# 大數假說

• 重力常數反比於宇宙的年齡：$G \propto 1/t\,$
• 宇宙帶有的質量正比於宇宙年齡的平方：$M \propto t^2$

## 發展背景

$\frac{r_H}{r_e} \approx 10^{42} \approx \frac {R_U}{r_e}$,
$r_e = \frac {e^2}{4 \pi \epsilon_0 m_e c^2}$,
$r_H = \frac {e^2}{4 \pi \epsilon_0 m_H c^2}$,
$m_H c^2 = \frac {Gm_e^2}{r_e}$

$\frac {e^2}{4 \pi \epsilon_0 Gm_e^2} \approx \sqrt {N} \approx 10^{42}$.

$G = \left(\frac{c^3}{M_U}\right)t$

## 狄拉克對大數巧合的詮釋

$\frac {ct}{r_e} \approx 10^{40}$,

$\frac{4 \pi \epsilon_0 G m_p m_e}{e^2} \approx 10^{-40}$.

• 附加生成：新的物質從空間中均勻產生。
• 倍數生成：新的物質伴隨原有的物質產生。

## 參考資料

1. ^ 1.0 1.1 1.2 S. Ray, U. Mukhopadhyay, P.P. Ghosh. Large Number Hypothesis: A Review. arXiv:0705.1836 [gr-qc]. 2007.
2. ^ H. Weyl. Annals of Physics. 1917, 54: 117.
3. ^ H. Weyl. Annals of Physics. 1919, 59: 101.
4. ^ A. Eddington. Proceedings of the Cambridge Philosophical Society. 1931, 27.
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.