special relativity

The Addition of Velocities

The velocity of light is the universal speed limit.


In Newtonian physics velocities can be added together.

In relativity velocities cannot be added simply. At low speeds simple velocity addition is a good approximation. At speeds approaching c simple addition is not at all correct.

It is fundamental in relativity that velocities cannot be added together to exceed the speed of light.


The following are a list of points to be mindful of when studying the animation.

  • The velocity of the top spacecraft can be selected from the controls below the animation.
  • The speed of the apples relative to the spacecraft can also be selected.
  • The top spacecraft fires the apples in exactly the same way as the bottom spacecraft.
  • The right apple speed is not the addition of spacecraft speed and apple speed.
  • With the top spacecraft velocity set to 0.01c the addition of velocities is almost correct.
  • With higher spacecraft velocities the simple addition of velocities becomes grossly incorrect
  • The velocity of the right apple never exceeds 1.0c.