# Geometric Unit System¶

This is an introduction to the geometric unit used widely in the theoretical contexts of Physics.

In Physics, there are many important constants, such as light speed in vacuum $$c$$, (reduced) Plank constant $$\hbar$$, absolute permittivity $$\varepsilon_0$$, etc. If we include all these constants in an equation, the expression can be cumbersome. To solve this problem, the simplest way is to introduce the following convention

$c=1,\ \ \ \ \ \hbar=1$

Therefore, all multiplication of these constants in the equation will disappear. But wait! You may immediately notice a problem: the dimension! Yes, it seems that the above equation violates a fundamental requirement — balance of dimension. The left hand side is a physical constant with dimension, but the right hand side is a pure number.

Well, this in fact does not matter so much. You can view it as a redefinition of units. For example, to make light speed $$c=1$$, all we need to do is to redefine the time unit as the time within which light travels a unit length. This is called Geometric Unit System. As a result, the convention $$c=1$$ will be equivalent to $$[L]=[T]$$, where $$[L]$$ stands for the length dimension and $$[T]$$ for time dimension. Similarly, it is easy to figure out that $$\hbar=1$$ leads to $$[L]=[M]^{-1}$$.

Hope you get the point. Now you should not feel unfamiliar with sentences like “momentum has a dimension of $$[L]^{-1}$$”. The theory of dimension analysis guarantees that there will not be a problem with this convention as long as you do a correct calculation.