6.1: Prelude to the Fundamental Forces

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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)

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