Can someone help me with the argument here? I understand the part about showing that solving Schrodinger's equation is NP-hard and thus extremely difficult for large inputs (ie large physical systems). But when we make a statement such as "Problem X is NP-complete," we're making a formal claim about solving that problem with a particular symbolic model of computation.

Is it obvious that such a model of computation applies to the universe?

My layman's understanding is that there's still debate about whether the physical universe is fundamentally discrete or continuous. If the latter, then all the time the universe is effectively performing infinite-precision calculations, which we know to be impossible under the standard symbolic model of computing.