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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.

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marked as duplicate by Kyle Kanos, John Rennie, stafusa, Sebastian Riese, ZeroTheHero Sep 23 '18 at 23:28

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Your question is a little vague. So I'm going to have to guess a little as to what you really want to know.

As to really understanding quantum mechanics, some very smart people have claimed it to be impossible. Here is Feynman talking about this.

https://www.youtube.com/watch?v=SczWCK08e9k

We get the "shut up and calculate" attitude.

https://en.wikiquote.org/wiki/Shut_up_and_calculate

Formal quantum mechanics would refer to something like axiomatic quantum mechanics.

https://en.wikipedia.org/wiki/Axiomatic_quantum_field_theory

There are a number of research programs doing this sort of thing. But the purpose is not to produce anything simplified as such. The goal is to produce something that is mathematically self consistent, and at the same time agrees with experiment. Being simple is a secondary goal. It only enters along the lines of not putting in things that are not required as opposed to making it easy to understand.

There are also a number of toy theories, and theories that have some particular aspect intended to illustrate some interesting feature. Phi-4 theory, for example, has (among many other characteristics) the keen feature of not having to worry about spinors since the fields are all scalar. It makes doing your first path integral a lot simpler.

https://en.wikipedia.org/wiki/Quartic_interaction

Theories exhibiting solitons are a lot of fun.

https://en.wikipedia.org/wiki/Category:Solitons

And theories with exact solutions are also very instructive.

https://en.wikipedia.org/wiki/Category:Exactly_solvable_models

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