In the opening of Fullmetal Alchemist, it says...
Human kind cannot obtain 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 that world's one and only truth.
But why did the Elric brothers believe this to be the one and only law of alchemy? If this was explained in one of the episodes of Fullmetal Alchemist or Brotherhood, please list it too, thanks.
Okay, so, there's a couple things in play here you need to be aware of. Keep in mind that some of this is slightly speculative.
First, it is only in the dub that Alphonse states it to be the "one and only" truth. The original commentary states,
その頃【ころ】、ぼくらは、それが世界【せかい】の真実【しんじつ】だと信じて【しんじて】いた。
"When we were young, we believed that to be the truth of the world."
Second, though, I think there is an important reason that Alphonse brings this up. Starting at episode 43, the pre-OP commentary changes to the following:
He who obtains [the Philosopher's Stone] is exempt from the rule of Equivalent Exchange and does not have to sacrifice anything to obtain something.
(Note: This statement is somewhat wrong: During this unusual exchange, there is still something lost, but it's not apparent to whomever it is doing the transmutation.)
In their adventure, Ed and Al basically learned that human lives are given an alchemical value; since they both believe human life to be invaluable, this shakes the foundation of the principle of Equivalent Exchange that they grew up learning.
This seems to be the only reason that Alphonse used the past tense with "believed"; the Philosopher's Stone shattered what they believed Equivalent Exchange truly meant. To him, Equivalent Exchange can no longer be the "one and only" truth.
This idea also holds true in Brotherhood. The Philosopher's Stone is essentially identical, and the brothers learn the same terrible details of it.
Alchemy in the real world is recognized as a protoscience that contributed to the development of modern chemistry and medicine.
Both Ed and Al say that Alchemy is a science and that the input must be equal to their output, equivalent exchange is this because for what you give up (your input) you will recive something of equal value (your equal output)
There are 2 parts to Equivalent Exchange which can be read up on the Wikia page, The Law of Conservation of Mass and The Law of Natural Providence. I should point out that Scar is still following The Law of Conservation of Mass as what is he doing is breaking objects apart but not reforming, when Ed goes to repair Al after getting his arm back he checks that they did pick up every tiny fragment hinting at this.
Now one can say that the Red Stones or Incomplete Philosopher's Stone can bypass however in a sense they don't, the Red Stones are created by combining materials and get used up over time thus they don't have a Rebound. the Incomplete Philosopher's Stones have the rebound because they are used to bypass Equivalent Exchange however it's unpredictable when the alchemical forces begin stabilize themselves, Marcoh and the State Alchemists during Ishval War were just lucky it never occurred during the war and after it Marcoh seemed to reduce it's usage.
The Philosopher's Stone on the other hand may be the only exception, using it one can bypass Equivalent Exchange however one needs to follow Equivalent Exchange to make one in the first place by sacrificing lives. In Brotherhood, because the first known Philosopher's Stone came from knowledge from Dwarf the Philosopher's Stone may be keeping the alchemical process balanced by doing something that is beyond the realm of human understanding which only Truth understands
