e + and e − have opposite momentum,, The energy-momentum relation E^2 = m^2+p^2 can be seen to define the "mass" of a system.

The energy-momentum relation E^2 = m^2+p^2 can be seen to define the "mass" of a system. For single particles, the rest mass is simply the energy of the particle at rest e +   and e −   have opposite momentum, http://physics.stackexchange.com/questions/175444/is-rest-mass-conserved-in-special-relativity What does conservation of mass mean in classical mechanics? Weight and mass are the same , we know the mass by weighing it, and if we add 1 kilo of sugar to another kilo of sugar, we will have two kilos of sugar. That is what is meant classically that the mass is conserved. Dissolving a kilo of sugar to a kilo of water will give you two kilos of sirop. The same is not true at the elementary particle level and where the energies are high enough for special relativity to hold. In special relativity as you state , m 2 =E 2 −p 2   As one of the other answers state, this m^2 is the "length" of the four vector in the four vector space of Lorenz transformations. In a similar way that the length of a ruler is invariant in three dimensions the mass of an elementary particle does not change. But in three dimensions also adding vectors can have a variable result, depending on the angles of the vectors. Similarly in the four dimensions of special relativity the addition of other particles with their energy and momentum will give an m', but this m' will not be the sum of the constituent particle masses, but the "length" of the new four vector. For this specific system of particles this length will be conserved , if no new four vectors enter the problem. The masses though of the elementary particles will add up to less than the invariant mass of the system they compose, the sum will be the lowest limit(, if all are at rest in the center of mass of the system.) Thus there is no conservation of mass a la classical physics