Playing with the formula

The following examples, which get progressively more unreal, test the relativistic addition of velocities according to the formula we have just derived. We never get an answer greater than c!

Example 1. Two velocities which should 'add up' to more than the speed of light

Speed of (imaginary) plane = 0.9 c Speed of (imaginary) bullet = 0.9 c v = 0.9 c, V = 0.9 c

Example 2. Trying to add to the speed of light.

An imaginary object travelling at the speed of light fires a bullet forwards with a speed V.

Example 3. c + c = ? An imaginary photon fires another photon forwards.

Example 4. c — c = ? An imaginary object, travelling with a velocity c, fires a bullet backwards with muzzle velocity c.

v = c V =-c VR =-„ = —, which is indeterminate.

Such a calculation requires care. Let us assume a more physically plausible situation, in which our imaginary object approaches the speed c in the positive x direction and fires a photon backwards, i.e. in the negative x direction.

In the other frame the photon also travels with speed c in the negative x direction.

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