\begin{align}
m_p=\sqrt{\frac{\hbar c}{G}}&=2.18\times{10}^{-8}\rm{kg}&\rm{{10}^{7}\ E. coli}\phantom {100000000000000000000}&\phantom {10000}(1)\nonumber\\
l_p=\sqrt{\frac{\hbar G}{c^3}}&=1.63\times{10}^{-35}\rm{m}&\rm{Radius\ of\ proton\ ={10}^{-15}\ m}\phantom {10000}&\phantom {10000}(2)\nonumber\\
t_p=\sqrt{\frac{\hbar G}{c^5}}&=5.39\times{10}^{-44}\rm{s}&\rm{Cosmic\ inflation\ ends\ at\ {10}^{-32}s}\phantom {10000}&\phantom {10000}(3)\nonumber\\
E_p=\sqrt{\frac{\hbar c^5}{G}}&=1.95\times{10}^9\rm{J}&\rm{Sun\ emits{\ 10}^{26}\ Js^{-1}. \text{ A-bomb}\rm={10}^{12}}\ J&\phantom {10000}(4)\nonumber\\
&=1.22\times{10}^{19}\rm{GeV}&
&\phantom {10000}\nonumber
\end{align}
Max Planck 1858-1947 |
Whilst it is unimaginable that we will see things shorter than ##t_p## or smaller than ##l_p##, particle masses ('point masses') greater than ##m_p## are commonplace in GR and energies greater than ##E_p## are happening all the time. Can anybody help me make sense of the ##m_p,E_p## parts? And why are those 'greater than' and the others 'less than'?
I found out when I asked on physics forums. Read it at Commentary 4.5 Planck dimensions.pdf (2 pages).
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