# Definition of electric charge as rationalized charge

1. Dec 4, 2012

### voltan

definition of electric charge as "rationalized charge"

Hi All,

I wonder about the meaning of the term "rationalized" when saying "rationalized electron charge." Does this mean that the charge is given in natural units?

Thank you very much!

Best

2. Dec 5, 2012

### Simon Bridge

Re: definition of electric charge as "rationalized charge"

Natural units would be expected to make the Coulomb constant k=1... which is termed "non-rationalized".

Rationalized charge is given in Lorentz–Heaviside units, which has k=1/ε0... on, making charge units: Coulombs per root-permittivity-of-free-space.

http://en.wikipedia.org/wiki/Natural_units
In the SI unit system, electric charge is a separate fundamental dimension of physical quantity, but in natural unit systems charge is expressed in terms of the mechanical units of mass, length, and time, similarly to cgs. There are two common ways to relate charge to mass, length, and time: In Lorentz–Heaviside units (also called "rationalized"), Coulomb's law is F = q1q2/(4πr2), and in Gaussian units (also called "non-rationalized"), Coulomb's law is F = q1q2/r2.[1] Both possibilities are incorporated into different natural unit systems.

3. Dec 5, 2012

### Meir Achuz

Re: definition of electric charge as "rationalized charge"

'Rationalized' means that q^2 is divided by 4pi wherever it appears. These are also called
'Heaviside units'. This leads to simplification of some equations at the cost of complication of others, and considerable confusion.
In 'Gaussian units q^2 is divided by 1, which is an easier number to memorize.
QEDers are split on which to use, so be careful in reading a QED paper to check which it is.
S.I. units go on to also divide by epsilonzero which complicates all equations.
Fortunately, most QED papers don't use SI.
In natural units, hbar and c are one. The electron charge is dimensionless, and
e^2=1/137.036 in gaussian natural units, or e^2/4pi=1/137.036 in Heaviside natural units.