Is classical reality completely deterministic?

TL;DR

This paper challenges the traditional view of classical determinism by providing counterexamples in electrodynamics, showing that classical systems can exhibit indeterministic behavior, and proposing a modified path integral approach.

Contribution

It demonstrates that classical electrodynamics can have non-unique solutions, indicating classical indeterminism, and introduces a new path integral formulation to model such systems.

Findings

Counterexamples of non-unique solutions in classical electrodynamics.

Classical strings can split due to indeterminism.

Proposes a modified path integral for indeterministic classical systems.

Abstract

The concept of determinism for a classical system is interpreted as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally assumed to hold for all autonomous classical systems. We give counterexamples of this view. Our analysis of classical electrodynamics in a world with one temporal and one spatial dimension shows that the solution to the Cauchy problem with the initial conditions of a particular type is not unique. Therefore, random behavior of closed classical systems is indeed possible. This finding provides a qualitative explanation of how classical strings can split. We propose a modified path integral formulation of classical mechanics to include indeterministic systems.