# 大數假說

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

## 發展背景

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

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

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

## 狄拉克對大數巧合的詮釋

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

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

• 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. S. Ray; U. Mukhopadhyay; P. P. Ghosh. Large Number Hypothesis: A Review. 2007. [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.