
452 Classical Mechanics
PP P
E
c
µµ
µ
∑
=−
2
2
2
.
Combining this with Equation 13.39, we arrive at the relationship
P
E
c
mc
2
2
2
0
−=−
or
EP
c
222
0
. (13.40)
The total energy E and the momentum P
μ
of a moving body are different when measured with
respect to different reference frames. But the combination P
2
– E
2
/c
2
has the same value for all
frames of reference, namely,
0
. This relationship is very useful. Another very useful relationship
is
PvEc=
/
2
. From Equation 13.35, we see that γm
0
= E/c
2
; combining this with the rst equation
of Equation 13.36 gives the very useful relationship
Ec=
/
2
.
The relativistic momentum, however, is not quite ...