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If an unmovable object were to exist (physics at this time says it is impossible) it would have to have several properties. For the sake of discussion we are not counting the movement of the atoms and particles that make of this hypothetical object relative to themselves:

A: The object cannot absorb or radiate energy. Heat energy would cause the object to expand and contract, thus moving.

B: Any energy then, must be annihilated rather then stored or stored in a non-conventional state. A singularity could potentially be an unmoving object.

C: The object cannot be subject to gravity besides itself. Given a sufficiently large mass such that no other objects can exert a gravitational pull this could be possible, however unlikely to the point that the object's mass would have to be substantially greater then the sum of all other mass in the universe besides itself.

D: The object cannot exhibit rotation.

E: All observers at all speeds and distances must agree the object is not moving which again lends itself to the fact it must ignore gravity's effect.

F: Since movement is relative the object must always appear to be at the same location at all times. See E.

There are several other theoretical circumstances that could be applied to an unmovable object however physics clearly show that in the conventional universe an unmovable object is unlikely due to basic fundamental laws.

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