What happenes when an unnstoppable object meets a un moveable object?
Isaac Asimov answered this question rather neatly, I thought. I can't remember in which of his many books I read it (it was a long time ago), but the gist of his argument was this: A universe in which there exists such a thing as an irresistible force is, by definition, a universe which cannot also contain an immovable object. And a universe which contains an immovable object cannot, by definition, also contain an irresistible force. So the question is essentially meaningless: either the force is irresistible or the object is immovable, but not both.
This was my first introduction to philosophy. It was also my first introduction to the notion that ideas which are actually incoherent, when analysed, can nevertheless be extremely useful metaphors. I can think of no better way to describe some encounters between two-year-olds and their mothers, for example.
The correct setup would be "What would happen if an immovable object were confronted with an unstoppable force." We will have to further define out unstoppable force as having infinite momentum (right?) and the immovable object having infinite inertia (right.) Therefore, our unstoppable force would have an infinite energy (measure this in joules/calories/whatever) and the unstoppable force would be able to absorb infinite energy.
There would be an endless transfer of energy.
The two would appear as if they are resting, but are actually transferring their infinite energies from one to the other. Equilibrium or a relation would never be established since we're dealing in the infinite regarding energy.