The shortest possible distance between two "objects", or two of anything is referred to as the Planck distance. I believe that this distance is 10-33 of a centimeter. I realize, though, from a common sense perspective this wouldn't make sense, since it would appear that this distance, too, can be halved. But, in terms of quantum physics, this is the smallest distance that anything can occur in the fabric of space-time and, in terms of superstring theory, is the absolutely smallest size possible. For a good explanation of this concept, sans mathematical abstractions, I'd urge you to read "The Elegant Universe".