Fig. 2: Dirac’s insight for the relativistic equation describing an electron5.

The idea is to take the square root of the operator \({p}_{x}^{2}+{p}_{x}^{2}+{m}^{2}\) (see also main text) ‘without’ taking the square root in the usual way. This calls for deploying matrices rather than scalar quantities. As shown in the figure, the three Pauli matrices immediately pop up, explaining naturally the existence of spin in an electron.