The paradox of infinitesimal granularity: Chaos and the reversibility of time in Newton's theory of gravity

TL;DR

This paper explores how fundamental quantum uncertainties and chaos in Newtonian gravity lead to macroscopic irreversibility, despite the time-symmetric nature of physical laws, highlighting the paradox of infinitesimal granularity.

Contribution

It introduces a novel link between quantum wave function collapse, chaos in gravitational systems, and the emergence of irreversibility in classical physics.

Findings

Irreversibility fraction scales as a power law with numerical precision

Wave packet reduction introduces fundamental uncertainties in phase space

Superposition of multi-body systems underpins the paradox of infinitesimal granularity

Abstract

The fundamental laws of physics are time-symmetric, but our macroscopic experience contradicts this. The time reversibility paradox is partly a consequence of the unpredictability of Newton's equations of motion. We measure the dependence of the fraction of irreversible, gravitational N-body systems on numerical precision and find that it scales as a power law. The stochastic wave packet reduction postulate then introduces fundamental uncertainties in the Cartesian phase space coordinates that propagate through classical three-body dynamics to macroscopic scales within the triple's lifetime. The spontaneous collapse of the wave function then drives the global chaotic behavior of the Universe through the superposition of triple systems (and probably multi-body systems). The paradox of infinitesimal granularity then arises from the superposition principle, which states that any multi-body system is composed of an ensemble of three-body problems.