Real Numbers are the Hidden Variables of Classical Mechanics

TL;DR

This paper argues that real numbers serve as hidden variables in classical mechanics, implying that classical physics is inherently indeterministic and challenging the notion of physical realism of real numbers.

Contribution

It demonstrates that real numbers function as hidden variables in classical systems, drawing parallels with quantum indeterminism and questioning their physical reality.

Findings

Real numbers act as hidden variables in classical mechanics

Classical mechanics is fundamentally indeterministic

Real numbers should not be considered physically real

Abstract

Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with quantum theory and conclude that the common real numbers are, de facto, the hidden variables of classical physics. Consequently, real numbers should not be considered as "physically real" and classical mechanics, like quantum physics, is indeterministic.