This question came up at Grand Tribunal 2007, and Mark Shirley gave what I thought was a really good answer. I'll see if I can do it justice.
Arcane Connections are formed according to two laws: the Law of Sympathy and the Law of Contagion. That is, they either mystically resonate with the target, or they were once part of the target. The latter case is primarily what we're concerned with here, and a common example is a hair from a person's head. A hair from my head was once part of me, so it is an Arcane Connection to me because of the Law of Contagion. I was never part of the hair that came from my head, so by that same Law I am not an Arcane Connection to it.
I believe it was Nathan Hook who brought up the question of a stone that is split in half: are the two halves Arcane Connections to each other? There's probably some wiggle room here, but the simple answer is no, because each half was never part of the other half. Each piece would be an Arcane Connection to the stone, but where is the stone?