Prove that the electromagnetic wave equation:
(d^2ψ)/(dx^2) + (d^2ψ)/dy^2) + (d^2ψ)/(dz^2) − (1/c^2) * [(d^2ψ)/(dt^2)]= 0 is NOT invariant under Galilean transformation. (i.e., the equation does NOT have the same form for a moving observer moving at speed of, say, v in the x direction).
*note: all the "d"s in this equation are the partial derivatives.
t'=t, x'=x-vt, y'=y, z'=z
The Attempt at a Solution
-from what i understand to solve this involves the chain rule for partial derivatives.
-looking at the equation i cant help but jump to something with the gradient of ∇ψ, but i dont know where to go from there.