I hate to admit this, but this question kept me up last night. Once again, I recognize that the question can’t be answered as stated, but I was trying to find a way it could be answered without violating too many laws of physics. I’m guessing that’s what the originator wanted – not an ABSOLUTELY(!) correct answer but the *least wrong</> incorrect answer.
In my earlier post I was trying to be succinct and only got as far as cryptic. I stated that motion was relative and force wasn’t. I was referring to relativity theory – not the part about the speed of light, but the part that says there is no absolute reference frame. An immovable object is not moving only in a relative sense. A viewer on a passing train would see the heretofore immovable object moving along nicely without requiring an irresistible force or any force at all! Simply by changing the reference frame an immovable object can be moving and an unstoppable object can be stopped.
Assume, tho, for the sake of the question, that our reference frame is one in which the immovable object is not moving and the unstoppable object is fast approaching. What happens? I would say one of three things: A. the objects pass through each other (good answer, PapaBear). B. The objects rebound from one another (good answer, MarkMal). or C. the objects coalesce.
Physically, I think that A. is the least likely. Dissolving the objects into constituent particles begs the question. The interaction of the particles would still move some of the immovable object and stop some of the unstoppable object.
C., on the other hand, is IMHO physically most likely. The only way an object can be immovable is to have infinite mass. Likewise the only way to be unstoppable is to have infinite momentum which implies infinite mass. And unless the objects are infinitely large, in which case they would already be in contact, they must be infinitely dense. So we have the collision of two infinitely massive and infinitely dense objects. What happens? They collide, coalesce and form a single infinitely massive, infinitely dense object. The cosmological term for such an object is a singularity, at which point, by definition, the laws of physics no longer apply! So anything can happen.
Finally, I think B. is the most satisfying answer. Before the collision we had an unmoving immovable object and a nonstopped unstoppable object. After the collision, we have (tada!) an unmoving immovable object and a nonstopped unstoppable object. The moment of collision is hard to describe but if we wink at that, the universe is pretty much the same before and after.
So, I have to vote for B. The object rebound.
Next question: Can God make a rock so large he can’t lift it?
“non sunt multiplicanda entia praeter necessitatem”