I tried to understand QCD a few years back but it was said that the force needed to confine quarks couldn't be calculated and was still in the process If a theory is so complicated that you need super computers to even attempt a solution, wouldn't it be a candidate for getting cut by Occam's razor? What was wrong with Bag models?
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1$\begingroup$ If your main criteria for cutting up theories depend on the ability to calculate things with an abacus, then Newtonian mechanics doesn't pass muster, either. All but about a handful of Hamiltonian systems are non-integrable. $\endgroup$– CuriousOneCommented Apr 30, 2015 at 1:07
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Mathematical models that fit all known observations and can predict with accuracy future ones are not dependent on the method of calculation, but on how predictive they are.
The standard model of particle physics has been validated by experiment and the arithmetic is done mainly with computer calculations both due to the complexity and to the large number of events that have to be generated in order to carry out the integrations necessary for predictions (Monte Carlos). QCD fits the data, particularly as there are no free quarks.
Searching for "bag models" one finds people active in calculating with such models , it is a research frontier and the mathematics is in no way simpler . They are trying for soliton solutions of QCD currently., so are on the next level from the simple QCD symmetries, not replacing the basic theory.
