I'm studying out of Classical Electrodynamics by Ohanian and in chapter 2 (Electrostatics) he makes the following claim while discussing the electric field: I'm a little confused by this, and I can't seem to find any sources that share this view. I'm even more confused because in the preceding paragraph he says: So I'm just not sure what he's trying to tell me. Is the electric field literally a state of matter, analogous to solid, liquid, and gas? If so, then which matter is taking on that state? Or is it, as claimed in the previous paragraph, a property of space at each point that is altered due to the presence and location of electric charges? Would this be true of scalar fields as well as vector fields? If it's defined for scalar fields, then how does this square with the fact that a potential field is only defined up to an arbitrary constant such that at two points x and y we could for instance have V(x) = φ(x) + 3 and V(y) = φ(y) + 8? If we assume that the electric potential field is a form of matter then this would seem to suggest that there is a form of matter whose intrinsic physical properties could take on different values at different locations (I would not expect a 5 kg mass to suddenly have a mass of 2 kg if I walk to the other end of the room). If we assume that the electric potential field is a property of space, then this would seem to suggest that space isn't homogeneous since space would be physically different at two points. Or would this be avoided by saying that the potential field is not matter or a property of space, in which case why do we allow the electric field to be? Or am I just completely overthinking this and this was just a little attempt at philosophy, or there's something he's going to explain later in the book that would make this clear? Someone please help me, this is giving me a headache. EDIT: The title of this post is meant to say "My E&M textbook claims that fields are a form of matter", how do I fix that?