Please Note: This is a fringe hypothesis at best. The forces described here may or may not exist in real life. Don't get your heart set on finding them!
In Trigamon we have taken great pain to fit "magic" into the Standard Model of Particle Physics (and we do). Some people might wonder why, but it's human nature to try to make sense of the universe. Not only do I find it lazy writing to call something magic and not explain how magic works, but also people like to develop arbitrary rules for magic, which doesn't make sense unless magic is a physical mechanism. (The mechanism for magic presented here is free to use for any scientists or writers, just please cite us and provide the link.)
In this article, we identify a mechanism in quantum physics, that with a bit of imagination and luck, might provide a way to make magic (or effects that resemble magic spells) real. And although the non-mainstream Pilot Wave Theory explains this bit quantum weirdness without the possibility of a magical force, pilot waves give us a much simpler explanation to magic in the Trigamon universe. (See the end of the article)
There's no point to magic unless characters can use it to do stuff. Trigamon is meant to be a parody anime; and this dictates most of our requirements right off the bat. We have to power magical girls and the like. And while some spells might be simple, means magic has to do some pretty complicated stuff.
Many stories (such as Eragon and the EarthseaSeries) employ magic as a language. But this runs into trouble since languages are designed for intelligent observers. One solution would be to make the universe intelligent, as is ultimately done in Samurai Flamenco, but this makes me nervous as it has some pretty horrifying implications. Instead in Trigamon, magic is a machine language, akin to a computer programming languages. Magical spells can be thought of as "scripts" that are run on the computer that is the universe.
The Trigamon Universe is not a computer. As popular as hypothesis that the universe around us might be a simulation are these days, I feel that this as a story mechanic opens a hole with no bottom, and also gives people the wrong impression about quantum mechanics.
For the purposes of magic in "Trigamon", the universe has all the computational power of an extremely fast (non-deterministic) Turing Machine[1]. Given this, casting a magic spell in the universe is analogous to running a computer program on computer. The incantation is the instructions to the universe, which ultimately results in exerting a force on an object.
Every force we feel on the classical scale is the result of the forces of quantum mechanics, and magic should be no exception. If a fundamental requirement of magic is casting spells to alter things in the universe, then this force needs to enable humans to alter the behavior of things at the quantum level. Strangely, a mechanism like this actually exists as a well documented phenomenon in quantum physics. It's known as The Observer Effect.
Before I start expanding on The Observer Effect to create a theory of magic, it's important to make one thing clear: The observer effect is scientific fact, whereas everything I build upon it is somewhere between theoretical physics and my imagination. The real-world observer effect gives rise to the phenomenon known as particle-wave duality, which causes particles to behave differently when an observer is watching. Here it's explained far better than I can do.
In Trigamon, magic is all built on the observer effect. If the behavior of individual particles can be modified by human actions, then somehow, it should be possible to stack these modifications on top of each other until something is noticeable on the everyday level. But doing this is incredibly difficult. To put this into computer terms, if the observer effect on a single particle is a bit, then magic is a modern computer, fully equipped with a graphical user interface.
Any theory of magic needs to explain why it doesn't work in real life. As simple as the computer metaphor is, the metaphor isn't perfect. Bits and transistors are something humans built, and as a result understand. We still have yet to perfect our understanding of quantum mechanics. Furthermore, ones and zeros don't line up exactly with observed and unobserved particles. We, humans, built the hardware for the computers we use. We did not build the hardware of the universe, and we still have yet to figure it out.
Second, the spells that characters use in the Trigamon series are closer to a high-level computer language such as C, Java, or Python than to machine code. (Python is probably closest in function). These high level languages couldn't exist unless people wrote compilers and/or interpreters for them in lower-level languages. In the Trigamon universe, these magical compilers/interpreters were designed by super-advanced civilizations billions of years prior to the start of the story. We, in our universe, have no such luxury.
Every force has an equation behind it. Gravity has F = (G × m1 × m2) ÷ r2[1], Electromagnetism has F = (K × q1 × q2) ÷ r2, and if someone can point us to the equations for the strong and weak nuclear forces, we'd greatly appreciate it[4]. The equation for the magical force an object feels is as follows:
The equation for magic is pretty simple. F is the force felt by an object, which is the same as Z, or magic power. Magic power is then equal to T (temperature, or kinetic energy) times m (mass) times i, which is √(-1). You can break it down and re-arrange the terms, but this equation fits very nicely with the popular view of magic, in that magic is imaginary. In this case, magic is just imaginary energy, which is why magic can be used to accelerate objects beyond the speed of light.
Since we added magic to the standard model, one would think that there must exist a boson that transfers magic energy between particles. Unfortunately for that line of thinking, magic is more like Gravity on this one. Just like the Graviton, no magical boson has ever been observed (in the Trigamon series), and probably cannot exist, since it would have to have to be bound to the caster's instruction, which would result in some very weird properties. Instead Trigamon uses a different model to explain magic.
Einstein's General Theory of Relativity explains Gravity as the result of a change in the geometry of space-time due to the presence of mass: this allows light to be bent around massive objects and explains why orbits are stable. Magic also has this type of effect on space-time, but instead of geometry, magic modifies the "texture" of the universe. By texture, We don't mean the physical texture which is technically part of the geometry, but rather the equations that determine how matter and energy behave, this giving rise to effects like the observer effect.
Also to be fair, the equation for magical force just gives the amount of magical force working on an object, and not the vectors of the force the object is feeling. The equation behind that is unknown at this time.
Bending reality around an observer on the quantum scale means that an observer must exist on the quantum scale, which is a bit of a problem for a scientist. Luckily, we can solve this problem in physics by invoking a tiny bit of metaphysics. In the case of magic, the observer is the soul, or rather the soul's ability to measure. For our purposes, the soul can be thought of a subatomic particle that exists somewhere in the human body. (This is a simplification, we'll cover the soul in depth a bit later).
In order for a particle to be observed, and thus be acted upon by magic, then somehow, information has to be getting transferred from that particle to the soul that is doing the observing. Because the quantum world is weird, the number of proxies doesn't matter.
Although the concept of particle-wave duality is standard for particle physics, there is a model that explains the double-slit experiment without the need to add another force, that being Pilot Wave Theory. The existence of pilot waves actually allows for an even simpler model of magic: that magic is just a force emitted from conscious objects that affects pilot waves of subatomic particles. Affect enough particles (with strong enough magic) and you create effects large enough to been seen on the macroscopic scale.
Next: Karmic Mechanics[1] Based on what I've gleaned from looking into Quantum Mechanics, there's no reason to assume that the universe would be deterministic
[2] Except Gravity, which they still haven't figured out on the quantum scale.
[3] Technically, the equations behind Gravity are more complicated: see Einstein's General Theory of Relativity
[4] Seriously.