Natural units

Natural units are system of units of measurements in which a number of fundamental constants are set to 1 and are dimensionless. Then, physical measurements are expressed not in the common International System (SI) units, but as multiples or fractions of physical constants. This is the reason behind the name: natural units attempt to remove the "human element" from measurements by relying only on constants of nature.

There are several variations of natural units, depending on which constants are set to 1. They are widely used in any branch of physics that deals with fundamental physics, like particle physics. Besides the semantic and philosophical value, natural units are useful to make math easier as they can eliminate a considerable number of constants and hence make notation cleaner.

One common variation sets the following constants to unity:

where:

• $c$ is the speed of light,
• $\hbar$ is the reduced Planck constant,
• $G$ is the gravitational constant,
• $\varepsilon_{0}$ is the vacuum permittivity; $1/4\pi \varepsilon_{0}$ is sometimes called the Coulomb constant,
• $k_{B}$ is the Boltzmann constant.

In this system, for instance, speed would be expressed as a fraction of the speed of light. In fact, using the relativistic $\beta$, we normally have $\beta=v/c$, but since $c=1$ we now have $\beta=v$. Thus $v\in[0,1]$ instead of $v\in[0,299\ 792\ 458\text{ m/s}]$.