
Relativity
"Relativistic"
Combination of Velocities
Let us now consider two
observers, A and B, who are both making
measurements on the motion of a third body C.
If 
u is the
velocity of B relative to A 
and 
v is the
velocity of C relative to A 
...
what will be the velocity of C relative to B
? 
Using a method similar to the
"light flashes" method (see "Measuring Relative
Velocities"), it can be shown that the velocity of C
relative to B (v’) is given by
Detailed
proof of this relation
Examples
1.
Suppose
that u = 0·5c and v = 0·9c
Then, using the equation above gives 
v’ =
1·4c/(1 + 0·45c²/c²) = 0·965c 
Note
that the Galilean transformation gives 1·4c 
2. 
Now
consider the same situation but with u = 100ms^{1}
and v = 300ms^{1
}^{This
time we find that both the Galilean transformation and
Einstein's equation give v’ = 400ms1, in
other words if v << c then Einstein's equation
reduces to the simple relation v’ = v  u} 
3. 
Now we will
consider the situation in which the same two observers
are measuring the velocity of a light beam. 
If u is still 0·5c, then we
have v’ = 1·5c/(1 + 0·5c^{2}/c^{2}) = c
This example simply
illustrates that the equation used to calculate v’ agrees
with Einstein’s initial postulate that the velocity of
light is a constant.

