Confused about invariant mass in particle collision

[iacephysics]

Ok, when you use positrons to shoot at stationary electrons in a collider with enough energy so that you make a pair of proton and antiproton. The total energy of the pair would be E = T + MC^2, where M is the total invariance mass of the pair, namely 2*938Mev, or I can use E^2 = (pc)^2 + (Mc^2)^2, and M here is still the invariant mass. I got the correct answer using M = 2 times the mass of the rest mass of a proton, as said previous, 2*938 Mev. What I am trying to understand here is why the invariant mass here is the sum of two masses, when in most cases, invariant mass is not linear, you can't add two masses and conserve the sum.

 

[Meir Achuz]

Ok, when you use positrons to shoot at stationary electrons in a collider with enough energy so that you make a pair of proton and antiproton. The total energy of the pair would be E = T + MC^2, where M is the total invariance mass of the pair, namely 2*938Mev, or I can use E^2 = (pc)^2 + (Mc^2)^2, and M here is still the invariant mass. I got the correct answer using M = 2 times the mass of the rest mass of a proton, as said previous, 2*938 Mev. What I am trying to understand here is why the invariant mass here is the sum of two masses, when in most cases, invariant mass is not linear, you can't add two masses and conserve the sum.

I am not sure what you are asking.
E=T+2Mc^2 is just a definition of T. It is appropriate to use the sum of the masses there because E=2Mc^2 when T=0.
In E^2=(pc)^2+(Mc^2)^2, the M is the mass of one proton.