Despite how much I like anime, I’ve never been a big fan of incredible events with no viable scientific explanation. This includes things like flying through the air with no apparent form of propulsion, creating vast quantities of energy from nothing, and penetrating the armour of a vehicle using a weaker material by using shear willpower. This is one of the reasons why Martian Successor Nadesico was and still is one of my favourite anime: it used the latest theories of quantum mechanics and newest technological advancements of the 90s to explain how things like instant transport and the terraforming of Mars was possible. When there was no way to explain something (like the generation of particles to perform a gravity blast), the topic was simply avoided rather than trying to make up something fake and untrue.
With that said, one of the things that have been bothering me this season are the esper powers, and the general use of the term “esper” in anime. The word “esper” was derived from the acronym ESP, which stands for “extra-sensory perception.” As the name implies, someone with ESP has an extra (or 6th) sense that the rest of us don’t have, and are generally known as psychics. An esper, in this sense, does not refer to someone that can shoot lightning bolts out of their body since that’s not a sense but an an ability. To be fair though, words often change meaning when they’re introduced through a different culture or language, so the definition of an esper in Japan might be different from the rest of the world.
Now Let's start with my opinion/theories about teleportation.
The only way that I could think of that would allow you to teleport from one place to another is if 4-dimensional beings existed. If they do exist, it could be possible that one of them has taken a liking to you and is bending space for her. Lets imagine for a moment that 2-dimensional beings in the shape of squares lived on a piece of paper in your hand. You would be able to see inside a square since you’re looking at it above, but the squares on the piece of paper would not be able to see inside each other since they can’t move into the 3rd dimension (above) the piece of paper. It would then be possible for you to see a set of instructions within a square explaining where it wants to go and all you would have to do is fold the piece of paper to line up the square with its destination so it can just move over. You might be like that square, where a 4-dimensional being is able to read her thoughts by watching the electrical signals in her brain. This could explain why you can only move things she’s in contact with because she would have to push it to the other side once space is bent.
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So to sum things up, You would have to be some kind of monster do be able to do the things in the anime, and even then she wouldn’t be able to perform some of her moves. Four dimensional beings would also have to exist for you to be able to teleport the way she does without an energy source. Basically, The espers do not work except under very extreme assumptions, and even then some of them still don’t work. I guess it’s a good thing that the target audience is too caught up fantasizing to care about if she/he could technically exist or not.
If you have other ideas on how esper powers might work, feel free to share. Any nerds reading this can also point out any mistakes I’ve made since this is mostly stuff I remember from school.