I argue that dimensional analysis provides an answer to a skeptical challenge to the theory of model mediated measurement. The problem arises when considering the task of calibrating a novel measurement procedure, with greater range, to the results of a prior measurement procedure. The skeptical worry is that the agreement of the novel and prior measurement procedures in their shared range may only be apparent due to the emergence of systematic error in the exclusive range of the novel measurement procedure. Alternatively: what if the two measurement procedures are not in fact measuring the same quantity? The theory of model mediated measurement can only say that we assume that there is a common quantity. In contrast, I show that the satisfaction of dimensional homogeneity across the metrological extension is independent evidence for the so-called assumption. This is illustrated by the use of dimensional analysis in high pressure experiments. This results in an extension of the theory of model mediated measurement, in which a common quantity in metrological extension is no longer assumed, but hypothesized.

我认为，维度分析为模型介导的测量理论的怀疑性挑战提供了答案。当考虑将具有更大范围的新颖测量程序与先前测量程序的结果进行校准的任务时，就会出现问题。令人怀疑的担忧是，新颖的和先前的测量程序在其共享范围内的一致性可能仅由于在新颖的测量程序的专有范围中出现系统误差而变得明显。或者：如果两个测量程序实际上测量的量不同怎么办？模型介导的测量理论只能说我们假设存在一个共同的量。相比之下，我表明，整个计量范围内尺寸均匀性的满足是所谓假设的独立证据。这可以通过在高压实验中使用量纲分析来说明。这导致了模型介导的测量理论的扩展，其中计量扩展中的常见量不再被假定，而是被假设。