Determinism and Indeterminism as Model Artefacts: Toward a Model-Invariant Ontology of Physics

TL;DR

The paper tackles the question of whether determinism or indeterminism reflects true ontology or merely representational choices. By analyzing model-equivalence across classical and quantum systems, it introduces a model-invariance criterion that identifies ontologically robust features—such as conservation laws, symmetries, and invariant probability currents—that persist under empirically equivalent reformulations. It reframes foundational issues like the measurement problem as questions about representation and coarse-graining, rather than requiring new fundamental dynamics. The resulting fallibilist structural realism emphasizes invariant relational structure over the specifics of any given mathematical completion, offering a practically meaningful ontology for modern physics that remains open to empirical refinement. This approach has potential implications for quantum foundations, classical chaos, and the interpretation of dynamical laws, by highlighting the primacy of empirically accessible structure over representational commitments about underlying microdynamics.

Abstract

This paper argues that the traditional opposition between determinism and indeterminism in physics is representational rather than ontological. Deterministic-stochastic dualities are available in principle, and arise in a non-contrived way in many scientifically important models. When dynamical systems admit mathematically equivalent deterministic and stochastic formulations, their observable predictions depend only on the induced structure of correlations between preparations and measurement outcomes. I use this model-equivalence to motivate a model-invariance criterion for ontological commitment, according to which only structural features that remain stable across empirically equivalent representations, and whose physical effects are invariant under such reformulations, are candidates for realism. This yields a fallibilist form of structural realism grounded in modal robustness rather than in the specifics of any given mathematical representation. Features such as conservation laws, symmetries, and causal or metric structure satisfy this criterion and can be encoded in observable relations in mathematically intelligible ways. By contrast, the localisation of modal selection -- whether in initial conditions, stochastic outcomes, or informational collapse mechanisms -- is not invariant under empirically equivalent reformulations and is therefore best understood as a gauge choice rather than an ontological feature. The resulting framework explains how certain long-standing problems in the foundations of physics, including the measurement problem and the perceived conflict between physical determinism and free agency, arise from the reification of representational artefacts. By distinguishing model-invariant structure from modelling conventions, I offer a realist ontology for modern physics that combines empirical openness with resistance to metaphysical overreach.