Magnitude of Vectors in Special Relativity

[MrBillyShears]

So for finding the magnitude of a vector, velocity for example, we use v=√(v_x²+v_y²+v_z²), but in special relativity, velocities can not exceed c. Is their a different formula for magnitude in SR, or could a velocity like(in natural units) v=(.9,.9,.9) not exist, since the magnitude comes out to be about 1.5588c, which obviously exceeds c?

 

[UltrafastPED]

See http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/vec4.html

 

[Meir Achuz]

That vector could not be a velocity. Velocity is limited by v_x^2+v_y^2+v_z^2<1.

 

[MrBillyShears]

Ok, thanks I get it now.

 

[Chestermiller]

In special relativity, all vectors should really be regarded as 4 dimensional. UltrafastPED's reference give the method for how to get the magnitude of a 4D vector.

Chet

 

[WannabeNewton]

How much about 4-vectors do you already know?