Gödel's theorem does applies to mathematical systems of axioms, and I don't think it's clear how it translates to physics. To take an extreme example, you could

Gödel's theorem does applies to mathematical systems of axioms, and I don't think it's clear how it translates to physics. To take an extreme example, you could answer any physical question about a universe that's made up of a single particle traveling in a straight line, even though doing so requires a mathematical system complex enough for Gödel's results to apply. On the other hand, there are a number of interesting undecidable questions (in ZF, the axiom of choice and the continuum hypothesis are examples).