@Typewriterman:
Thanks, that does answer my questions about how their abilities work in the anime. Building on that though, as I mentioned here in reply to Zedrich, I wanted to consider how the espers in Railgun/Index would be able to use their powers in the real world using known physical laws and properties.

In the world of To Aru, where MAGIC exists, the development of ESPer abilities is thus: people who are unaffiliated with the use of magic must conceptualize themselves having powers. Now, people can’t just CHOOSE whatever powers they want, they must find what sort of power that they themselves can develop.

Thus, statistically speaking, there will be a hodgepodge of different REALITIES that exist and only one that a person can apply to themselves. Along with the help of varying exercises and treatments, those powers are developed in a way that is more and more applicable to real life. Essentially, the strength, speed, what-have you, can only become more prevalent based on an ESPer’s mindset and self conceptualization of being in possession of abilities.

That is why they are ESPers and simply not people with abilities.

NEXT! Those abilities, as they are developed from one’s Personal Reality, must at the same time adhere to varying physical rules in order to exist. So, understanding of properties is important to the handling of abilities once they have taken form.

THEN! An Involuntary Movement is not used directly with the concept of ESPer abilities, but is a result of an ESPer’s abilities. All ESPers give off very very faint but just barely traceable forms of radiation/energy, which like an ESPer’s fingerprint in regards to their ability.

Putting this all together, it isn’t a matter that Misaka herself is creating electromagnetism by purely physical means, but she has mastered her conceptualization of her powers, and as a Level 5, showed how applicable her abilities are to further research in Academy City. The electricity itself does need to follow normal physics once it materializes, but there is of course exaggeration of its properties for story’s sake, such as a coin’s ability to retain its form after being imbued with billions of volts of electricity, flying at supersonic speeds.

This view of ESP as described by To Aru Majutsu no Index hopefully answers the primary complaints brought up by your blog, Nopy.

It has a high possibility of being something like ‘altering your immediate reality’ using your imagination – something like Emiya Shiro’s ‘Unlimited Blade Works’ but does not forcefully violate reality. And so we have Kamijou Touma’s ‘Imagine Breaker’ which negates/normalizes that reality, no matter what. The fact that it works on magic spells as well probably means it is some kind of ‘abnormality cancellation program’ if you can think of spells and abilities as computer programs run on a computer-like universal control system like Yggdrasil (Ah! My Goddess).

An Involuntary Movement (AIM) is most likely leftovers of the mental projection of their personal reality, the energy of which is psychic in nature. Using brainwaves as protocol, any two people with identical bwave patterns can communicate, exchange data, etc. as seen in the ‘Level Upper’ and the ‘Sisters’ arcs. It may even allow the usage of multiple abilities, just as Kiyama Harumi demonstrated during her fight with the Anti-Skill squad. The only drawback with the Level Upper was the coma side effect due to alteration of brainwave patterns. By extension, the AIM Burst (powered by that same network), being a collective of all the network users’ imaginations, personal realities and thoughts, is able to use multiple skills as well.

The principle behind Misaka Mikoto’s ‘Railgun’ ability is actually not ‘Electromagnetism’ (that would apply to a ‘coilgun’ which is powered by electromagnet coils) but rather, an application of the so-called ‘Lorentz Force’ – the same force that makes electric arcs on a widening metal fork move upwards. Misaka’s electrical capacity is stated as being from 1 to 5 million(?) volts, with unknown amperage ratings. In the operation of a real railgun, it is the high electrical potential between two conducting rails that propels the metal projectile (once it closes that circuit by sliding between the rails) by using Lorentz Force. It IS capable of propelling projectiles at extremely high speeds, as observed from a US Navy railgun firing test.

There is a high possibility that Misaka Mikoto does this by controlling the electric potentials/currents in the air around her intended projectile to create ‘rails’ made of eletric current in the air – so any recoil will probably be gusts of wind. It can even be adjusted to accommodate the intended projectile, which can vary in size – from a mere arcade coin (burns up like a meteor due to high-speed atmospheric friction, thus resulting in the 50- meter range) to large metal slabs (the detached robot claw in Episode 24 and the manga equivalent, which resulted in a much longer range than Therestina expected, leading to her ‘first’ defeat.) My guess is that her constant use of arcade coins to limit her range to 50 meters is a self-imposed power limit, used to hide the fact that she can fire her railgun at longer ranges with better projectiles.

The reason why this marks her as a Level 5 is simple – the amount of belief in their personal reality and the concentration required to control electricity to THAT extent is quite difficult to achieve – that and the high-speed damage-dealing potential of her railgun. The fact that she was originally a Level 1, and by ‘extraordinary hard work and determination in overcoming obstacles’ became Level 5 as a consequence, leads to the conclusion that she must have worked on finding a new move using her power, basing it on personal research, found out about the principles of railgun operation (Lorentz Force), and then practiced and trained very hard to control her electricity and firing that coin.

Find me a person who can flick a coin up in the air and flick it again with their thumb the same way she does, as if it were second nature/instinct – it is harder than it seems. Though, directly firing it from her hand without the aerial coin flick is also possible – and both of them do the same thing – shoot the coin on the electric rails to fire it as a railgun round. (even a real railgun requires the projectile to be moving when it hits the rails, otherwise it will arc weld itself stuck on the rails)

btw, Kazari Uiharu’s power is quite nice to have for PC overclocking. Negation of entropy or maintenance of current temperature is pretty good at Level 1 that i can only imagine what she can do with higher levels.

If she were paired with A Certain Legendary species as her pet, and given a Gracidea Flower with a gatituous feeling, i think she might turn into Thermomaster Forme Uiharu and maybe gain a level or two..

I have only watched A Certain Scientific Railgun, so i dont really know about the Index side of things, but that is my thoughts on the principles of operation there.