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diff --git a/physics/units.page b/physics/units.page index 385136c..bfc78bc 100644 --- a/physics/units.page +++ b/physics/units.page @@ -3,11 +3,11 @@ format: rst categories: physics toc: no ... + ====================== Units ====================== -.. contents:: SI Units -------------------- @@ -26,7 +26,7 @@ Natural Units Natural units are a system of units which replace (or re-scale) the usual mass, length, and time bases with quantities which have "natural" (physical) constants associated with them. The two constants usually chosen are the speed -of light (c) and Plank's constant (:m:`$\hbar$`); the gravitational constant +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 @@ -36,18 +36,18 @@ Working with natural units simplifies physical relations and equations because many conversion factors drop out. Given the relations between cgs units (gm, cm, sec) and natural units (c, -:m:`$\hbar$` , eV), we can find the natural units of an arbitrary quantity -:m:`$[Q]=[gm]^{a}[cm]^{b}[sec]^{c}=[c]^{\alpha}[\hbar]^{\beta}[eV]^{\gamma}$`: +$\hbar$ , eV), we can find the natural units of an arbitrary quantity +$[Q]=[gm]^{a}[cm]^{b}[sec]^{c}=[c]^{\alpha}[\hbar]^{\beta}[eV]^{\gamma}$: -:m:`$$(\alpha,\beta,\gamma)=\left(\begin{array}{ccc} -2 & 1 & 0\\ 0 & 1 & 1\\ 1 & -1 & -1\end{array}\right)\left(\begin{array}{c} a\\ b\\ c\end{array}\right)=(-2a+b,b+c,a-b-c)$$` +$$(\alpha,\beta,\gamma)=\left(\begin{array}{ccc} -2 & 1 & 0\\ 0 & 1 & 1\\ 1 & -1 & -1\end{array}\right)\left(\begin{array}{c} a\\ b\\ c\end{array}\right)=(-2a+b,b+c,a-b-c)$$ or in reverse: -:m:`$$(a,b,c)=\left(\begin{array}{ccc} 0 & 1 & 1\\ 1 & 2 & 2\\ -1 & -1 & -2\end{array}\right)\left(\begin{array}{c} \alpha\\ \beta\\ \gamma\end{array}\right)=(\beta+\gamma,\alpha+2\beta+\gamma,-\alpha-\beta-2\gamma)$$` +$$(a,b,c)=\left(\begin{array}{ccc} 0 & 1 & 1\\ 1 & 2 & 2\\ -1 & -1 & -2\end{array}\right)\left(\begin{array}{c} \alpha\\ \beta\\ \gamma\end{array}\right)=(\beta+\gamma,\alpha+2\beta+\gamma,-\alpha-\beta-2\gamma)$$ Plank Units ---------------- -Plank units (defined by Plank soon after defining his constant :m:`$\hbar$`) 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 |