MC ask about Magic
Shopkeepers' Explanation:
In the 21st century, First Wizard Merlin was an illusionist, in essence similar to magicians in circus that relies on sleight of hands but instead of simple tricks uses principles of optics, physics and advanced machineries to get the result. In short magicians with the brain of a scientist that used science for his tricks.
Merlin was fascinated with pseudo science - ESP, telekinetik, telephaty, etc and when Nozomi Otori comes forward with his Particle Physics and Otori's Dark Equation derived from his Particle/Wave/Dark Matter Trinity he make his own theory of telekinetik.
If Brainwave is another form of particle and dark matter also another form of particles, it is possible for a certain brainwave reacts with some dark matter to produce the phenomenon of telekinetik. In the same veins, informations (our thoughts) contained in the brainwaves can be transmitted via the dark matters into other brains capable of receiving such "information dark matters". That was the basic of Telepathy.
While Otori and other scientist busied themselves with the task of finding the quanta that forms particles to create the Periodic Table of Particles, Merlin used whatever results they gained from their experiments for a specific goal: Particle Manipulation by Thoughts (Brainwaves). He succeeded in findings which particles reacts to brainwaves. He called them Mana.
With his discovery, he recruited many peoples who shares his ideas. Along the way they were grouped into three factions:
1. Merlin and his bands of scientists, illusionists and magicians who pursue the manipulation of mana to produce produce physical phenomenons such as fire ball, lightning bolt, etc, etc with the help of catalysts and a lot of computation which is handled by advanced computer in the form of phase computer (by that time semi dark matters has replaced silicone semi conductors, and everybody posses their own phase computer with the computational ability of a silicone super computer as their own smartphones).
2. The Espers who wants to elevate their abilities pursued the raw power of the mind, finding particles that are highly compatible with the brainwaves that can be manipulated with their thoughts.
3. The Martial Artists. An intelligent martial artist discovered in his experiments that breathing exercises and some martial art moves makes his brain produces the brainwaves similar to that of the espers. He realised that what the martial artists called "Qi" are actually brainwave manipulable particles. He announced his discovery and joined Merlin's Laboratory with a wave of martial artists seeking to enrich their arts.
And then the bomb blows. The world suffered nuclear winter. By the time the Fallout Shelters opened their gates to release their druids to reclaim the nuclear wasteland and terraform them into habitable minor(closed) ecosystemic dominions (in the manner of Sid Meier's Civilization), the magical factions has separated ways to pursue their own interest.
Merlin and his scientists/magicians form the Wizards, casting spells with the help of spellbooks (phase computers) and spell components.
The espers who pursued the raw powers of the mind become the Sorcerers, they've come to called the group of particles highly compatibles with brainwaves as the Force, and for some reason called themselves as the Jedi. (HERE COMES THE JEDI!) Some amongst them even believe that they're not originally Terran, but comes from another far far away galaxy.
The martial artist developed Qi Manipulation into an art and before the Fallout they've demonstrated how far they've gone in the art: Qi Manipulation has gone far in the way of telekinetic manipulation of sword that they were able to ride swords to fly in the sky. As such they are called Magic Swordman, but some amongst them tried ways to collect Qi into their own body, particularly into a place below the navel called the Dantian. They called themselves Cultivators.
in short Dungeon and Dragons meets Star Wars meets Xianxia.