Anyone who has taken a JD Jackson based course has derived this result. Special relativity is a fairly obvious consequence of E&M in hindsight. FWIIW, this is

Anyone who has taken a JD Jackson based course has derived this result. Special relativity is a fairly obvious consequence of E&M in hindsight. FWIIW, this is a terrible proof with bad notation (you don't need to write out the matrix), which doesn't actually prove the interesting piece, which is the fact that the permittivity of free space is the same no matter what your frame of reference is.