Addition of velocities when the speeds are relativistic

Let us now go a million times faster. Let us imagine a hopefully fictional situation of faster and faster planes firing faster and faster rockets. What happens if the velocities when combined give a result greater than the speed of light?

The Galilean transformation gives a result which is impossible. We must use the transformation which is in accordance with the relativity principles — the Lorentz transformation.

The Lorentz transformation of velocities

The basic difference between the classical and the Lorentz transformation is that the time scales in the two frames are different. Rates of change in S are calculated with respect to t, whereas in S' they are calculated with respect to t'.

x

= g (x

- vt)

y'

=y

z'

=z

- cr J

2 dx

dt c2 J

Relativistic addition of velocities: Vr =

(V = muzzle velocity, v = plane velocity, VR = resultant velocity)

0 0

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