How do we know a game has transposed from the opening to the middlegame?

then do you have one?...hopefully.....

No, I think it's a very vague and gradual thing.

I've seen one book or article or something, can't remember, that divided the game into five phases: opening, transition into middlegame, middlegame, transition into endgame, endgame. Not that that helps really, but it's clear that there's no single move exactly where it goes from opening to middlegame.

But does it matter for anything?

I think that it might be based on feel, sort of you have a sense as to when you are in the middle game. Most people probably don't think about when the middle game starts because they're so caught up in their game. But during the game you sort of have a feel as to when it is once again. Most likely it varies from game to game, since there are hundreds of thousands, if not millions, of combinations of moves and ideas that make an opening, twice because of your opponent, the middle game could come quickly with swift attacks, or come slowly with long developing lines. So with that I think saying a specific amount of moves is wrong.

It probably comes down to when you start to get your hands dirty. You are thinking longer about moves, thinking "should I attack the kingside or queenside?", coming up with a battle plan, you start to predict what is going to happen for either side if you do this move or that move and he/she does this move or that move, and you are actually focusing on the task at hand, which is getting the opponent's king, instead of getting your king to a safe spot (sort of leaving your king alone for a little bit) and getting your pieces in good places, I guess developing if you will.

hmmm......so if I keep feeling it's still in the opening, it'll still be the opening-way up to move 50?

 I guess.....it's possible.....if ur opponent thinks the same then maybe. The first of my paragraphs is questionable....mainly focus on the second paragraph.

 ^^^  I'm not the only one who thinks it has something to do with the rooks. 

Since the minor pieces start on the squares between the rooks and the royalty, and the rooks are viewed as "heavy artillery" by most players, I think this is why you can say that development has finished when the rooks are connected and/or moving.  Yes, it's possible that a rook can be taken early (q.v. the Vienna Game) or not move at all during a game, but these situations are rarely encountered at a master level, since defense is more precise, development, and piece safety are practiced better.

In games when the rooks don't move or see each other, the middlegame becomes less of a concern, and an arbitrary move limit for the onset is probably reasonable.

Middle game starts once your pieces are all devoloped and the Rooks are connected

Same thing, said.