I'm not generally one to plug fanfic, but...this is seriously the most amazing thing I've ever read. And I'm only on chapter 5.
And it only gets better.
Harry was breathing in short pants. His voice came out choked. "You can't DO that!"
"It's only a Transfiguration," said McGonagall. "An Animagus transformation, to be exact."
"You turned into a cat! A SMALL cat! You violated Conservation of Energy! That's not just an arbitrary rule, it's implied by the form of the quantum Hamiltonian! Rejecting it destroys unitarity and then you get FTL signaling! And cats are COMPLICATED! A human mind can't just visualize a whole cat's anatomy and, and all the cat biochemistry, and what about the neurology? How can you go on thinking using a cat-sized brain?"
McGonagall's lips were twitching harder now. "Magic."
And it only gets better.