Quite a vague question here, and I'm not entirely sure I'll be able to get a satisfying answer out of this one, but here goes. Fields such as the electric or magnetic field are introduced as vector fields that allow you to calculate a force at a certain point in space. In this interpretation they are conceptually on exactly the same footing as an 'action at a distance' theory such as Newton's gravity. However, as you progress in electrodynamics, you learn that the fields have energy and momentum stored inside them. Now I understood how energy could be stored in a certain charge configuration (and thus it could be modeled as 'stored inside of the field'). But the idea of the electromagnetic field having a certain amount of momentum seemed bizarre to me. Does this mean I have to abandon the idea of the field being something purely mathematical altogether, or is there some sort of analogy or explanation that can help me understand it? Thanks.