>Again you aren't talking about Classical Mechanics. Your Demon wants to predict what will happen to the ball at time t_2, and wants to make that prediction based on the state of the universe at time t_0.
>Suppose that the correct prediction is "the ball does not exist at time t_2, because an Invader appears at time t_1 \in (t_0, t_2) and vaporizes the ball before t_2." If your Demon is capable of making such a prediction then he/she must be able to
It must be able to integrate equations of motion. That's all.
>Express in the notation of classical Newtonian mechanics the position and velocity of the Space Invader at time t_0, so that I can deterministically show that the invader MUST begin to slow at time t_1 and destroy the ball prior to time t_2.
Wrong. "Space invader" exists only at ONE point - it has infinite speed and can't slow down.
>You CANNOT do so because v=infinity and x=everywhere (or x=emptyset) is not a valid expression of position and velocity of a body in Newtonian Mechanics. In Newton's formulas, the infinitely fast object DOES NOT EXIST within the classical universe, but his formulas allow it to be the finite-time limit of a classical process.
Newtonian mechanics has no problems with infinitely fast objects, as long as you don't collide them with something else.
That makes them a little bit like black holes - they are singularities, but they are fairly well-behaved