Assume a stationary fundamental particle in an idealized vacuum – particle a. Now, fire an identical particle – particle b – at particle a in a straight line at speed x. Given the properties of a fundamental particle (perfectly incompressible point) I assume particle a will transfer all its kinetic energy to particle b, without any loss. The collision would result particle a coming to a full stop and particle b continuing particle a's original trajectory at speed x. Is that correct, so far? Now add a third identical fundamental particle to the equation... Again, start with particle a stationary. This time fire particles b and c at particle a at speed x from exactly opposite positions, so they both strike particle a from opposite sides, simultaneously. My first response was to think particles b and c will both transfer their kinetic energy to particle a, which will return an equal amount of energy to each particle, causing particles b and c to return in the direction from which they came at speed x. There's something about that answer that just doesn't sit right with me, and I can't quite figure out what it is...
It could. Fundamental particles are, by nature, incompressible, dimensionless points. That, along with the idealized vacuum, assures a perfectly lossless transfer of kinetic energy.
I was asking this to clarify that particle interaction is to be disregarded, that the conditions are equivalent to ideal balls rolling on a frictionless table. From there I was going to suggest that you consider the way a cue ball recoils when it strikes a stationary ball. Ideally, then you could simply treat this as a simple case of elastic collision.
