# Elastic Collisions and Violation Thereof in the Case of Shattering

In Taylor's Classical Mechanics, he includes the following discussion as a follow up to a discussion of energies of interaction and how elastic collisions arise in cases where the force of interaction of the inbound particles is conservative and goes to $$0$$ at large separations (ie. all inbound kinetic energy of the two particles is recovered after the particles separate):

The foregoing discussion may suggest that elastic collisions should be a very com- mon occurence. All that is needed is two particles whose interaction is conservative. In practice, elastic collisions are not as widespread as this seems to imply. The trouble comes from the requirement that it be two particles that enter and leave the collision. For example, if we fire one billiard ball at a second with sufficient energy, the two balls may shatter. Similarly, if we fire an electron with sufficient energy at an atom, the atom may fall apart or, at least, change the internal motion of its constituents. Even in the collision of two genuine particles, such as an electron and a proton, relativity tells us that, with sufficient energy, new particles can be created. Clearly, at high enough energy, the assumption that the two objects entering a collision can be approximated as indivisible particles eventually breaks down, and we cannot assume that collisions will be elastic, even if all the underlying forces are conservative.

Now, I am curious as to why we have the restriction that the particles cannot shatter or else the collision is not elastic. I am assuming that this is because, if there is shattering that goes on, then the otherwise constant energies of interaction between the internal particles of the "macro-particle" that shattered are not constant throughout the period of observation (ie. the rigid-body assumption no longer holds for that shattered object). Is this correct, or am I missing something deeper that Taylor is getting at?

As for the case when constituents shatter-the particle identity has changed: what went in was one particle $$A$$: whats coming out are multilple particles $$A_i$$. The $$A\to A_i$$ reaction may eat up energy* making the collision inelastic.