The most interesting aspects of Special Relativity are its 'paradoxes.' We
put 'paradoxes' in quotes because Special Relativity is, in fact, an
entirely self-consistent theory that contains no true paradoxes (that is,
no paradoxes that cannot be resolved with a little careful thought). The
fun part is thinking through the apparent paradoxes to find where the
logical error that leads to the inconsistency lies. We have already
encountered several of the classic paradoxes of Special Relativity, and in
this topic we will uncover several more.
The first section examines the relativistic Doppler
effect, which is an interesting and useful extension of the Doppler
effect in classical mechanics. It is especially important because
relativistic speeds need to be considered for one of the main instances in
which the Doppler effect becomes important, the red-shift of light
reaching us from far galaxies. The second section deals with
the most famous 'paradox' of relativity: the so-called Twin Paradox. The
third section extends what we have learned about energy,
momentum an d 4-vectors to more
interesting problems involving the decay of and collision between
particles.
The aim of this SparkNote is to demonstrate that Special Relativity, as
unfamiliar and unintuitive as it may seem, does have important
applications in areas of physics ranging from the very small
(sub-microscopic particle interactions) to the very large (motion of stars
and galaxies, cosmology). Moreover, the relationship between the electric
and magnetic forces and fields is bound up with Special Relativity; the
interaction ultimately produces oscillations of the electromagnetic field
that is light itself. The results of Special Relativity are not as
abstract as they at first appear to be!