Energy of two colliding particles

[Dawei]

Homework Statement

Two identical particles are smashed together. They each have the same energy E. What is the energy measured for one of them by an observer in the rest system of the other?

Homework Equations

E = γmc²
E = γ(E' + vp)

The Attempt at a Solution

I've already found the speed of each particle, which is .99998C . Obviously I can't just double that since it would give me a non-real value for gamma. I know that the answer is 5 orders of magnitude greater than the energy for an individual particle.

 

[tiny-tim]

Hi Dawei!

You should be able to get this directly from the Lorentz transformation equations.

Alternatively, see http://en.wikipedia.org/wiki/Addition_of_Velocities_Formula"

 

[turin]

Two identical particles are smashed together. They each have the same energy E. What is the energy measured for one of them by an observer in the rest system of the other?

You do not need a Lorentz transformation. Hints: What does the dot product of the 4-momenta tell you in the CM frame (in terms of energy and mass)? What does it tell you in the rest frame of one of the particles (in terms of energy and mass)? Is this dot product a Lorentz invariant?