The experiment paradox in physics

Modern physics is founded on two mainstays: mathematical modelling and empirical verification. These two assumptions are prerequisite for the objectivity of scientific discourse. Here we show, however, that they are contradictory, leading to the `experiment paradox'. We reveal that any experiment performed on a physical system is - by necessity - invasive and thus establishes inevitable limits to the accuracy of any mathematical model. We track its manifestations in both classical and quantum physics and show how it is overcome `in practice' via the concept of environment. We argue that the scientific pragmatism ordains two methodological principles of compressibility and stability.