# How to start a proof that shows that proper mass is the same for S and S' frame

1. Oct 8, 2012

### chris_0101

1. The problem statement, all variables and given/known data

As the title of this post suggests, how does one show that the proper (invariant) mass is the same for two reference frames where the S' frame is moving away from the S frame at a velocity of +v. Note that this is a two mass system of m_1 and m_2 with speeds of u_1 and u_2, respectively.

I'm not too sure how to start this problem

2. Relevant equations

E = E_1 + E_2 ---> energy
p = p_1 + p_2 ---> momentum

Lorentz transformation for mass:

m' = $\gamma$m

3. The attempt at a solution

I've tried multiple solutions with no avail and my attempts are too long and complicated for me to post. However, I did try to solve this:

E^2 - p^2c^2 = m_o^2c^4 = E'^2 - p'^2c^2

but I'm not sure if this is correct or not because it does not involve the speed of the two frames +v.

Any help would be great