- We commonly consider forces carried by spin-0, spin-1 or spin-2 particles. If we only consider linear field equations, these give three different linear partial differential equations. When we consider *static* solutions these all boil down to the Laplace equation, and the solution of the Laplace equation produced by a point charge gives a 1/r² force.
The key idea goes back to Hooke, who imagined little particles of force shooting out in all directions in a spherically symmetric way, and thus a force of intensity 1/r² because the area of a sphere is proportional to r². This was long before Gauss' theorem made the idea precise!
