물리학에서 결정론과 비결정론의 표상적 대립과 모델 불변성 기반 구조 실재론

📝 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.

💡 Analysis

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.

📄 Content

Determinism and Indeterminism as Model Artefacts: Toward a Model-Invariant Ontology of Physics David Nolland Abstract This paper argues that the traditional opposition between deter- minism 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 determin- istic 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 fal- libilist 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 in- formational 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 ex- plains 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 repre- sentational 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. 1 Introduction Since the Scientific Revolution, it has been common to treat the contrast between determinism and indeterminism as a deep metaphysical divide in 1 arXiv:2512.22540v2 [physics.hist-ph] 10 Jan 2026 our description of the natural world. With the advent of quantum mechanics, fundamental physics has largely shifted from deterministic equations of motion to ones with intrinsically stochastic features, and it is often taken for granted that the underlying structure of the world must therefore consist of an admixture of lawlike determination and intrinsic randomness. This paper challenges that assumption. I argue that both determinism and indeterminism as commonly understood are representational artefacts of our models rather than ontologically significant features of the world. Beginning with the Bernoulli map, I illustrate how a deterministic dynam- ical model can be reformulated as a stochastic one in a way that preserves the preparation–measurement correlation structure, rendering the two models empirically indistinguishable for the relevant observables. Drawing on work by Werndl (2009) and Ornstein & Weiss (1991), I argue that representational duality of this kind is not confined to this specific toy case but is a recur- ring feature of deterministic dynamical systems exhibiting chaotic behaviour under suitable coarse-grainings. If attention is focused on structure that is invariant under equivalent reformulations, there is a sense in which this duality also extends to dy- namical regimes not characterised by chaotic divergence, but exhibiting either apparently irreducible stochasticity or long-term dynamic stability. I indicate how this extends to quantum theory: coarse-graining necessarily leads to stochastic transition rules that may be governed by either deter- ministic or indeterministic completions of empirically verifiable quantum transition rules. Thus there exist fully deterministic and fully stochastic formulations of quantum mechanics that display the same general pattern of model-equivalence. These specific cases reflect a general and well-established structural du- ality between deterministic and stochastic models. On the one hand, any stochastic process can be represented deterministically on an appropriately defined path space, with its stochasticity carried by a probability measure over trajectories (Kolmogorov 1950). On the other hand, deterministic mod- els with fine-grained but inaccessible microstates routinely admit stochastic coarse-grained descriptions that capture observable behaviour while suppress- ing microstate detail (Van Kampen 2007; Sklar 1993). As Werndl (2011) emphasises, these two representational possibilities underwrite a broad class of observational equivalences between deterministic and indeterministic models. Taken together, they show that whether a model is presented in deterministic or indeterministic form depends on representational choices. This raises an obvious questi

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