From b234b981acb135ed00a7ecf444dde6fe33d9f0f3 Mon Sep 17 00:00:00 2001 From: bnewbold Date: Sun, 24 Jan 2010 10:12:18 +0000 Subject: fixes --- physics/units.page | 13 +++---------- 1 file changed, 3 insertions(+), 10 deletions(-) (limited to 'physics') diff --git a/physics/units.page b/physics/units.page index bfc78bc..f6b0d68 100644 --- a/physics/units.page +++ b/physics/units.page @@ -1,10 +1,3 @@ ---- -format: rst -categories: physics -toc: no -... - -====================== Units ====================== @@ -30,7 +23,7 @@ of light (c) and Plank's constant ($\hbar$); the gravitational constant (G) is a possibility for the third constant/unit, but energy (in electron-volts: eV) is often used instead because it gives more useful relations and because there is no accepted theory of quantum gravity to unite -these three constants. See _Plank Units for more on using G as a unit. +these three constants. See Plank Units for more on using G as a unit. Working with natural units simplifies physical relations and equations because many conversion factors drop out. @@ -39,7 +32,7 @@ Given the relations between cgs units (gm, cm, sec) and natural units (c, $\hbar$ , eV), we can find the natural units of an arbitrary quantity $[Q]=[gm]^{a}[cm]^{b}[sec]^{c}=[c]^{\alpha}[\hbar]^{\beta}[eV]^{\gamma}$: -$$(\alpha,\beta,\gamma)=\left(\begin{array}{ccc} -2 & 1 & 0\\ 0 & 1 & 1\\ 1 & -1 & -1\end{array}\right)\left(\begin{array}{c} a\\ b\\ c\end{array}\right)=(-2a+b,b+c,a-b-c)$$ +$$(\alpha,\beta,\gamma)=\left(\begin{array}{ccc} -2 & 1 & 0\\ 0 & 1 & 1\\ 1 & -1 & -1\end{array}\right) \left(\begin{array}{c} a\\ b\\ c\end{array}\right)=(-2a+b,b+c,a-b-c)$$ or in reverse: @@ -47,7 +40,7 @@ (a,b,c)=\left(\begin{array}{ccc} 0 & 1 & 1\\ 1 & 2 & 2\\ -1 & -1 & -2\end{arra Plank Units ---------------- -Plank units (defined by Plank soon after defining his constant $\hbar$) are a version of _Natural Units using the gravitational constant G as the the +Plank units (defined by Plank soon after defining his constant $\hbar$) are a version of Natural Units using the gravitational constant G as the the third unit (instead of the common measure of energy). When converted back into mass-length-time units we get three quantities which define the "Plank Scale", which may provide estimation of the domain where quantum gravity effects become -- cgit v1.2.1