Suppose you have a pool table (with no pockets) with a ball in the middle and another ball in one corner. The ball in the corner is hit toward the middle ball. The balls collide and each ball ends up on opposite sides of the table. The 'x-position' of each ball along the walls at each end of the table is observed for one of the balls after they collide. Because of the conservation of momentum, if you observe the x-position of one ball after the collision, you know the x-position of the second ball because of the conservation of momentum (e.g. if I find one ball in one corner, I will know the other ball will be located at the opposite corner due to the conservation of momentum).
So my first thought was that the collision of the balls is like the balls being entangled such that when the experiment is over, I only need to measure the position of one ball to know the position of the. other without directly measuring it. Secondly, if a third ball lightly hits one of the other balls after the original collision, then the accuracy with which I can predict the position of the second ball after measuring the final position of the first ball will not be perfect, but there will still be a correlation, and the strength of the correlation will depend on how hard the third ball hit one of the first two after the original collision. To me, that seems anbalagous to decoherence.
Assume that you cannot observe the trajectories of the balls as they move on the table, you can only measure the final positions of the balls along the walls. My question is, is this example just equivalent to the 'put a left hand glove in one box and a right hand glove in another box' example that is often used to show how quantum entanglement does not work? Or does it make no sense whatsoever as an analogy for quantum entanglement?