Ultimate stochastic entities (Q1059073)

We take the view that everything that is known about a physical system can be described by a ''stochastic entity'' (\({\mathcal A},\Delta)\), which consists of a ''manual'' \({\mathcal A}\) of experiments that can be performed on the system, and a set \(\Delta\) of possible stochastic states (probability measures) on the logic of the manual. We next consider what happens when new information about the system is learned and describe precisely how one then obtains a new stochastic entity more elaborate than the first. Finally, we show that as information about the system continues to grow, the increasingly elaborate stochastic entities describing the system necessarily acquire mathematical properties often assumed for mathematical convenience in papers on quantum mechanics.