Final answer:
A physical process capable of computing non-Turing-computable functions, if effective and physically realizable, would challenge the Church-Turing Thesis by suggesting there are computable functions outside the scope of Turing machines, altering the foundational understanding of computation in computer science and artificial intelligence.
Step-by-step explanation:
The question explores the potential existence of a physical process that allows for the calculation of functions not computable by any Turing machine and whether this would refute the Church-Turing Thesis. The Church-Turing Thesis is an hypothesis concerning the nature of computability, suggesting that anything that can be computed algorithmically can be computed by a Turing machine. The thesis is foundational for theoretical computer science, effectively defining the limits of what is computationally possible.
If a physical process existed that could compute functions beyond the capability of any Turing machine, it would suggest there are methods of computation outside the scope of the Church-Turing Thesis. However, a refutation of the thesis would require that such a process be effective, meaning that it could be realized and utilized within the physical universe consistent with the known laws of physics, while not proceeding in infinitesimal steps (as such processes would take infinitely long).
In essence, the Church-Turing Thesis posits that our standard computational models (Turing machines) capture the entirety of what can be computed. A discovery of a calculable function outside this model, which is physically attainable and not just a theoretical construct (like a process with infinitesimal steps), would challenge our foundational understanding of computational theory and potentially lead to groundbreaking advancements in fields such as computer science and artificial intelligence.