(See attached for full problem description)
If electromagnetic wave equation for vacuum is where W is either magnetic B or electric E field vector, show that by using Galilean transformation wave equation will be changed to which has completely different form than given wave equation. Hence, Galilean transformation violates the first relativity postulate that all physics laws have the same form in all inertial reference frames.
Repeat the analysis but use Lorentz coordinate transformation, and show that in this case wave equation has the same form
(Hint: Use the chain rule to express derivatives and in terms of and )
The solution performs an analysis on Galilean transformations and Lorentz coordinate transformations based on electromagnetic waves.