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". In order, though, to better understand it, suffice it to say that even so-called "empty" space is not empty at all, but is defined within the context of a structure that has a theoretical limit to its size. The subject of string theory is, of course, not completely accepted to date, mostly because we don't have the ability to test its assumptions (our instruments can not directly measure effects that occur within Planck distances), but the mathematics explain very neatly, if a priori, all of what is seen in the universe, particularly concepts such as how gravity and Einsteinian relativity mesh with quantum physics, i.e., the macro and the micro aspects of our universe. One of the interesting thing about the Planck distance is that, theoretically, once an object shrinks to this size, any further attempt to shrink it results in its expansion. Again, though, your answers are to be found in string theory and quantum physics and I'd urge you to read the above, unless you are familiar with advanced mathematics.