Immovable Object/Unstoppable Object

I was thinking about this in the bath tub... I got to thinking... A lot of times when people think about this they think that there is a paradox when the collision happens, but hypothetically wouldn't the paradox actually be the immovable object?

Do we have evidence that such a thing could even possibly exist?
Supposing we go the route of Black Hole and slowing time and all that, nothing is stopped there. The passage of time is just really slow.
Supposing we go the opposite route of precisely calculating forces stopping a particle wouldn't that mean all energy is expended and thus no mass and no particle, thus no object?

The only thing I can think of that one could say is stopped is when an object "bounces" off another object, but is that considered "stopped"?

Another way to look at this would that may fix the paradox is that the object is the same. If the object had all the energy of the universe no time would pass to it relative to the universe (making the object immovable) while simultaneously the it would likely be traveling at light speed... So the answer to the question is a restating of the question with what the objects are... What happens when two light beams interact with each other... don't they cancel each other out or something?

Source: http://cosmoquest.org/forum/showthread.php/138494-Immovable-Object-Unstoppable-Object

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