According to the Alcoholic Chain-Smoking Loli's explanation, normal Espers are able to choose what type of candy comes out of the box (or whether the cat is dead or not). Instead of the result being an unknown until the box opens, Espers guarantee the outcome. Affecting enough of those minute changes lets them shift reality enough that they create a power.Originally Posted by Kraco
Mikoto presumably distorts the precise location of an electron, and another and another. The electrons rub together and align until she generates sufficient electromagnetic engeries. Similarlly, Accelerator distorts something as minute as the spin direction the subatomic particles (basis for Schrödinger's Principle). Stacked together, he controls where and how fast they are collectively going. Someone like Kuroko (played by the lovely Satomi Arai, Sayoko in CG) with teleportation probably shifts the judgment on the precise location of her composite particles and associated ones around her until, *Poof* she's somewhere else.
Magic does this all by violating physics just the same, only using the divine to do the dirty work that Espers do subconsciously. Magic seems more like a conscious will driving the same guarantees that Espers accomplish unconsciously. Magicians always beseech intervention to their benefit (or their opponent's misfortune). Index's Walking Church supposedly used to accomplish the same thing as Touma's ability, but in addition consciously didn't allow shifts that would harm the wearer, explaining why physical attacks like Kaori's also should have failed.
Touma on the other hand forces the choice back into the box. He recreates that uncertainty, rendering both magic and ESP abilities useless. That's why he doesn't have any power without something being used against him. That same uncertainty always exists outside the influence of an Esper, so he normally doesn't affect anything. But when Mikoto blasts him with a lighting bolt of modified electron locations, he just ensures that their locations are again unknown, and the effect is dispelled. Perhaps his bad luck is, like Index claimed, just a side affect of him cancelling out the standard level of benevolence the divine imparts on all human beings. When all is uncertain, things just happen as they will (for comedic effect).