Akira: Full Explanation
1. Akira is set in an alternative world: as soon as the 60s, a secret military starts experimenting on kids. Some of these class of kids, several years prior to the event, includes the 3 future Esper kids we see and young Akira, who all show great promises
2. They are able to manipulate the fabric of the universe (mind, energy, matter, organic...), in fact it's hinted at the beginning of the movie when we see a blurry/noisy picture like an ocean of quarks that turns out to be blood, the doctors indicator is nothing but an oscillating melody translating their power in harmonics, and the end fades out on a universe.
3. They give these kids drugs to enhance their powers and for unknown reason, Akira ends up unleashing his power to explode over old Tokyo, which is the explosion we see at the beginning of the movie. It's uncertain how or why, but this follows with a WWIII.
4. The movie starts several years later, in a newly built Neo Tokyo. The government and military continue their experiences on the now mutant children, while they managed to seal the remains of Akira in silicon plates submerged in tubes and hidden.
5. Tetsuo runs into one of the Esper child, and because he has pre-existing mutant condition, it triggers powers in him, which are echoed by Akira's telepathic presence which calls Testuo in order to be liberated. When Testuo retrieves the remain of Akira, his power start to unleash in a disorganized creation of organic matter forming like a newborn baby.
6. The Esper child then get there to convince Akira to use his powers to stop Testuo (whose explosion may have been even more destructive), and when they agree on it, the tubes housing Akira are destroyed thus liberating him. He then creates an explosion so powerful that it destroys Neo Tokyo.
7. But this is not just a nuclear explosion, and that's why the Espers are able to save Kaneda: this creates a big-bang like explosion where time, space and dimensions are confused leaving some time for Kaneda to see the past, the present and the future (in form of flashbacks), and then a new universe is formed by Akira's consciousness.
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Bridging with quantum theory and Nietzsche übermenschen theory, we then understand that these powered child were but the first mutants and that more and more will come, with the capacity of realizing the full human potential which is that of creating one's own reality.