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.

翻译：实验科学通常依赖于实验室程序，这些程序在有限步骤后以物理量的数值报告终止。本文认为，一旦固定了实验方案、背景条件和报告规则，这些程序可被理解为算法过程。假设明确的物理-丘奇-图灵桥接原理，可重复实验因此计算出一个从可允许输入到输出的映射，相应的函数以适用于这些输出的意义存在。此外，可计算分析能够解释为何该结论与有限精度测量相容——因为在此情形下，关键在于对指定精度的系统性逼近，而非单步生成精确实数。方案依赖性及随机性均不削弱存在性论断，相反，它们规定了给定方案实现何种映射，以及在主张独立于方案的单一物理量时需要附加哪些假设。因此，本文区分了三个常被混淆的问题：函数是否存在、是否可计算，以及不同方案下获得的结果何时可被视为对同一物理量的测量。