The Theory of Relativity 145
E = γE
0
(12.17)
m = γm
0
(12.18)
Equation 12.17 relates the energy as measured by two observers, while Equation
12.18 is the relation between masses. The 0 subscript, as usual, denotes the proper
quantity. In Equation 12.18, m
0
is also known as the rest mass as well as the proper
mass. These equations tell us that two observers will measure different energies and
masses depending on their relative speed.
Either of these equations also explain why no object with mass can travel at the
speed of light. If u = c, then β = 1, which would make γ = 1/0, which is in nite.
Since there is not an in nite amount of energy or mass in the universe, then no mas-
sive object can ever attain the speed of light.
The relation E =