You might find this link useful. In AIT, when you try to "estimate" (we are talking about non computable values here, in the general case ) the complexity of a finite string, those constants (related to the programming language) matter. Only in the asymptotic limit the original theory makes sense. The second point is that you are talking about a scientific theory (physics), so the guiding principles ( for example the mathematical framework , Lagrangian, Hamiltonian formalism, min action principle , etc) are part of the "programming language", you need more than just the computation of a <PERSON> machine (in the definitions, though Turing machines might be enough to define some principles). That one line of compact mathematical notation representing the standard model is based on such principles, and some of them are metatheoretical. Anyway, if you study <PERSON>' s work in greater depth, you might find some answers.
A more interesting problem to think about (I think ) is this. Maybe the Lagrangian/Hamiltonian/min action mathematical framework represents just one "programming language". 915
Maybe there are others, even more powerful out there. This problem allows a multitude of perspectives, this is just one of them.
You can also consider a more simplistic approach, discarding any metatheoretical arguments and complex analogies. <PERSON>'s sixth problem (1900) deals with the axiomatization of physics. Depending on the nature of the axioms, you could have in principle a Turing machine encoding these axioms (if ever found). Then you could define the complexity of the scientific domain under consideration (in this case physics) as the length of a binary string encoding the inner workings of this Turing machine. A similar approach has been considered for mathematics (automatization of the process of mathematical discovery), but <PERSON> incompleteness results showed the serious limitations of this process (well, there's a lot to be said here, and there might be ways to deal with these limitations, but there is no room here for that discussion). A similar phenomenon might appear as related to physics, and there are scientists who consider a full axiomatization of physics impossible.
As for the standard model, I would dare to guess that a few million bits of information should be sufficient, as an upper bound. I might be exceeding a true, tighter upper bound by two orders of magnitude. 484