Timed Measurement Theory
Eduardo Skapinakis and José Félix Costa
We consider the role of a Turing machine in controlling measurement experiments and the corresponding revision of Measurement Theory, incorporating the notion of physical time in a theory we show to be realised by all types of measurements of extensive quantities found in the scientific literature. Surprisingly, when we try to mechanise certain aspects of the experimental procedures with Turing machines, we uncover that quantities have an inherent measurement complexity. We demonstrate that there is a relationship between the structure of a real number and the amount of time required to measure its digits, which leads to the emergence of complexity classes associated with measuring of the digits of a real number and a new form of uncertainty: When algorithms govern experiments in Physics, then, even in the limit of the application of the theory, even in the absence of measurement errors, precise measurements of quantities cannot always be made.
Keywords: Measurement theory, forms of physical measurement, measurement with approximations, computational models of measurement, measurement complexity