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diff --git a/physics/units b/physics/units deleted file mode 100644 index b1968f4..0000000 --- a/physics/units +++ /dev/null @@ -1,53 +0,0 @@ -====================== -Units -====================== - -.. contents:: - -SI Units --------------------- -The SI system uses meters-kilograms-seconds. It also defines the Coulomb as -a unit for measuring electric charge, which introduces redundant conversions -between mass-length-time units and the electric charge. - -cgs Units --------------------- -The cgs system uses centimeters-grams-seconds, and also defines electric charge -in terms of the fundamental quantities of mass, length, and time. The unit of -charge is "esu" or electrostatic unit. - -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 -(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. - -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:`$[Q]=[gm]^{a}[cm]^{b}[sec]^{c}=[c]^{\alpha}[\hbar]^{\beta}[eV]^{\gamma}$`: - -:m:`$$(\alpha,\beta,\gamma)=\left(\begin{array}{ccc} -2 & 1 & 0\\ 0 & 1 & 1\\ 1 & -1 & -1\end{array}\right)\left(\begin{array}{c} a\\ b\\ c\end{array}\right)=(-2a+b,b+c,a-b-c)$$` - -or in reverse: - -:m:`$$(a,b,c)=\left(\begin{array}{ccc} 0 & 1 & 1\\ 1 & 2 & 2\\ -1 & -1 & -2\end{array}\right)\left(\begin{array}{c} \alpha\\ \beta\\ \gamma\end{array}\right)=(\beta+\gamma,\alpha+2\beta+\gamma,-\alpha-\beta-2\gamma)$$` - -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 -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 -important (similar to how the speed of light and Plank's constant provide -estimation of when special relativistic and quantum mechanical effects become -important). - - |