If I am not wrong quantum mechanics is about measurements of different physical properties and probabilities of getting different outcomes. We have a mathematical construct to explain it, that is how state of a system is defined in a Hilbert space etc.
I just know complexity theory in layman's terms as of now. But if I am not wrong a Turing machine is an abstract mathematical construct which can explain the working of all algorithms ( again in layman terms, I know there are different types of Turing machines ).
I am compelled to think that is there a branch of mathematics which deals with abstract constructs. I mean like a Turing machine ( or automata ) explains the working of all algorithms is there a mathematical theory/construct which subsumes all other mathematical constructs needed to explain various physical phenomena's. I mean is it possible to explain all mathematical theories ( like the ones needed to explain quantum mechanics ) with a single one, as if everything was part of a big automata.
I am sorry for vague terminologies, its not related to my work but is something I have been thinking about lately just for fun.