I've heard that quantum mechanics is really hard to teach people how to fully understand. Maybe there are some statements that some people seem to be able to prove are true according to a certain quantum theory but those statements are not normal statements and other people can't ever be made to understand what those statements mean. I'm wondering if despite that, a formal system has been created by some of those who claim to fully understand a certain quantum theory and other people can be taught how to write a formal proof in that system and taught how to formalize the question of the density of water at any internal energy and pressure as a string of characters that represents a statement in that system and write a formal proof of the formalization of statement of its density as a function of pressure and internal energy without worrying about not being able to learn what the statement actually means.
More specifically, my question is whether a formal system has been created for a simplified theory of the universe electrons and nuclei are point charges with no nuclear chemistry and gravity, dark matter, and the cosmological constant don't exist. If so, has that system also been mathematically proven to be consistent. I'm pretty sure that if the system includes the second law of thermodynamics as an axiom, then it's inconsistent because according to this answer, the second law of thermodynamics hasn't been proven to be an absolute law.
I read the first bit of the Wikipedia article Quantum logic and it didn't say whether it was the type of formal system I described here. I don't really feel like reading more because I don't want to take the risk that after wasting a lot of my life doing a whole lot of reading on that topic, it will be all for nothing and I will still not understand what they're saying.