4-momentum of particles in lab and CM frame

[MarekS]

The question:
Suppose two identical particles, each with mass m and kinetic energy T, collide head-on. What is the kinetic energy of one in the rest system of the other?

The solution:

Is given on pg 109 of Griffiths' Introduction to Elementary Particles.

Griffiths writes down the total 4-momenta of the system in the lab frame and in the CM frame.

The zeroth component in the CM frame is 2E/c. So I guess that E is the energy of one of the particles in that frame.

The zeroth component in the lab frame is E'+mc^2, however. Why is mc^2 added for the lab frame? Why not have 2E'/c as in the CM frame?

Thank you!

 

[fzero]

The zeroth component in the lab frame is E'+mc^2, however. Why is mc^2 added for the lab frame? Why not have 2E'/c as in the CM frame?

The mc^2 is the energy of the particle that is at rest. E' is the energy of the particle that's moving.