There was an old thread but for some reason it is now closed...(adsbygoogle = window.adsbygoogle || []).push({});

So I'd have to restate this question:

Why does any text book doesn't bother to derive the 3-vector-velocities addition formula using the more general 4-vector formalism?

In detail, the Lorentz Transformation: U[itex]^{1'}[/itex]=γ(v)(U[itex]^{1}[/itex]-β(v)U[itex]^{0}[/itex])⇔γ(υ[itex]^{'}_{x}[/itex])υ[itex]^{'}_{x}[/itex]=γ(v)[γ(υ[itex]_{x}[/itex])(υ[itex]_{x}[/itex]-cβ(v))] (where υ[itex]_{x}[/itex] the velocity in Σ,υ[itex]^{'}_{x}[/itex] the velocity mesured in Σ', and v the relative velocity between the two systems) solved for υ[itex]^{'}_{x}[/itex] should grant υ[itex]^{'}_{x}[/itex]=(υ[itex]_{x}[/itex]-v)/(1-vυ[itex]_{x}[/itex]/c[itex]^{2}[/itex]) right?

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# Derivation of Velocity-Addition Formula

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