Lorentz velocity addition

Knowing, relativity, space & time / By /

This post follows on the Gamma factor post here.

The form of velocity addition based on the Lorentz transformation is related to a combination of additive and harmonic addition. Galilei velocity addition is

u=v+u'

Lorentz velocity addition is

u=(v+u') \boxplus \left (\frac{v}{c} \boxplus \frac{u'}{c} \right )^{-1}

which equals

u=\frac{v+u'}{1+\frac{vu'}{c^{2}}}

In this way the Lorentz transformation attempts to combine arithmetic and harmonic addition.