Physical Causal Closure

• Physical causal closure is the thesis that every physical event has a sufficient physical cause, defining a framework where physical effects are fully explainable by preceding physical conditions.
• The concept is analyzed through both ontological and epistemic formulations, distinguishing between deterministic state evolution and interventionist causal relations.
• Debates over closure span multiple disciplines, influencing interpretations in quantum mechanics, consciousness research, and the study of interlevel causal interactions.

Physical causal closure is the thesis that physical events are causally sufficient unto themselves, commonly expressed as the claim that for every physical effect there is a sufficient physical cause. In recent arXiv literature, however, the term is not used univocally. It appears as an ontological doctrine about sufficient physical causes, an epistemic constraint on admissible theories, a stance-dependent claim whose meaning depends on whether one speaks in the language of physics or in the language of causation, and a target of criticism in consciousness studies, quantum foundations, biology, and theories of self-determining systems. The resulting debate concerns not only whether closure holds, but also what domain, level, or descriptive framework it is supposed to govern (Kleiner et al., 2021, Ohmura et al., 6 Apr 2026, Ellis, 2020).

1. Canonical formulations of closure

In its standard ontological form, physical causal closure is stated as: “For every physical effect, there is a sufficient physical cause.” Kleiner and Hartmann translate this familiar doctrine into an explicitly epistemic condition on theories of consciousness. Let $P_T$ be the set of physical events a theory $T$ is committed to, and let $P_P$ be the set of physical events that natural science predicts, explains, or otherwise determines for the actual world. A theory obeys closure iff there exists an injective embedding

$i : P_T \to P_P$

so that the theory does not posit any changes to the physical events explained, predicted, or otherwise determined by natural science. On this formulation, a theory may redescribe the physical story, but it may not add, remove, or modify physical events or their physical properties as described by science (Kleiner et al., 2021).

This epistemic version is stronger than a mere slogan. It says that closure is not only a thesis about what causes what, but a restriction on what a theory may count as part of the physical world. Kleiner and Hartmann further argue that the usual ontological causal closure implies this epistemic embedding condition. A theory that violates the embedding condition thereby changes the physical story told by science and, on their account, violates standard causal closure as well (Kleiner et al., 2021).

A distinct reconstruction appears in work on the “Physical Stance” and the “Causal Stance.” There, physical determinism belongs to the Physical Stance, where the world is described in the language of state variables, dynamical laws, symmetries, and conservation laws, whereas physical causal closure is definable only within the Causal Stance, where causation is represented by asymmetric, intervention-sensitive relations. On that view, physical determinism and physical causal closure should not be equated, because the former is a nomological thesis about state evolution while the latter is a causal thesis about what kinds of causes physical events can have (Ohmura et al., 6 Apr 2026).

2. Determinism, asymmetry, and causal vocabulary

A central fault line in the literature concerns whether closure is simply another name for deterministic physical lawfulness. The “Causal Stance” analysis rejects that identification. In the Physical Stance, physics “does not distinguish cause and effect as asymmetrical roles,” and “causality is an undefined term in physics.” By contrast, the Causal Stance introduces asymmetry through manipulability and intervention, using Pearl’s assignment operator “$:=$” rather than symmetric equality. The stock example is Newton’s law: $f = ma$ is symmetric as a physical law, whereas $a := f/m$ expresses a causal direction grounded in intervention (Ohmura et al., 6 Apr 2026).

On this reconstruction, Jaegwon Kim’s influential formulation is internally coherent only because it effectively identifies physical causation with deterministic physical lawfulness. Once causation is treated in the interventionist manner emphasized by “currently dominant theories of causation,” that equation fails. The consequence is methodological as well as metaphysical: closure cannot be read directly off the formal language of physics, because the causal asymmetry closure presupposes is not encoded there (Ohmura et al., 6 Apr 2026).

This does not entail that physics is causally inert. A different line of argument, developed in a quantum setting, contends that time-symmetric unitary dynamics still support a genuine causal asymmetry because interactions generically create entanglement and almost never disentangle systems. By connecting entanglement measures, quantum algorithmic complexity, and the Principle of Independent Mechanisms, Williams argues that one can infer a direction of causation between quantum states related by unitary evolution. This is not a restatement of closure, but it shows that the absence of an explicit cause-effect distinction in basic equations does not by itself eliminate causal direction from microphysics (Williams, 2022).

3. Closure as a constraint on consciousness science

The sharpest recent challenge to physical causal closure arises in the scientific study of consciousness. Kleiner and Hartmann analyze experiments in terms of an experiment $M$, a set of possible outcomes $O_M$, and, for a theory $T$, a set $T$0 of outcomes that the theory allows. Their key move is to focus on the fact that measurement results must be physically stored or transmitted: on hard disks, SSDs, paper, sound waves, transient voltage states, or other physical media. Accordingly, data supervene on physical events, and the measurement outcomes of a consciousness experiment can be represented by a function $T$1 from possible physical worlds to possible stored result data sets, with

$T$2

This links a theory’s physical commitments directly to its admissible measurement outcomes (Kleiner et al., 2021).

On that basis they prove a result stated as “Theorem 1. The closure of the physical is unscientific.” Here “unscientific” is defined narrowly: an assumption is unscientific if it implies that any two different theories obeying that assumption are empirically indistinguishable. If two theories both satisfy closure, their physical commitments embed into the same $T$3, and because measurement results are determined by the physical configuration of the measuring and storage devices, the two theories yield exactly the same set of possible outcomes for any experiment. No experiment can distinguish them (Kleiner et al., 2021).

The scope of this argument is explicitly broad. It is applied to Integrated Information Theory, Global Neuronal Workspace, Higher Order Thought theories, Attention Schema Theory, predictive processing–based theories, epiphenomenalist or property-dualist theories with fixed physical effects, and illusionist or eliminativist theories, provided they relate consciousness to physical events and accept the relevant closure condition. It is also indifferent to the paradigm: report-based experiments, no-report paradigms, NCC studies, and introspective self-measurement all produce physically stored results and therefore fall under the same result. The consequence, as formulated by the authors, is a challenge to any research programme that aims to ground a physical functionalist or identity-based understanding of consciousness on empirical observations while retaining closure (Kleiner et al., 2021).

4. Quantum theory, locality, and the limits of simple closure

Quantum theory has generated both strengthened and weakened versions of closure. Kent’s “causal quantum theory” is an explicit attempt to enforce a strong relativistic notion of local causal closure. It assumes that measurements or collapses are well-defined physical processes, localised in space-time, never give perfectly reliable outcomes, and influence only events within the future light cone. Probabilities at a point depend only on the local state determined by events in its past light cone, so for spacelike separated measurements $T$4. The theory is therefore Bell-locally causal in the intended sense, but it achieves that by giving up standard spacelike entanglement correlations and becomes experimentally vulnerable through Bell-type and single-particle multi-detection tests (Kent, 2018).

A different result goes in the opposite direction. In “Causation does not explain contextuality,” arbitrary causal structure is allowed: retrocausality, global constraints, indefinite causal order, non-Markovian environments, and other exotic possibilities are all absorbed into an ontic process $T$5. Even with this generalization, no model satisfying $T$6-mediation, instrument non-contextuality, and process non-contextuality can reproduce all quantum process probabilities. The paper’s conclusion is that quantum predictions require a deeper form of contextuality that cannot be removed by replacing ordinary causal order with more exotic causal structures. In that sense, a non-contextual, causally closed physical description is unavailable if quantum theory is exactly correct (Shrapnel et al., 2017).

Other contributions complicate the picture further. Williams argues that entanglement growth and quantum algorithmic complexity ground a causal asymmetry within microscopic quantum dynamics, whereas “Physics beyond Causality” presents a speculative framework in which the observer’s space-time representations form a closed logical system only for an internal observer, while “off-site” continuums and initiated fields undermine any single global causal closure of the observed space-time domain (Williams, 2022, Novikov-Borodin, 2009).

5. Organizational and interlevel closure

A major contemporary strategy is to shift discussion from closure of the physical domain as a whole to closure of organized systems. In “Closure of Self-Determining System Based on Causal and Constitutive Relations,” a self-determining system is one in which causes originating within the system influence the system itself. System boundaries are defined not by causal isolation but by closure of causal-constitutive loops. Causal relations are interventionist; constitutive relations are mereological and non-causal. A genuinely constitutive relation must involve at least two causally independent variables, and this minimal requirement yields two interdependent causal-constitutive loops, implying a dual-process organization. The framework is explicitly compatible with openness to external causes, because inputs may remain outside the loops while internal causes and mechanisms are organizationally closed (Ohmura et al., 19 Jun 2026).

George Ellis develops a related but broader interlevel view. “The Causal Closure of Physics in Real World Contexts” argues that strict causal closure is rarely the right concept for engineering systems and biology. Real systems are spatially open, so what exists in practice is at most Effective Spatial Closure, and that holds only ceteris paribus and can be violated by “Black Swan Events.” More importantly, causal closure in the hierarchy of emergence is “a strictly interlevel affair.” Effective Theories can be defined at each level, but their existence does not imply that any one level is causally complete by itself. Ellis argues that the particle physics level is not causally complete by itself in solid state physics, digital computers, or biology, because these domains involve downward causation, time-dependent constraints, and “Inextricably Intertwined Levels” (Ellis, 2020).

In “Physics, Determinism, and the Brain,” Ellis applies the same theme to neuroscience. He distinguishes synchronic from diachronic emergence and argues that brains are open, learning systems whose effective constraints change through time. On this view, microphysics is universally valid but does not fix brain outcomes “as a matter of principle,” because actual neural and behavioral trajectories depend on biology, higher-level organization, stochasticity, and even social context. The resulting closure is not microphysical isolation but an interlevel network of upward emergence and downward causation extending across biological and social levels (Ellis, 2020).

6. Contemporary reconstructions and open controversies

Recent proposals diverge on whether closure should be rejected, relativized, or rebuilt. Assembly Theory offers a reconstruction within physics rather than against it. It defines an object’s assembly index as the minimum number of recursive joining steps necessary for a distinguishable object to exist and combines that quantity with copy number to provide a metrology of causation and contingency. High assembly index objects appearing in countable copies indicate persistent constructive mechanisms and a “selective threshold” in assembly space. Life, agency, intelligence, and technology are then treated as causal structures above that threshold, with no appeal to non-physical forces; the physical base remains causally sufficient, but causal organization becomes an objective material property (Cronin et al., 2 Jan 2026).

A more revisionary response appears in work on consciousness. “Why Consciousness Should Explain Physical Phenomena: Toward a Testable Theory” argues that the reductionist assumption that micro phenomena are explainable by micro-level laws alone is an assumption of intra-level causal closure. If that assumption is retained, macro phenomena become epiphenomenal. To avoid epiphenomenalism and preserve scientific testability, the paper rejects intra-level causal closure and proposes a dual-laws model in which macro-level psychological laws, implemented through a self-referential feedback control mechanism, influence micro-level neural behavior. The authors accordingly retain causal monism while denying that any single micro level is explanatorily closed under its own laws alone (Ohmura et al., 6 Nov 2025).

The “Causal Stance” framework sharpens the same issue by arguing that, for theories of mind and consciousness, it is necessary to construct a linguistic framework within which physical causal closure does not hold in the Causal Stance while physical determinism remains intact in the Physical Stance. This suggests that the central controversy is no longer simply whether closure is true or false. The deeper issue is which notion of closure is at stake: single-level or interlevel, ontological or epistemic, global or local, non-contextual or explicitly stance-dependent (Ohmura et al., 6 Apr 2026).