Physics without Determinism: Alternative Interpretations of Classical Physics

TL;DR

This paper challenges the deterministic view of classical physics by proposing that indeterminism can be integrated through finite information quantities, linking classical and quantum interpretations and exploring implications for emergence and measurement.

Contribution

It introduces a novel indeterministic interpretation of classical physics based on finite information quantities, contrasting with traditional infinite-precision assumptions.

Findings

Classical physics can be modeled with finite information quantities.

Indeterministic interpretations relate to quantum measurement problems.

Potential for new emergence and causation theories in physics.

Abstract

Classical physics is generally regarded as deterministic, as opposed to quantum mechanics that is considered the first theory to have introduced genuine indeterminism into physics. We challenge this view by arguing that the alleged determinism of classical physics relies on the tacit, metaphysical assumption that there exists an actual value of every physical quantity, with its infinite predetermined digits (which we name \emph{principle of infinite precision}). Building on recent information-theoretic arguments showing that the principle of infinite precision (which translates into the attribution of a physical meaning to mathematical real numbers) leads to unphysical consequences, we consider possible alternative indeterministic interpretations of classical physics. We also link those to well-known interpretations of quantum mechanics. In particular, we propose a model of classical indeterminism based on \emph{finite information quantities} (FIQs). Moreover, we discuss the perspectives that an indeterministic physics could open (such as strong emergence), as well as some potential problematic issues. Finally, we make evident that any indeterministic interpretation of physics would have to deal with the problem of explaining how the indeterminate values become determinate, a problem known in the context of quantum mechanics as (part of) the ``quantum measurement problem''. We discuss some similarities between the classical and the quantum measurement problems, and propose ideas for possible solutions (e.g., ``collapse models'' and ``top-down causation'').