...normal laws of physics actually break down and time slows down as you try to travel from well hiddedn town to another.
Ah yes, there are sections of Michigan's Upper Peninsula (the U.P.) that are like that. Long periods of time just disappear while traveling there.
To answer the original question, being from the U.P. I think we identify with that name MUCH more than we ever identify as from Michigan. And likewise, I don't think much of Michigan recognizes us as a part of the state either.
I remember going off to college a billion years ago, from the U.P. down to MSU (the REAL university system in Michigan). If you hold up your left hand palm out, it is basically the shape of the Lower Peninsula of Michigan, where the trolls* live. When dorm-mates talked about where in Michigan one was from, they would automatically hold up their left hand and ask "Where?" When I pointed to a spot above and to the left they would look puzzled and ask if I meant Canada.
If someone from the U.P. (
a Yooper) identified with any particular state, it would probably be Wisconsin rather than the rest of Michigan.
* Troll, one who lives under the bridge (Mackinac Bridge, not to be confused with the Mackinaw Bridge)