How does the law of equivalent exchange work in FullMetal Alchemist?

The law of equivalent exchange governs the use of alchemy in Fullmetal Alchemist, and rules have consequences.

In Fullmetal Alchemist: Brotherhood , the practice of alchemy is at the pinnacle of science. It enables its practitioners to alter the composition of matter through the process of transmutation, a skill useful both in combat and in everyday life. Despite its many uses, alchemy is a science and, as such, is subject to the laws of the FMA universe.

That said, the fundamental principle of alchemy revolves around the law of equivalent exchange. While this may sound complicated, the simple concept is absolute: you can't make something out of nothing. To create something, you have to exchange something else of equal value, and then it's lost. The law of equivalent exchange limits the infinite potential of alchemy, and the series explores why this is actually a good thing.

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FMA's law of equivalent exchange limits alchemy

The law of equivalent exchange is a fictionalized version of the first law of thermodynamics, which states that energy can neither be created nor destroyed, but only transformed. Light can be transformed into heat, electricity into sound, and so on. In Fullmetal Alchemist , Equivalent Exchange is based on two fundamental laws: Conservation of Mass and Conservation of Providence.

The Law of Conservation of Mass stipulates that an object cannot be created from nothing, and if it is deconstructed, it will be reduced to components whose sum is equal in mass. For example, an object with a mass of one gram can only be transmuted into an object with a mass equal to one gram. If a one-gram object is deconstructed, the process will produce components whose sum is equal to the same weight.

The Law of Natural Providence states that objects composed of a particular material or element can only be transmuted into objects of similar composition. For example, stone objects can be transmuted into other stone objects, but not into objects composed mainly of water. In other words, lead cannot become gold. There are, however, a few notable exceptions to this rule.

The three laws of alchemy

• Don't transmute gold
• Do not act against the government
• Do not attempt human transmutation

The taboo of alchemy: human transmutation, rebound and truth

Alchemy, while capable of miraculous feats, is not without its limits. Reviving the dead through the process of human transmutation is impossible, and is considered a taboo act in the world of alchemy. In order to revive a deceased person, his original soul and body must be transmuted, Alphonse Elric declaring that a wandering soul can only return to its original body and vice versa. This is why his soul begins to reject the armor, as it is not his true vessel.

Fullmetal Alchemist establishes that the value of a human soul is unquantifiable and that, just as something cannot be created without an object of equal value being lost, something of infinite value can never be exchanged equally. This doesn't stop alchemists from trying, because sometimes the pain of losing a loved one outweighs logic. If a human transmutation is carried out, the alchemist responsible pays a heavy price, as bartering a soul of infinite value with materials of finite value unbalances the alchemical equation, causing a rebound.

The rebounds take a toll on the perpetrator of the taboo in order to rebalance the exchange: Alphonse loses his body and Edward loses a leg while trying to resuscitate their mother, Edward also loses an arm while binding Alphonse's soul to the armor. In an unrelated case, Izumi Curtis is robbed of numerous organs after attempting to resuscitate her baby. The price will be high even if the taboo is committed unwittingly or against everyone's will, as Roy Mustang finds himself deprived of his sight despite having been forced to perform a human transmutation by his Father and the Homunculi.

The law of equivalent exchange can be reversed with a philosopher's stone

The punishment for human transmutation is severe, not only because it goes against the law of equivalent exchange, but also because defying this law means that a human has effectively tried to play God - and God in Fullmetal Alchemist is none other than Truth. All those who attempt a human transmutation are teleported through their own personal Gate of Truth (which enables alchemy to be performed) and brought before the being whose name the gate bears. Truth is God in the sense that it possesses infinite knowledge, including that of alchemy, world history and much more. When it passes through the Gate of Truth, this infinite knowledge is displayed and absorbed by the targeted alchemist. Alongside this knowledge, entry into the realm of Truth also enables the alchemist to perform alchemy without using a transmutation circle (the fundamental law of equivalent exchange still applies).

How the philosopher's stone is involved in human transmutation

Using a philosopher's stone is the only way to perform a human transmutation without causing rebound. Indeed, philosopher's stones are composed of several souls, allowing their contents to be exchanged equally while performing human transmutations. However, while technically possible, the morality of this act is questionable, as the creation and use of a philosopher's stone is unethical from the outset. This is also why Ed and Al openly refuse to exploit a philosopher's stone to overturn the law of equivalent exchange, even if it means achieving their goals in an instant.

The power of alchemy itself can be exchanged

The only other example of successful human transmutation in Fullmetal Alchemist is Edward Elric's final transmutation, in which he offers Truth his own Gate of Truth, and thus his ability to use alchemy, in exchange for Alphonse's soul and body. As the values available are incalculable to begin with, whether this satisfies the law of equivalent exchange can be left to speculation. However, it is undeniable that at this moment, Edward sacrifices absolute power, an idea which, if realized, has infinite value, to save his brother.

Truth is an omniscient being as well as the mirror image of the alchemist in front of her, and as such, she can discern that person's most precious possession. For Edward, alchemy is what makes him who he is, and is undoubtedly his most precious possession. His willingness to sacrifice what was most valuable to him was more than enough to satisfy the Truth, thus fulfilling the Law of Equivalent Exchange.

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