The scalar field example gives us a number of tools that can be applied to any relativistic field theory. We started with a physical model for longitudinal “density” waves (balls and springs) and shifted from a material (with intrinsic wave speed v) to the vacuum (with intrinsic wave speed c). That shift took us from real fields describing explicit physics for our model system to fields that do not have explicit physical manifestation – the scalar field φ satisfying ▪2φ = 0 is not necessarily the density or pressure of anything. The theory of electricity and magnetism has, at its core, a vector field (the combined electric and magnetic potentials) that is an object in its own right, and does not correspond to a macroscopic property of materials – of course, the potential can be used to find the forces on objects, and it is these force-mediating fields that form the bulk of classical field theory. Electricity and magnetism provides a vehicle for discussing the appropriate form of field equations (and their precursors, the action and Lagrange densities) that support specific physical ideas – superposition, and special relativity, for example. Complementing these physically inspired properties, E&M is a good place to think about gauge freedom and the role that gauge-fixing can play in revealing the underlying physics while simplifying (in some cases) the field equations. We can use these ideas to “go backwards”, that is, to start with an action that yields linear field equations with finite propagation speed for waves (written in some gauge), and see what physical interpretation we might give to the resulting fields.