Consider a classical isolated relativistic elastic collision of two free scalar point masses in 1 D. The aim is to get the final velocities of the particles given
- initial rest masses and
- initial velocities
in some inertial reference frame.
The question is as follows: Is there any motivation to assume that the rest masses of each particle after the collision are same as before?
If not so,
- is it correct to say that the above problem becomes solvable only once the rest masses after collision are also given?
- For that matter, is it correct to further say that nothing (the no of particles produced or their masses) about the system after the collision is known except the 4 momentum of the system?
Please note that the fact that we are asking the collision to be elastic doesn't imply the assumption being asked about--it only says the total kinetic energy be conserved(or does it?) which is already taken care of in 4 momentum conservation. Also note that though rest mass of the system is necessarily $\ge$ sum of individual rest masses, it doesn't rule out the masses to stay the same across the collision.