A particle's four-momentum has components

PHYSICS · Subjective · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Special relativity: spacetime and kinematics

The Geometry of Gravity, Ch Minkowski spacetime and relativistic dynamics, completed

Problem

A particle's four-momentum has components pμ=(5,3,0,4)p^\mu = (5, 3, 0, 4), all in units of GeV/c\mathrm{GeV}/c, with p0=E/cp^0 = E/c. Someone computes the invariant square as pμpμ  =?  52+32+02+42=50 (GeV/c)2p^\mu p_\mu \;\overset{?}{=}\; 5^2 + 3^2 + 0^2 + 4^2 = 50\ (\mathrm{GeV}/c)^2 and concludes that the particle is spacelike, i.e. tachyonic. Find the error in this working, give the correct value of pμpμp^\mu p_\mu, and state what kind of particle this four-momentum describes.

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