From 511ef83ac1f545254129c5af89ac91ce719b2461 Mon Sep 17 00:00:00 2001
From: bnewbold <bnewbold@eta.mit.edu>
Date: Sun, 8 Feb 2009 15:13:58 -0500
Subject: start of physical units item

---
 physics/units | 53 +++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 53 insertions(+)
 create mode 100644 physics/units

(limited to 'physics')

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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).
+
+
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