Okay, so the biggest problem any science person is going to have with Fullmetal Alchemist: Brotherhood is that, while there's so much emphasis on the conservation of matter (Law of Equivalent Exchange), Amestrian alchemy obviously seems to ignore any kind of conservation of energy (This is addressed directly in the 2003 anime, but I'm talking about Brotherhood only). Any alchemist can fix a broken radio if he's got all the parts, but where does the energy needed to put it all back together come from?
Well, we all know that story from FMA about how, after the fall of Xerxes, Hohenheim went east to Xing and taught the people alkahestry (where he's known in legend as the Eastern Sage), and the Dwarf in the Flask went to what became Amestris (and taught the people there alchemy). Okay, so you know how Father's always sitting in that chair underneath Central Command with all the pipes coming out of it? And how May is always freaked every time she goes to Central because she says it feels like there's a bunch of people squirming around underground? Well, what flows through those pipes is Father's Philosopher's Stone (aka the souls of Xerxes), and this is what provides every alchemist in Amestris with the energy required for their transmutation circles. You can see this in how Father can simply "turn off" everyone's alchemy at will (like in the episode where Ed first meets Father), but Scar's, May's, and Hohenheim's alkahestry still works. Father simply stops the flow of the Stone through the pipes and every alchemist is helpless.
This would mean that all of alchemy in Amestris is fueled by Father's Philosopher's Stone. So, even though Ed swore he never wanted to use a Philosopher's Stone for anything, he'd been using one for his alchemy his whole life.