The formulas are really not very complex. The Standard Model is a single Lagrangian with a couple of dozen constants.
https://visit.cern/node/612
You can expand that Lagrangian out to look more complex, but that's just a matter of notation rather than a real illustration of its complexity. There's no need to treat all of the quarks as different terms when you can compress them into a single matrix.
General relativity adds one more equation, in a matrix notation.
And that's almost everything. That's the whole model of the universe. It just so happens that there are a few domains where the two parts cause conflicts, but they occur only under insanely extreme circumstances (points within black holes, the universe at less than 10^-43 seconds, etc.)
These all rely on real numbers, so there's no computational complexity to talk about. Anything you represent in a computer is an approximation.
It's conceivable that there is some version out there that doesn't rely on real numbers, and could be computed with integers in a Turing machine. It need not have high computational complexity; there's no need for it to be anything other than linear. But it would be linear in an insane number of terms, and computationally intractable.
https://visit.cern/node/612
You can expand that Lagrangian out to look more complex, but that's just a matter of notation rather than a real illustration of its complexity. There's no need to treat all of the quarks as different terms when you can compress them into a single matrix.
General relativity adds one more equation, in a matrix notation.
And that's almost everything. That's the whole model of the universe. It just so happens that there are a few domains where the two parts cause conflicts, but they occur only under insanely extreme circumstances (points within black holes, the universe at less than 10^-43 seconds, etc.)
These all rely on real numbers, so there's no computational complexity to talk about. Anything you represent in a computer is an approximation.
It's conceivable that there is some version out there that doesn't rely on real numbers, and could be computed with integers in a Turing machine. It need not have high computational complexity; there's no need for it to be anything other than linear. But it would be linear in an insane number of terms, and computationally intractable.