Neo-Bohrian Interpretations of Quantum Mechanics

• Neo-Bohrian interpretations are rigorous models that recast Bohr’s epistemology into dual classical and quantum frameworks to resolve the measurement problem without invoking wave-function collapse.
• They employ operator-algebraic methods, paraconsistent logics, and contextual Boolean frames to formalize the quantum-classical interface and ensure objective outcomes in measurement.
• This framework bridges deep philosophical insights and mathematical precision, guiding experimental practices and inspiring research in non-Boolean probability and quantum kinematics.

Neo-Bohrian interpretations of quantum mechanics constitute a rigorously analytic, context-sensitive recasting of Bohr’s epistemologically grounded stance, systematising foundational quantum concepts to resolve the measurement problem, clarify complementarity, and articulate the ontological and logical architecture of quantum phenomena in the post-classical era. These frameworks reject representational wave-function realism and evade instrumentalist ambiguities by emphasizing a dual ontology of systems and contexts, formalizing why classical concepts and non-Boolean event structures are indispensable for the articulation of empirical claims. Neo-Bohrian views are now delineated by new postulates, operator-algebraic methods, paraconsistent logics, and a spectrum of realist and agent-centered positions that systematize the quantum-classical divide within a contemporary epistemological framework.

1. Foundational Neo-Bohrian Postulates and Formal Structure

Neo-Bohrian interpretations ground quantum theory on two analytic postulates (V, 2023):

• Postulate A (Complementary Modes of Description): Quantum systems admit two mutually exclusive modes of description—symbolic (the wave function $|\psi\rangle$ for probabilistic predictions) and representative (the record of classical outcomes upon measurement). Formally, Schrödinger evolution,

$$i\hbar\frac{\partial}{\partial t}|\psi(t)\rangle = H|\psi(t)\rangle,$$

is symbolic, predicting outcome probabilities via Born’s rule,

$P(a_k) = \langle\psi|P_k|\psi\rangle$

for spectral projectors $P_k$ of observable $A$. Upon measurement, the only valid description is the definite outcome and its classical record; $|\psi\rangle$ is suspended until subsequent noninteracting unitary evolution.

• Postulate B (Apparatus as Epistemic Condition): The apparatus constitutes the epistemic condition of access—it enables assignment of quantum properties but is not itself part of the corresponding quantum description. It must be excluded from the frame in which it functions, analogous to the impossibility of observing one’s own sensorium.

This architecture rigorously segregates the symbolic probability calculus from representative empirical outcomes (V, 2023), dissolving the measurement problem without appeal to dynamical collapse or ad hoc boundaries (Heisenberg cut).

2. Measurement Problem, Contextual Realism, and Classicality

The Neo-Bohrian programme explicitly counters the traditional von Neumann–Dirac two-process account by remapping the quantum-classical interface onto the interplay of contextually defined Boolean frames and noncommutative quantum event structures (V, 2023, Bub, 20 Dec 2025, Grangier, 28 Dec 2025).

• Collapse and Definite Outcomes: No stochastic collapse occurs; descriptive tension is resolved by toggling between exclusive symbolic and representative layers. Classical measurement contexts induce the emergence of Boolean subalgebras within the global non-Boolean quantum event lattice (Bub, 20 Dec 2025).
• Classical Contexts as Co-Primary: Quantum systems always appear within classical contexts: realism becomes contextual objectivity, where quantum states and probabilities have objective status only relative to the defined apparatus or record (Grangier, 28 Dec 2025). Infinite tensor-product constructions model macroscopic apparatuses as classical by sectorizing the Hilbert space into non-interfering Boolean sectors (superselection rules), ensuring effective classicality in the $N \to \infty$ limit.
• Contextual Probability Assignment: Assignment of measurement outcomes requires specification of a Boolean frame—maximal commuting set of projectors. Probabilities are context-dependent and computed via the Born rule. There is no global classical phase space but a patchwork of overlapping Boolean frames, each underwriting unique empirical descriptions (Cuffaro, 2023).

3. Logical and Epistemological Foundations: Complementarity, Paraconsistency, Intuitionism

Neo-Bohrian logic refines complementarity and contextuality through paraconsistent and intuitionistic frameworks, repositioning quantum theory’s logical foundation (Ronde, 2014, Hermens, 2010):

• Epistemological Paraconsistency: The clash between “wave” and “particle” is epistemic, encoded by complementary but incompatible classical descriptions—paraconsistent logics accommodate mutually exclusive viewpoints without trivializing the theory. Each context is non-trivial and definable in its measurement regime.
• Ontological Paraconsistency: Superpositions $$|\psi\rangle = \alpha|{\uparrow}_x\rangle + \beta|{\downarrow}_x\rangle$$ represent ontological contradictions in an indeterminate potentiality. Paraconsistent logic $L$ allows both $P$ (“spin-up”) and $\neg P$ (“spin-down”) before actualization, dissolving classical constraints on mutually exclusive actualities.
• Intuitionistic Contextuality: Adopting an intuitionistic logic structure (Heyting algebra), the law of excluded middle holds only within a context (maximal Abelian subalgebra), not globally. Propositions about non-commuting observables are undecided outside context, revealing why classical distributivity and global truth assignments fail in quantum theory (Hermens, 2010).

4. Ontology, Completeness, and Methodological Realism

Neo-Bohrian interpretations are grounded in methodological, not metaphysical, realism (Cuffaro, 1 Dec 2025):

• Dual Senses of Completeness:
  • Metaphysical: Theory exhaustively describes physical reality; hidden variables or universal wave-function realism.
  • Methodological: Theory provides resources for describing any probabilistic phenomenon to arbitrary precision, given contexts and the quantum formalism; completeness is certified by Gleason’s theorem, establishing the sufficiency of the Born rule for all probability assignments on Boolean subalgebras.
• Natural Generalization: Quantum theory generalizes classical probability by relaxing commutativity of observables, structuring empirical content around overlapping contexts, and encoding nonclassical correlation constraints (elliptope inequalities) impossible in classical models.
• Non-Boolean Ontology: The system-apparatus partition and the status of quantum events are fundamentally tied to context. Objective probability assignments arise from Hilbert-space geometry, not ignorance, and the global non-Boolean event lattice is primary—hidden-variable assignments or single global truth maps are ruled out (Kochen-Specker theorem).

5. Measurement, Single-World Objectivity, and Interpretational Landscape

Neo-Bohrianism secures single-world objectivity and factuality within the contextually sanctioned Boolean frame, avoiding branching worlds or pure subjectivism (Bub, 2018, Bub, 2017):

• Contextual Actualization: Only the chosen Boolean frame actualizes a single outcome; quantum probabilities are normative for the context, not assignments over “hidden” ontic realities. Collapse is a conditionalization onto the measured Boolean subalgebra, not a physical discontinuity.
• Interpretational Distinctions:
  • Many-Worlds: Drops single-world assumption; all outcomes realized via branching.
  • QBism: Quantum probabilities are subjective degrees of belief; experiences and outcomes are personal to the agent, with the Born rule as a coherence constraint (Fuchs, 2017, Fuchs et al., 2013, Mohrhoff, 2019).
  • Neo-Bohrian: Objective, context-dependent probabilities; empirical objectivity and single-world definiteness anchored in contextually defined Boolean frames (Bub, 2017, V, 2023).
• Sectorization and Stability: Operator-algebraic sectorization provides classicality via exponential suppression of interference terms for large $N$; superselection sectors label stable macrostates, supporting classical records without modifying quantum dynamics (Grangier, 28 Dec 2025, Bub, 20 Dec 2025).

6. Extensions, Critiques, and Foundations

Neo-Bohrian frameworks open new avenues in operator-algebraic quantum foundations, the formalization of context, and the reconciliation of quantum and classical regimes:

Methodology	Quantum–Classical Interface	Role of Probability
Infinite tensor-product	Boolean sectors/domain of pointer	Sui generis, non-representational
Contextual objectivity	Boolean frame per measurement	Objective, but context-relative
Paraconsistent logic	Potentiality, contradictory properties	Real properties prior to measurement
Intuitionistic logic	Context-dependent Boolean subalgebra	Law of excluded middle local

Conceptual critiques, notably by Bub, challenge the physical legitimacy of infinite idealizations but are countered by CSM approaches that regard infinities as formal tools mirroring thermodynamic/statistical limits and modeling classical contexts as methodological presuppositions (Grangier, 28 Dec 2025). Neo-Bohrian interpretations thus provide a rigorous technically precise and conceptually robust ontology for quantum foundations, setting them apart from the Everettian, Bohmian, and subjective Bayesian landscape.

7. Philosophical Consequences and Research Directions

Neo-Bohrianism reconfigures quantum foundations by translating Bohr’s pragmatised-Kantian epistemology into analytic methodology:

• Epistemic Primacy of Classical Concepts: Classical language and Boolean frames are necessary for empirical communication (“all evidence must be expressed in classical terms”), ensuring intersubjectivity of outcome records (V, 2023, Cuffaro, 1 Dec 2025).
• Methodological Modesty: The focus shifts from metaphysical ambition (reconstructing reality) to methodological sufficiency—quantum theory as a non-failible toolkit for organizing experience, rather than a literal mirror of the microphysical order (Cuffaro, 1 Dec 2025).
• Experimental Practice and Contextuality: Emphasis on context and classical concepts steers foundational research from hidden-variable pursuits towards the structure of quantum information and the operational impact of non-commutative geometry.
• Non-Boolean Probability and Quantum Kinematics: Quantum probabilities are not ignorance measures but kinematic features, enforced by the geometry of Hilbert space and the contextuality of measurement frames (Bub, 20 Dec 2025).

Neo-Bohrian interpretations thus offer a self-consistent, technically rigorous framework that honors Bohr’s original insights while systematizing them within the analytic, formal, and operational paradigms of contemporary quantum theory (V, 2023, Bub, 20 Dec 2025, Grangier, 28 Dec 2025, Cuffaro, 1 Dec 2025, Bub, 2018).