How Do You Calculate the Magnitude of a 4-Vector?

[Jonsson]

Hello there,

Given any 4-vector $x = (x_0,x_1,x_2,x_3)$, hvor do I compute its magnitude? I couldn't find a simple explanation online.

For example I want to compute the magnitute of the momenergy 4-vector of a photon traveling in the positive x-direction where $E$ is the energy of the photon and $P_\mu = (E,E,0,0)$. What is incorrect in the following computation of its magnitude?
$$
(P_\mu\,P^\mu)^{1/2} = (E^2-E^2)^{1/2} = 0
$$

Surely the magnitude of the vector should not be $0$? Can you help? Thank you for your time.

Kind regards,
Marius

 

[Dale]

It is 0. You did it correctly. The magnitude of the four momentum is the mass and light is massless.