only going 5 m/s.Now let’s look at Postulate 2 more closely.
1) The Relativity of Velocity
Let’s say that the man in the train speeding by the platform at 40 m/s throws a ball
down the aisle, parallel to the direction of motion of the train, at a speed of 5 m/s
as measured by him. As measured by the woman standing on the platform, the ball
would be moving at a speed of 40 + 5 = 45 m/s. It seems clear that we’d just add
the velocities.
This simple addition of velocities does not, however, extend to light or even to
objects moving at speeds close to that of light. Imagine a spaceship moving at a
speed of c toward a planet. If the spaceship emitted a light pulse toward a planet,
the speed of that light pulse, as measured by someone on the planet, would not be
c + c = c; Postulate 2 says that the speed of light would be c, regardless of the
motion of the spaceship. Since we haven’t been able to travel at speeds even
remotely approaching that of light, this result seems very strange.
An Exceptional
Exception
Lest these examples
give you any funny ideas,
remember that Postulate
2 asserts that you cannot
travel faster than the
speed of light, even if you
apply postulate 1.The correct, relativistic formula for the “addition” of velocities—that is, the one
that follows from the theory of relativity—looks like this. Imagine that a reference
frame, Sme, is moving with velocity u past you. Now if an object moves at velocity
v (parallel to u), as measured by me in my reference frame, then its speed as
measured by you would not be vyou = u + v, but would instead be
At normal, everyday speeds, u and v are so small compared with the speed of light
that the fraction uv/c^2 is negligibly small, nearly zero. In this case, the denominator
in the formula above is nearly 1, and it becomes the formula vyou = u + v. It’s only