Equivalent Exchange
The rule Edward believes can explain the world
Edward and Alphonse begin the series with a simple formulation: to obtain something, something of equal value must be given.
That principle is useful for understanding ordinary transmutation, but the 2003 anime gradually turns it into a philosophical problem rather than a perfect accounting equation. Human lives, grief, war and the Philosopher's Stone all expose how difficult "equal value" becomes once the thing being exchanged is not a pile of matter.
Why it matters
Equivalent Exchange begins as Ed's certainty. By the end of the series, whether the world actually guarantees fairness in return for effort has become one of the show's central questions.
You Need the Right Material
Alchemy reshapes what is present; it does not grant arbitrary wishes
Ordinary alchemy works on existing material. An alchemist needs enough understanding of the substance being changed to break it down and reconstruct it into a viable new form.
That is why transmutation is powerful without being unrestricted magic. A clever alchemist can use the environment brilliantly, but cannot simply demand any object from nothing.
Rebound
When the attempted exchange goes catastrophically wrong
Alchemy can fail violently when the attempted transmutation exceeds what the alchemist can properly control or supply. Human transmutation is the series' most important example: the brothers do not receive their mother back, and the failed exchange takes their bodies instead.
How you can tell
A rebound is not just an attack misfiring. It is the transmutation itself collapsing back onto the person attempting it, often with consequences far beyond the intended result.
Failed Human Transmutation Creates Something New
SPOILER!
2003 continuity · the origin of several Homunculi
In the 2003 anime, a failed attempt to recreate a dead person can leave behind a malformed body connected to that attempted resurrection. With Red Stone material and outside intervention, that being can become a Homunculus.
This is the continuity-specific rule behind Sloth, Wrath and Lust's histories.
Why it matters
Human transmutation does not merely punish the alchemist and end. The mistake can keep living long enough to confront the person who made it.