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authorUser <bnewbold@daemon.robocracy.org>2009-10-13 02:52:09 +0000
committerUser <bnewbold@daemon.robocracy.org>2009-10-13 02:52:09 +0000
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-======================
-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).
-
-