6.1: Prelude to the Fundamental Forces

The fundamental forces are normally divided in four groups, of the four so-called “fundamental” forces. These are often naturally classified with respect to a dimensionless measure of their strength. To set these dimensions we use $\hbar$, $c$ and the mass of the proton, $m_p$. The natural classification is then given in Table $\PageIndex{1}$. Another important property is their range: the distance to which the interaction can be felt, and the type of quantity they couple to. Let me look a little closer at each of these in turn.

Table $\PageIndex{1}$: A summary of the four fundamental forces

Force	Range	Strength	Acts on
Gravity	$\infty$	$G_N\approx 6\, 10^{-39}$	All particles (mass and energy)
Weak Force	$<10^{-18}$m	$G_{F}\approx 1\, 10^{-5}$	Leptons, Hadrons
Electromagnetism	$\infty$	$\alpha \approx 1/137$	All charged particles
Strong Force	$\approx 10^{-15}$m	$g^{2}\approx 1$	Hadrons

In order to set the scale we need to express everything in a natural set of units. Three scales are provided by $\hbar$ and $c$ and $e$ – actually one usually works in units where these two quantities are 1 in high energy physics. For the scale of mass we use the mass of the proton. In summary (for $e=1$ we use electron volt as natural unit of energy)

$$\begin{align*} \hbar &= 6.58 \times 10^{-22} \text{ MeV s}\\ \hbar c & = 1.97 \times 10^{-13} \text{ MeV m}\\ m_{\mathrm{p}} & = 938 \text{ MeV}/c^2\end{align*}$$