HILBERT’S SIXTH PROBLEM: DESCRIPTIVE STATISTICS AS NEW FOUNDATIONS FOR PROBABILITY

Abstract

Usually, the theory of probability has been made the foundation for the theory of statistics. But the physical significance of the concept of Probability is problematic, with no consensus. It would seem better to make the descriptive statistics of physical data the foundations of physical probability. This will answer a question posed by Hilbert in his Sixth Problem, the axiomatization of Physics. It is based on the auto-correlation function of time series. Almost all trajectories of a linear dynamical system (with sufficiently many degrees of freedom) are approximately equal, no matter their initial conditions, even when the system is not ergodic, as conjectured by Khintchine in 1943