My textbooks says in a region where there is no charge or current Maxwell's equations read divergence of E=0 Curl of E=-dB/dt all d are partial Divergence of B=0 Curl of B=ue(dE/dt) I get the math of showing that there are waves, but I don't get some of these conditions. 1st don't you need a charge in the 1st place to create an electric field? and then doesn't that charge have to move to created a magnetic field, which would be current? I mean with no charge and no current what makes the electric and magnetic field? I hear that light can be made by taking an electron and shaking it. Electron being an electron has charge and shaking it make the magnetic field. If that not right one demonstrate light form electron?