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From the expression for the total energy

(53) 
and the momentum

(54) 
of a relativistic particle, it is clear that

(55) 
except if the particle travels with the speed of light (), as then

(56) 
which are indeterminate (can have any value).
Thus, the only particles that can have zero rest mass are those which travel
at the speed of light.
In addition we can rewrite the last two equations as the single equation

(57) 
Exercise 1.14
Show this.
Thus

(58) 
and

(59) 
The photon (
) is a particle with zero rest mass but which
nonetheless carries a momentum
.
Exercise 1.15
Show the consistency of this with de Broglie's relation and ruminate on
your introduction to quantum mechanics via the wave particleduality
in your 1st year of physics.
Next: General Relativity
Up: Relativistic Mechanics [8 lectures]
Previous: Mass and Energy
Simon Connell
20060221