The maxwell's equations in vacuum are satisfied by a non trivial solution involving [tex]\vec E (t,\vec x)[/tex] and [tex]\vec B (t, \vec x)[/tex]. Correct me if I'm wrong. I don't really understand the physical interpretation of the solution. I know that if I'm given an initial condition then I can know the solution for all t and [tex]\vec x[/tex]. Assuming I'm given an initial condition... then I'd have that a varying electromagnetic field satisfies the Maxwell's equations for all the space and at any time. Does this mean that vacuum doesn't contain any charge (pretty likely) and further is like a soup of electromagnetic waves (which is what strikes me)? I mean, to my understanding, there's a non vanishing electromagnetic field in all the space at any time, all this in vacuum. Am I understanding this well?