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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

**. Am I understanding this well?**

__in vacuum__