“You’re asking what psychic powers are?” Komoe-sensei responded while flipping over the meat on the iron griddle.
Index nodded slightly while staring at the half-cooked meat.
“Simply put, it is based on Schrödinger’s theories, but you may not be familiar with them.”
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“So there are now two possibilities: the possibility that chocolates are inside or the possibility that hard candies are inside. Of course, only one of those can be true. However, when we’re just talking about possibilities, both possibilities are jumbled together.”
Komoe-sensei lightly waved the box for chocolates around.
“Those two possibilities appear as a single result once the box is opened to check on what the contents are. Originally, the contents had a 50% chance of being chocolates and a 50% chance of being hard candies, but once you look it changes to a 100% chance of being chocolates.”
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“Now then,” she said closing the box again. “Assuming the two possibilities were 50% chocolates and 50% hard candies, what do you think is inside this box, Sister-chan?”
“??? I don’t really get it, but I saw chocolates in there just now.”
“Yes. A normal person will choose the 50% chance of chocolates at this point.” Komoe-sensei waved the box around again. “But what would happen if there was a person who could choose the 50% chance of hard candies?”
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“When we refer to espers, we refer to someone whose ability to view the reality of the 50% chocolates vs. 50% hard candies differs from that of normal people. […] “Espers who are cut off from the proper reality gain a personal reality that differs from ours. As a result, they can distort a micro world using different laws. In other words they gain the power to destroy things without touching them or to see one year into the future by closing their eyes.”

Toaru Majutsu No Index vol.3 ch.1 pt.8