[SideQuark]

> … so there's a physical process that's undecidable.

No, since you cannot physically build a Turing Machine. A Turing machine requires infinite tape. Any physically realizable machine doesn’t have that, so has finite states, so is decidable: enumerate the states in finite time - it halts or repeats, so all programs on a finite state machine are decidable.

Your example is not an undecudable physical process.

Godel things also don’t apply: Godel theorems are about proof of this or that from within the same system. In logic one can prove such things from an outside system, then construct towers, avoiding Godel theorems. Godel theorems also require a model of integers including multiplication (without multiplication, such systems were proven complete and decidable). However the universe does not contain a model of integers, as the physical universe is not unbounded: relativity places a finite limit in spacetime on what can interact.

Mixing math as reality fails at these requirements.