1. The problem statement, all variables and given/known data Suppose two "small" particles of equal mass m collide, annihilate each other, and create another particle of mass M > 2m . (Note that the final state is just that one "big" particle, nothing else.) If one of the small particles is initially at rest, what must be the minimum total energy E of the other? Give your final result in terms of m and M. 2. Relevant equations The problem also asks me to set c=1. Invariant mass: (m)^2 = E^2 - p^2 Energy conservation: E_initial = 2m + E_k,m = E_final = M + E_k,M momentum conservation: p_initial = p_final 3. The attempt at a solution I've been wrestling with this problem in a lot of different ways (studying for finals), but cannot get the posted answer. I am confused about which quantities are conserved, since it seems there is no reference frame where all the particles are at rest. I'm not sure what values to equate in the energy four-vector. Here is one try, where I take the final momentum to be zero: Energy conservation: 2m + E_k,m = M => E_k,m = M - 2m momentum: p_initial = p_final = 0 Invariant mass: (m)^2 = E^2 - p^2 => (2m +E_k,m)^2 - 0 = M^2 - 0 => 4m^2 + 4mE_k,m + E_k,m = M^2 Already, I can tell that I've done something wrong. I also think that I'm solving for the wrong value here, since I don't have any idea of how to get the energy of the one 'moving' particle from E_k,m. I chose this (center of mass?) frame because I can't think of any other way to write the momenta of the particles in terms of the kinetic energies without doing Lorentz gymnastics that don't seem at all appropriate to the problem. Since it doesn't seem to help me, I think I must be misunderstanding the situation in some serious way, if not completely misapplying these principles. Thanks, A.