I also have some experience of an object seemingly moving of its own accord. This was the same object 3 times!! The first time I was in a different room, but heard a loud bang when it dropped on the floor. The second time I was in the room but was looking elsewhere, but the same thing happened. The third time I did see the movement, which wasn't as dramatic as the first two occasions.

This object has particular significance for me, so I interpret these movements as synchronicities.