"Humankind cannot gain anything without first giving something in return. To obtain, something of equal value must be lost. That is alchemy's First Law of Equivalent Exchange. In those days, we really believed that to be the world's one, and only, truth." Alphonse Elric
Equivalent Exchange is used in alchemy, and most closely resembles the law of conservation of matter of Antoine Lavoisier, one of the founders of modern chemistry. In the world of Fullmetal Alchemist, conservation of energy seems to be an unknown concept, thus other scientific laws such as Albert Einstein's E=mc² and the laws of thermodynamics do not directly apply; at least they appear that way until later in the series.
The alchemists treat Equivalent Exchange as a physical law placing limitations on transmutation and as a philosophical law they apply in attempts to explain the world.
Final Conclusion about the law
"Humankind cannot gain anything without first giving something in return. To obtain, something of equal value must be lost. That is alchemy's First Law of Equivalent Exchange. In those days, we really believed that to be the world's one, and only, truth. But the world isn't perfect, and the law is incomplete. Equivalent Exchange doesn't encompass everything that goes on here. But I still choose to believe in its principle: that all things do come at a price. That there's an ebb, and a flow, a cycle. That the pain we went through did have a reward and that anyone who's determined and perseveres will get something of value in return, even if it's not what they expected. I don't think of Equivalent Exchange as a law of the world anymore. I think of it as a promise between my brother and me - a promise that someday, we'll see each other again." Alphonse Elric
The world is too complex and too imperfect for any one law to explain everything. It is also said that there is no equivalency in trading a life for a life, implying that the creation or use of a Philosopher's Stone is inherently immoral.
