natural units
recall the units of the fundamental constants \[G\] and \[\hbar\]
\[\hbar ; [=] ; \frac{m \times l^2}{t}=J \cdot s\]
\[G ; [=] ; \frac{l^3}{m \times t^2}\]
note \[l\] is length \[m\] is mass, and \[t\] is time
give the Planck length, time, mass, and energy in terms of \[G\], \[\hbar\], and \[c\].
\[L_p = \sqrt{\frac{G \hbar}{c^3}}\]
\[T_p = \sqrt{\frac{G \hbar}{c^5}}\]
\[M_p = \sqrt{\frac{\hbar c}{G}}\]
\[E_p = \sqrt{\frac{\hbar c^5}{G}}\]
the relationship among theories of varying precision and the relationship of the phenomena of investigation to the fundamental constants from brilliant.org
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Note: This is a somewhat particle physics-influenced view of the world. Recent times have seen tremendous progress on ^^the in-between areas of this map such as condensed matter systems, statistical mechanics, and biophysics which are distinguished less by their scale as by the complexity of their interactions^^.
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