Unstoppable Force and Immovable Object

Oh, you. You just couldn't let me go, could you? This is what happens when an unstoppable force meets an immovable object. You are truly incorruptible, aren't you? Huh? You won't kill me out of some misplaced sense of self-righteousness. And I won't kill you because you’re just too much fun. I think you and I are destined to do this forever. - The Joker

From a logical standpoint, considering the logic as we know it, if there exists an infinite force, an unstoppable force, then it stands to reason that there cannot exist an immovable object. The definition of the immovable object similarly eliminates the possibility of having an unstoppable force because if we have an unstoppable force even the immovable object won't be able to stop it thereby making itself movable and voiding the existence of itself or by stopping the unstoppable force and putting a rest to it once in for all.

This has been discussed over the years in a lot of different places among a lot of different people and contexts and this is one of the well known logical paradoxes of the human world. Let's consider for a moment that an immovable object did exist. Now, according to Newton's first law of motion,

Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.

Now, consider the force mentioned in the equation above is the unstoppable force. If the object still fails to move then the force is not really unstoppable. Let's extend this, even if the force is not unstoppable, the object is still immovable. Meaning it would have infinite mass (in order to have infinite inertia). Because, unless the object has infinite inertia, it cannot be immovable. Is infinite mass even possible?

Einstein proved that an object gains mass as it moves closer to the speed of light and his equations suggest that if an object is accelerated at the speed of light then the mass of that object will become infinite. Out Universe is not infinite. It only stands to reason if the mass of an object is infinite then it would have infinite density due to lack of infinite volume.

A gravitational singularity or space-time singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system. These quantities are the scalar invariant curvatures of space-time, which includes a measure of the density of matter.

Congratulations people, the object moving at the speed of light has just stopped and is now the gravitational singularity. It has so much gravity that it now is the center of the universe as we know it. It's no longer moving at the speed of light. Does the singularity collapse at this point? I don't know. It might, I know of no studies in regards to this matter. The reason might be because infinite mass itself is not possible.

What if, however, we could accelerate a mass-less quantity to the speed of light? CERN thinks they have done that. So, was Einstein wrong? I hope yes. That would be exciting. And if it were really possible to accelerate a particle faster than the speed of light and not have the universe collapse on it – can we finally have an unstoppable force? I wonder…