|
|
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’ = 400ms-1, 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 + 0·5c2/c2) = 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.
|
|
The
Open Door Web Site 
