References: Griffiths, David J. (2007), Introduction to Electrodynamics, 3rd Edition; Pearson Education – Chapter 12, Post 31.
[Griffiths’s approach to the relativistic four-velocity is similar to that of Moore, although rather confusingly, he uses different notation (as well as keeping factors of in the equations rather than setting ). To keep the notation consistent with Griffiths, I’ll use his notation here, but anyone attempting to follow both books should beware\ldots ]
We can use the conservation of relativistic energy and momentum to analyze the interaction of elementary particles. For example, a pion at rest can decay into a muon and a neutrino. Conservation of energy and 3-momentum require
We can use the relation
to relate energy and momentum. Assuming the neutrino is massless (it isn’t quite, but it’s close) we have
while for the muon
But from 2 so
where the last line follows from 5.
The velocity of the muon can be found from