591804.
3. ^ H. Weyl. Eine neue Erweiterung der Relativitätstheorie. Annalen der Physik. 1919, 364 (10): 101. Bibcode:1919AnP...364..101W. doi:10.1002/andp.19193641002.
4. ^ A. Eddington. Preliminary Note on the Masses of the Electron, the Proton, and the Universe. Proceedings of the Cambridge Philosophical Society. 1931, 27: 15. Bibcode:1931PCPS...27...15E. doi:10.1017/S0305004100009269.
5. ^ E.A. Milne. Relativity, Gravity and World Structure. Oxford University Press. 1935.
6. ^ H. Kragh. Cosmology and Controversy: The historical development of two theories of the universe. Princeton University Press. 1996: 61–62.