As we all know, Earth is well... Earth. Where technology developed instead of alchemy, thus Earth advanced technology faster than the FMA world. But just because alchemy was not developed does not mean the laws, the methods of utilizing Alchemy, Eg; Transmutation Circles, don't exist. It's like saying it's possible to create machines that can fly, but the knowledge and science at the time is insufficient to be able to replicate that kind of existence.
The anime didn't really explain Earth properly, all it gave us was that Alchemy is not possible on Earth, but the Movie debunked that. Remember how Edward was able to reopen the gate using the transmutation circle? This proves that Alchemical energy comes from both sides of the Gate. According to Hohenheim, the death of people of Earth converts into Alchemical energy for people in the FMA world to use Alchemy with. A broken radio can be fixed with alchemy, you have the materials, but you need the energy. The light is the energy that comes from the other side of the gate. Same for Earth, when Edward activated the transmutation circle, he needed alchemical energy to open the incomplete gate to send the dead soldiers back to Earth.
The only reason why Hohenheim concluded that Alchemy was not possible on Earth was because he originally came from the other side of the gate. Same for Edward, he opened the Gate Of Truth from the FMA world, Edward gained knowledge along with the ability to transmute without the use of a circle. Basically what I'm trying to say is you have to open the gate from the side you opened it in order to gain the ability to use in that corresponding side. If Edward commited Human Transmutation in Earth, he would be able to use alchemy without a circle. Hohemheim and Edward can use Alchemy without a circle, but they've gotten so used to that method of utilizing Alchemy they never really considered drawing up the circles for themselves.
However, the only thing that debunks this whole theory is the fact that Envy cannot use his Homunculus ability to shapeshift. But I believe that's just a flaw in the Movie itself. Envy is powered by Red Stones, so he should be able to use his abilities as it is a form of Alchemy in itself, but that's all they're limited to as Homunculus cannot use Alchemy via transmutation circles nor utilize a Philosophers Stone. Because of that, if he can't even utilize his abilities then the Alchemy Edward committed on Earth would not be possible.
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