A formal theory of experimentation and its applications to quantum theory

Abstract: While it is widely acknowledged that quantum theory is strange, and that the world view it implies is elusive, there is considerably less consensus as to why this is the case. This article will explore the possibility that the theory may be opaque because the mathematical language it employs is inarticulate. To address this possibility, three interconnected mathematical theories will be developed, each specifically designed to handle aspects of quantum theory's subject matter. The first will describe dynamic systems in terms that are general enough to be applicable to any kind dynamics, including both classical and quantum. That description will then be used to construct a theory of experiments, with the aim of understanding what types of experiments scientific methodology allows. Finally, the theory of experiments will found a theory of experimental probabilities applicable to any collection of experiments, so long as their probabilities are internally consistent. The resulting over-arching mathematical language will then be applied to quantum theory. The initial application will investigate whether quantum theory can be used to describe experiments. It will be found that, in general, it can not; the difficulty lying in its ability to describe recording devices. Next, they will be used to investigate the types of worlds that satisfy quantum theory. To understand what quantum theory means is to understand all the ways in which which the theory can be satisfied. The nature and range of the possibilities will be delineated by first using our mathematical language to describing a very simple type of world that satisfies quantum theory. That construction will then be used to derive a range of different types of quantum worlds; a range that will be seen to be sufficiently inclusive to raise the possibility that all types of quantum worlds can be constructed from the original, simple one.