Magnitude of a velocity vector with special relativity

[Froskoy]

Hi,

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:

$$v^2 = \sqrt{v_x^2 + v_y^2 + v_z^2}$$

where $v_x$, $v_y$ and $v_z$ are the $x$, $y$ and $z$ 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, $v$ and the $x$ component of the velocity, what formula would you use to work out the $y$ component?

With very many thanks,

Froskoy.

 

[tiny-tim]

Hi Froskoy!

… if you knew the magnitude of the velocity, $v$ and the $x$ component of the velocity, what formula would you use to work out the $y$ component?

same formula!

the special relativity rule for adding relative velocities has nothing to do with "de-componenting" a single velocity ​