[ExI] Gödel and physical reality

[Giulio Prisco]

Gödel and physical reality. What are the implications of Gödel's
theorem for fundamental science and metaphysics?

What does Gödel’s theorem say about physical reality? Does Gödel’s
theorem imply that no finite mathematical model can capture physical
reality? Does the nondeterminism found in quantum and chaos physics -
it’s impossible to predict (prove) the future from the present and the
laws of physics - have something to do with Gödel’s incompleteness?
Many scientists e.g. Stanley Jaki, Freeman Dyson, and recently Stephen
Hawking ("According to the positivist philosophy of science, a
physical theory is a mathematical model. So if there are mathematical
results that can not be proved, there are physical problems that can
not be predicted…") have formulated this intuition. But I'm not aware
of any proof (or very strong semi-rigorous argument) that causal
openness in physical reality follows from Gödel's theorems (or the
related results of Turing, Chaitin etc.). Can anyone give me
links/ideas?