Shorter version: I am wondering if non-elastic collisions preserve time-symmetery; i.e., given a set of objects with positions and velocities known at a given time, we can calculate forward in time and predict when they will collide, but is it possible to calculate backward in time and see which objects were perhaps formed through inelastic collisions of two smaller objects?
Longer version: Given an isolated (isolated meaning there is nothing around for it to collide with) classical object and knowing its current position and velocity one can determine where it will be for all time and where it has been for all time. If the object were to be placed in some sort of force field we can still determine where it will be for all time and where it has been for all time. The reason we can know both where it will be and where it has been, I believe, is due to the time-reversal symmetry of physics (which, if I remember right, leads to the conservation of energy).
Moving to non-isolated objects, if we know the velocity and position of every object in a system such as the solar system we can similarly determine where all these objects will be and where they have been. Moving forward in time, some objects will collide and will either fracture or stick together. However, even though we can calculate collisions when moving forward in time, moving backwards in time it is a lot more difficult to determine when collisions occurred, especially if the result was the sticking together of two bodies.
In the specific example of the solar system, I could run a full simulation forward and know what the solar system will look like years from now (barring any unmodeled perturbations from passing stars) but I can't run the same simulation backwards and know when objects have experienced collisions or, running the simulation back in time very far, what the primordial solar system looked like before anything resembling the planets was formed.
There seems to be an asymmetry here: I can calculate collisions moving forward in time, but I can't always calculate collisions when moving back in time. Why is this? Is it due to these collisions quite often being inelastic collisions?