Collisions among sub-atomic particles in which the number of particles is not conserved are not quite so easily explained as merely involving the re-arrangement of particles and re-distribution of energy.
The most extreme example of this sort, and one that is often used in the physics literature, is pair annihilation. Consequently, let us consider a collision between an electron e− and a positron e+, which yields two photons (2γ). Symbolically, the reaction is written as follows:
e− + e+ → γ + γ (6)
According to the currently accepted Standard Model of particle physics, electrons and photons are both “fundamental particles,” by which physicists mean that such particles have no structure, i.e., such particles are not composed of other, smaller particles.
Furthermore, the photons that are the products in reaction (6) have zero rest-mass. Thus, in reaction (6), the rest-masses of the incoming electron and positron seems to “disappear” and an equivalent amount of energy “appears” as the energy of the outgoing photons.
Of course, Einstein's famous equation makes all of the correct predictions concerning the relevant masses and energies involved in reaction (6). So, for example, the total energy of the two photons is equal to the sum of the kinetic energies of the electron and positron plus the sum of the rest-masses of the electron and positron divided by c2.
Finally, although mass and energy seem to “disappear” and “appear” respectively when we focus on the individual constituents of the physical system containing the incoming electron-positron pair and the outgoing photons, the mass and energy of the entire system remains the same throughout the interaction.
Before the collision, the rest-mass of the system is simply the sum of the rest-masses of the electron and positron plus the mass-equivalent of the total kinetic energy of the particles. Consequently, the entire system (if we draw the boundary of the system around the reactants and products—which is, of course, a spatial and temporal boundary), has a non-zero rest-mass prior to the collision.
However, after the collision, the system, which now consists of two photons moving in non-parallel directions, also has a non-zero rest mass (see, for example, Taylor and Wheeler, 1992, p. 232).
