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diff --git a/physics/units b/physics/units new file mode 100644 index 0000000..b1968f4 --- /dev/null +++ b/physics/units @@ -0,0 +1,53 @@ +====================== +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). + + |