Abstract We propose that quantum mechanics emerges as the effective description of a deterministic physical reality from the perspective of an internal observer that constitutes a subsystem of a finite closed world. Because such an observer cannot access the complete ontological state of the world to which it belongs, its description is intrinsically incomplete. We refer to this fundamental limitation as subjective incompleteness . It naturally induces a factorization of the ontological state space with respect to gauge degrees of freedom that are indistinguishable to the observer. Within the proposed framework, the projective geometry of quantum state space is understood as a direct consequence of subjective incompleteness. This provides a common geometric origin for characteristic quantum phenomena, including nonlocality, contextuality, and intrinsic randomness.
Abstract We propose that quantum mechanics emerges as the effective description of a deterministic physical reality from the perspective of an internal observer that constitutes a subsystem of a finite closed world. Because such an observer cannot access the complete ontological state of the world to which it belongs, its description is intrinsically incomplete. We refer to this fundamental limitation as subjective incompleteness . It naturally induces a factorization of the ontological state space with respect to gauge degrees of freedom that are indistinguishable to the observer. Within the proposed framework, the projective geometry of quantum state space is understood as a direct consequence of subjective incompleteness. This provides a common geometric origin for characteristic quantum phenomena, including nonlocality, contextuality, and intrinsic randomness.
We propose a discrete ontological reconstruction of quantum mechanics based on a graph-theoretic model with deterministic cyclic dynamics. The model is founded on the hypothesis that quantum mechanics is an effective description of reality from the perspective of an internal observer, that is, an observer who is part of the finite system (world) being observed. A central element of the model is the principle of subjective incompleteness: in general, the set of states of the system (ontological states) exceeds the set of observable states and cannot be fully distinguished by the internal observer. This leads to taking the quotient of the set of ontological states with respect to indistinguishability and naturally induces a probabilistic structure in which probabilities are determined by the cardinalities of the corresponding equivalence classes. It is shown that the cyclic structure of the dynamics, combined with this quotient construction, leads to the emergence of complex amplitudes and the Born rule. Thus, the formalism of quantum mechanics arises as an effective description of a quotient-induced deterministic dynamics. It is further shown that the geometry of the edge space of a complete graph realizes a discrete phase space with an action of the Heisenberg–Weyl group, and that in the continuum limit the model leads to the Klein–Gordon equation. Within this approach, the structure of quantum mechanics appears as a representational level of description of the quotient cyclic dynamics.
Quantum mechanics is widely regarded as a fundamental theory of physical reality. In this work, we demonstrate that this status is not supported at the structural level. The quantum formalism is shown to be neither closed nor generative, relying on externally imposed elements such as probabilistic rules and measurement prescriptions. We introduce a closed variational framework based on a quartic functional, from which admissible configurations emerge through explicit variation. The second variation defines a Hessian operator whose spectral structure exhibits intrinsic discreteness and degeneracy, without the introduction of quantization postulates. We prove that apparent probabilistic behavior arises from structural degeneracy and indistinguishability of admissible configurations, rather than from intrinsic indeterminism. The role of wavefunction collapse is replaced by a global deterministic selection functional applied to the set of stationary solutions. Within this framework, quantum states, probabilities, and observables are reinterpreted as effective representations of an underlying deterministic structure. Consequently, quantum mechanics does not constitute a fundamental description of physical reality, but a statistical projection of unresolved structural configurations.
Quantum mechanics is often perceived as conceptually paradoxical because it appears to conflict with deeply rooted intuitions about fixed reality, determinism, and observation. This paper does not propose a new physical theory. Instead, it offers an epistemological reframing of quantum mechanics: not as a direct mathematical unveiling of a fully fixed pre-existing reality, but as a highly precise description of phenomenological structures emerging through observational conditions and interaction. The paper explores: the distinction between mathematical predictive success and ontological completeness, the role of human perception in constructing “fixed reality” intuitions, the phenomenological nature of qualities such as color and temperature, the possibility that some conceptual tensions in quantum mechanics arise from assumptions inherited from macroscopic cognition, and how quantum theory may be interpreted as describing observable structures rather than fixed hidden states. The work intentionally avoids mystical, anti-scientific, or consciousness-centric interpretations of quantum mechanics. It does not deny the existence of reality, nor reject modern physics. Rather, it attempts to clarify what exactly mathematical models are describing when applied to quantum phenomena. This text is positioned as a conceptual and phenomenological reorganization of perspective — a small doorway toward reconsidering how humans frame “reality” itself.
We propose a framework, referred to as the Intrinsic Observability Framework (IOF), in which the probabilistic structure of quantum mechanics arises from an intrinsic decomposition of the Hilbert space into observable and hidden degrees of freedom. The total system is described by a pure state evolving unitarily, while observable states are obtained by restricting the description to the observable sector via a partial trace over the hidden sector. A key assumption of the present approach is that this decomposition is a fundamental and non-contextual feature of the system, rather than a modeling choice or a consequence of environmental interactions. The hidden degrees of freedom introduced here are not interpreted as unmeasured physical variables, but as components that are fundamentally excluded from the space of observable quantities. Within the IOF, mixed states and probabilistic outcomes emerge from incomplete access to the full state, without invoking intrinsic randomness, external environments, or branching worlds. This distinguishes the present formulation from decoherence-based approaches, hidden-variable theories, and many-worlds interpretations. The proposed framework provides an alternative structural perspective on the origin of quantum probabilities while preserving the standard unitary formalism. We discuss its conceptual implications and outline directions for future work.
We propose an interpretation of quantum mechanics in which the wavefunction represents unresolved potential relative to an observer, measurement is deterministic resonance stabilisation, and Born-rule probability quantifies the observer’s incomplete access to the full entropic and phase-geometric state of the observer–system interaction. An observer is defined operationally as any bounded system capable of converting external entropy into internal coherence. On this view,superposition is not a set of co-existing realities but an unresolved field of possible coherence resolutions; collapse is not a stochastic discontinuity but a deterministic phase-lock between observer and system; and the classical world is the high-coherence limit in which environmental observation is dense enough to continuously stabilise macroscopic facts.The interpretation preserves the full predictive machinery of quantum mechanics while providing a unified account of the measurement problem, the Born rule, decoherence, entanglement, delayed choice, Wigner’s friend, and the quantum-to-classical transition. We formalise the framework through a resonance-selection rule, an observer equation of collapse, and a prime-modal state-space structure, and identify five classes of empirically accessible predictions.
The completeness problem in quantum mechanics concerns whether the formalism constitutes a logically closed and ontologically complete description of physical reality. Historically, this led to a persistent tension between operational success and ontological clarity. This note argues that the Nonlocal Unification (NU) framework can provide the necessary conceptual ingredients to resolve this problem. Specifically, we show that if information is taken as a fundamental and conserved quantity, then quantum mechanics may emerge as an operationally complete theory while simultaneously being conceptually incomplete as a base ontology. This reframing might dissolve the classical tension between completeness and hidden-variable extensions by replacing the ontology of states with an informational geometry governed by conservation.