Experiments, Computability, and the Existence of Physical Functions
For philosophers of science and computability theorists, it provides a conceptual framework linking experimental science to computability, but the contribution is primarily theoretical and incremental.
The paper argues that experimental procedures can be understood as algorithms under a physical Church-Turing bridge principle, showing that reproducible experiments compute functions from inputs to outputs, and that finite-precision measurement is compatible with this view via computable analysis. It clarifies that protocol dependence and stochasticity do not undermine the existence of such functions, but rather specify which map is realized.
Experimental science usually relies on laboratory procedures that, after finitely many steps, terminate with numerical reports on physical quantities. This paper argues that such procedures can be understood as algorithmic once the protocol, background conditions, and reporting rules are fixed. Assuming an explicit physical Church--Turing bridge principle, a reproducible experiment therefore computes a map from admissible inputs to outputs, and the corresponding function exists in the sense appropriate to those outputs. Furthermore, computable analysis allows us to explain why this conclusion is compatible with finite-precision measurement since in this case what matters is a systematic approximation to a requested accuracy, not the production of exact real numbers in a single step. Neither protocol dependence nor stochasticity undermines the existence claim. Rather, they specify which map is realized by a given protocol and what additional assumptions are required for stronger claims about a single protocol-independent quantity. The paper therefore separates three questions that are often conflated: whether the function exists, whether it is computable, and when results obtained under different protocols may be treated as measurements of the same quantity.