Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the Hamilton type 1 principal function, we show that classical action-based dynamics are generally undecidable, paralleling spectral gap undecidability in quantum systems. In near Kolmogorov-Arnold-Moser systems, stability hinges on Diophantine conditions that are themselves undecidable, limiting predictability via arithmetic logic rather than randomness. Phenomena like spin 3/2 systems and larger, quantum scars and Leggett inequality violations support this view, naturally explained by time symmetric classical action. This framework offers a principled resolution to the long standing dichotomy between unitarity and entanglement by deriving both as emergent features of a tractable rendering from a fundamentally non-separable classical variational geometry. Collapse and decoherence arise from representational limits, not ontological indeterminism. We propose an explicit experimental test using lateral double quantum dots to detect predicted deviations from standard quantum coherence at the classical chaos threshold. This reframing suggests the classical quantum boundary is set by computability and not by the Planck constant. Implications for quantum computing and quantum encryption are discussed.
Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the Hamilton type 1 principal function, we show that classical action-based dynamics are generally undecidable, paralleling spectral gap undecidability in quantum systems. In near Kolmogorov-Arnold-Moser systems, stability hinges on Diophantine conditions that are themselves undecidable, limiting predictability via arithmetic logic rather than randomness. Phenomena like spin 3/2 systems and larger, quantum scars and Leggett inequality violations support this view, naturally explained by time symmetric classical action. This framework offers a principled resolution to the long standing dichotomy between unitarity and entanglement by deriving both as emergent features of a tractable rendering from a fundamentally non-separable classical variational geometry. Collapse and decoherence arise from representational limits, not ontological indeterminism. We propose an explicit experimental test using lateral double quantum dots to detect predicted deviations from standard quantum coherence at the classical chaos threshold. This reframing suggests the classical quantum boundary is set by computability and not by the Planck constant. Implications for quantum computing and quantum encryption are discussed.
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 systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle probabilistic predictions of observables. After introducing the geometric theory of Hamilton-Randers spaces and reformulating it using Hilbert space theory, a Hilbert space structure is constructed from the Hilbert space formulation of the underlying Hamilton-Randers model and associated with the space of wave functions of quantum mechanical systems. We can prove the emergence of the Born rule from ergodic considerations. A geometric mechanism for a natural spontaneous collapse of the quantum states based on the concentration of measure phenomena as it appears in metric geometry is discussed.We show the existence of stable vacua states for the quantized matter Hamiltonian. Another consequence of the concentration of measure is the emergence of a weak equivalence principle for one of the dynamics of the fundamental degrees of freedom. We suggest that the reduction of the quantum state is driven by a gravitational type interaction. Such interaction appears only in the dynamical domain when localization of quantum observables happens, it must be a classical interaction. We discuss the double slit experiment in the context of the framework proposed, the interference phenomena associated with a quantum system in an external gravitational potential, a mechanism explaining non-quantum locality and also provide an argument in favour of an emergent interpretation of every macroscopic time parameter. Entanglement is partially described in the context of Hamilton-Randers theory and how naturally Bell's inequalities should be violated.
Quantum mechanics marks a radical departure from the classical understanding of Nature, fostering an inherent randomness which forbids a deterministic description; yet the most fundamental departure arises from something different. As shown by Bell [1] and Kochen-Specker [2], quantum mechanics portrays a picture of the world in which reality loses its objectivity and is in fact created by observation. Quantum mechanics predicts phenomena which cannot be explained by any theory with objective realism, although our everyday experience supports the hypothesis that macroscopic objects, despite being made of quantum particles, exist independently of the act of observation; in this paper we identify this behavior as classical. Here we show that this seemingly obvious classical behavior of the macroscopic world cannot be experimentally tested and belongs to the realm of ontology similar to the dispute on the interpretations of quantum mechanics [3,4]. For small systems such as a single photon [5] or a pair [6], it has been experimentally proven that a classical description cannot be sustained. Recently, there have also been experiments that claim to have demonstrated quantum behavior of relatively large objects such as interference of fullerenes [7], the violation of Leggett-Garg inequality in Josephson junction [8], and interference between two condensed clouds of atoms [9], which suggest that there is no limit to the size of the system on which the quantum-versus-classical question can be tested. These behaviors, however, are not sufficient to refute classical description in the sense of objective reality. Our findings show that once we reach the regime where an Avogadro number of particles is present, the quantum-versus-classical question cannot be answered experimentally.
This work presents a structural interpretation of the reduced Planck constant ℏ within the framework of the Structural Principle of Entanglement (PSE). In this theory, ℏ is not a fundamental physical parameter nor a quantum‑mechanical postulate. Instead, it emerges as the compressed image of a discrete action threshold selected by the regularized emergent structure. The PSE establishes a unidirectional ontological hierarchy: a prespatial structure without geometry, a fundamental reorganization governed by a coherence threshold, an emergent correlation that organizes continuity, a regularization process that filters coherent configurations, and a set of complexity thresholds that preserve discrete structural rigidity. Together, these elements produce a minimum action threshold that is structural rather than physical. Through a compressive and non‑invertible projection, this structural rigidity is formalized in the physical domain as the reduced Planck constant ℏ. As a result, the quantization of action, canonical non‑commutativity, precision limits, and the structure of the quantum state space are not primitive features of nature. They are consequences of the compressive projection and of the discrete rigidity selected in the emergent domain. Quantum physics therefore appears not as a set of fundamental axioms, but as an effective representation of a deeper emergent structure. In this view, ℏ is an ontological property of the PSE hierarchy: the physical signature of a discrete threshold rooted in the prespatial domain. Observable physical reality is a compressed representation of this emergent structure, and ℏ is its most fundamental imprint.
The quantization of action, discrete energy levels, and finite phase-space resolution are among the most fundamental yet conceptually opaque features of quantum physics. In standard theory, the universal constant is introduced empirically, and canonical quantization rules are postulated without deeper ontological justification. In this work we present a first-principles derivation of quantization based on the Structural Unified Field (SUF) framework. By treating physical entities as layered “existence objects” characterized by a boundary parameter and an existence function , we argue that structural identity requires a minimal nonzero layer separation . This structural irreducibility implies a universal minimal distinguishability in all attribute domains, which, when projected into phase space, yields a minimal phase-space cell and thus a universal minimal action unit. Upon mapping to physical units, this structural minimal action corresponds to Planck’s constant . The SUF interpretation thereby promotes quantization from an empirical postulate to a necessary consequence of the ontological geometry of existence. The resulting framework naturally accounts for discrete spectra, uncertainty relations, action quantization, canonical commutation relations, topological quantization phenomena, and the universality of . We discuss broader implications for the foundations of quantum theory, the quantum–gravity interface, and potential avenues for testing structural deviations.
Quantum mechanics is among the most successful physical theories, yet its formulation and empirical testing rely on classical structures. Following Lev Landau and Niels Bohr, this reliance is not merely pragmatic: quantum observables acquire empirical meaning only relative to classical reference frames, and, in practice, quantization starts from classical models. At the same time, the two domains display forms of mutual irreducibility: intrinsically quantum features (that is, spin and exchange statistics) have no counterpart in the phase-space ontology of classical point-particle mechanics, while classical trajectory chaos does not arise straightforwardly from unitary quantum evolution in closed systems. A hierarchy is commonly established between classical and quantum theories, namely, a claim of ontological and explanatory priority according to which quantum mechanics is fundamental and classical mechanics is only a limiting case. This claim is less secure than is often assumed; therefore, the traditional hierarchy deserves to be examined. In this paper, we argue that a quantum–classical framework provides an effective and structurally faithful representation of empirically accessible physical systems in regimes where quantum and classical degrees of freedom coexist within a single, consistent effective dynamical description. To give this point of view a firm theoretical basis, we discuss the quasi-Lie formal structure underlying quantum–classical hybrid dynamics, with applications ranging from gravity and condensed matter to open, driven systems in biology and complex media.