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I'm trying to get my head around how velocity vectors work in special relativity. For example, in classical mechanics, the magnitude of the velocity would be given by:

[tex]v^2 = \sqrt{v_x^2 + v_y^2 + v_z^2}[/tex]

where [itex]v_x[/itex], [itex]v_y[/itex] and [itex]v_z[/itex] are the [itex]x[/itex], [itex]y[/itex] and [itex]z[/itex] components of the velocity respectively.

What is the equivalent formula for use in special relativity. For example, if you knew the magnitude of the velocity, [itex]v[/itex] and the [itex]x[/itex] component of the velocity, what formula would you use to work out the [itex]y[/itex] component?

With very many thanks,

Froskoy.

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# Magnitude of a velocity vector with special relativity

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