## Chapter 7 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 $\hslash$, $c$ and the mass of the proton, ${m}_{p}$. The natural classiﬁcation is then given in table 7.1 . 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 7.1: A summary of the four fundamental forces
 Force Range Strength Acts on Gravity $\infty$ ${G}_{N}\approx 6\phantom{\rule{0.3em}{0ex}}1{0}^{-39}$ All particles (mass and energy) Weak Force $<1{0}^{-18}$ m ${G}_{F}\approx 1\phantom{\rule{0.3em}{0ex}}1{0}^{-5}$ Leptons, Hadrons Electromagnetism $\infty$ $\alpha \approx 1∕137$ All charged particles Strong Force $\approx 1{0}^{-15}$ 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 $\hslash$ 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)