Classical electromagnetism and special relativity The theory of
special relativity plays an important role in the modern theory
of classical electromagnetism. First of all, it gives formulas
for how electromagnetic objects, in particular the electric and
magnetic fields, are altered under a Lorentz transformation from
one inertial frame of reference to another. Secondly, it sheds
light on the relationship between electricity and magnetism,
showing that frame of reference determines if an observation
follows electrostatic or magnetic laws. Third, it motivates a
compact and convenient notation for the laws of
electromagnetism, namely the "manifestly covariant" tensor form.
Maxwell's equations, when they were first stated in their
complete form in 1865, would turn out to be compatible with
special relativity. Moreover, the apparent coincidences in which
the same effect was observed due to different physical phenomena
by two different observers would be shown to be not coincidental
in the least by special relativ