This work develops a theoretical framework in which the Planck constant ℏ is promoted from a fixed universal constant to a dynamical field ℏ(x), defining a continuum of quantum regimes. The quantum state space is extended into a bundle of Hilbert spaces labeled by distinct ℏ values, allowing quantum systems to evolve not only in spacetime but also along an additional ℏ-dimension. Within this framework, discrete quantum transitions emerge as projections of smooth trajectories in the extended (x, ℏ) space, while coherence and entanglement acquire a geometric interpretation. The theory introduces scalar excitations of the ℏ-field, termed hbarons, and predicts observable signatures in interferometry, atomic spectroscopy, quantum optics, and cosmology. Standard quantum mechanics is recovered in the limit ∂μℏ → 0. The model offers a unified geometric perspective on quantization, coherence, and entanglement, and provides concrete experimental pathways for testing variability of the Planck constant.
This work develops a theoretical framework in which the Planck constant ℏ is promoted from a fixed universal constant to a dynamical field ℏ(x), defining a continuum of quantum regimes. The quantum state space is extended into a bundle of Hilbert spaces labeled by distinct ℏ values, allowing quantum systems to evolve not only in spacetime but also along an additional ℏ-dimension. Within this framework, discrete quantum transitions emerge as projections of smooth trajectories in the extended (x, ℏ) space, while coherence and entanglement acquire a geometric interpretation. The theory introduces scalar excitations of the ℏ-field, termed hbarons, and predicts observable signatures in interferometry, atomic spectroscopy, quantum optics, and cosmology. Standard quantum mechanics is recovered in the limit ∂μℏ → 0. The model offers a unified geometric perspective on quantization, coherence, and entanglement, and provides concrete experimental pathways for testing variability of the Planck constant.
Abstract Modern physics has achieved extraordinary predictive success through continuous mathematical formulations. However, the underlying nature of space, time, and physical processes remains conceptually open. This work presents a conceptual framework in which physical reality is interpreted as a discrete phase-supported structure. Space is considered as a lattice of elementary units separated at approximately the Planck scale, while time emerges through successive phase-closure events. Within this picture, energy transport, quantum coherence, and observable events are not continuous processes but arise from structured phase propagation. A triadic propagation mechanism naturally generates hexagonal connectivity, while phase closure defines the emergence of physical events. Rather than proposing new physical laws, this work suggests a broader interpretational perspective, encouraging reconsideration of continuity-based assumptions and inviting exploration of phase-based descriptions of physical reality. Author’s Perspective : I would like to submit the attached manuscript entitled: “Quantum Phase, Discrete Space, and the Limits of Continuity: A Conceptual Framework Toward a Phase-Based Interpretation of Physical Reality” for consideration as a conceptual or perspective article in your journal. The work presents a unified interpretational framework in which physical processes are described in terms of discrete phase propagation and phase closure. Rather than introducing new physical laws, the manuscript offers a geometrical and phase-based perspective that aims
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.
This paper develops a theoretical framework that seeks to unify the foundational principles of quantum mechanics, general relativity, and thermodynamics by extending spatial geometry to include a compactified fourth spatial dimension. The central proposal is that many counterintuitive features of quantum systems—such as wave function collapse, superposition, entanglement, tunneling, and decoherence—emerge as phenomena from the projection of four-dimensional quantum states into observable three-dimensional space. Within this formulation, apparent quantum randomness is reinterpreted as a consequence of observing only a lower-dimensional slice of a higher-dimensional structure. A key innovation of the framework is the introduction of a scalar degree of freedom, termed the entropion field, which governs decoherence and encodes the thermodynamic arrow of time. The entropion field couples directly to both quantum fields and spacetime curvature, leading to modified Einstein field equations and an entropic extension of quantum field dynamics. This mechanism provides a consistent account of classicality emerging from quantum substrates, links entropy growth to projection dynamics, and clarifies how spacetime geometry constrains quantum evolution. The theory is presented through a structured progression of conceptual foundations, mathematical formalism, physical interpretation, and predictive consequences. Particular emphasis is placed on testable deviations from standard theories, including altered interference signatures in 4D-projected systems, entropion-modulated decoherence rates, and revised mechanisms of tunneling and entanglement. Broader implications are explored for quantum information theory, cosmology, condensed matter, and computational theory. Collectively, these results establish a geometrically grounded unification scheme that integrates the three major pillars of modern physics into a consistent and falsifiable framework.
Abstract In this work, we investigate the emergence of quantum structures within a purely geometric field framework based on a unified helical configuration. Building on the geometric foundations and limiting recovery principles established in the preceding papers of this series, we demonstrate that quantization arises as a consequence of topological and spectral constraints imposed on the underlying helical field, rather than being introduced as a fundamental postulate. We show that discrete spectral sectors naturally follow from global and local topological conditions on the field configuration space, leading to an intrinsic form of quantization without invoking canonical commutation relations or operator axioms. Effective quantum operators are constructed directly from geometric functionals of the helical field, yielding non-commutative structures as emergent features of constrained geometry. Within this setting, Planck’s constant appears as an effective parameter characterizing the spectral density of admissible configurations, rather than as a fundamental universal constant. The framework consistently recovers standard quantum kinematics in appropriate limiting regimes while remaining fully compatible with the classical and relativistic limits previously derived. This approach provides a coherent geometric interpretation of quantum discreteness, operator structure, and effective constants, thereby offering a unified perspective in which classical, relativistic, and quantum descriptions arise from a single geometric field without assuming independent foundational layers.
Quantum mechanics and quantum field theory (QM/QFT) offer precise mathematical tools for describing microscopic systems, but remain ambiguous with regard to the precise nature of collapse, measurement, and causal structure. This work introduces a structural reinterpretation of quantum evolution grounded in a conserved, Lorentz-compatible coherence substrate. Within this framework, wavefunctions are understood as phase-supported structures that evolve over finite causal intervals bounded by collapse events. We propose that Planck’s constant encodes structural thresholds of the substrate’s capacity to support coherent evolution. These limits define a minimum spatial and temporal envelope—referred to as the coherence tick—during which standard QM/QFT behavior is valid. Collapse is not introduced as a measurement postulate, but emerges as a necessary structural re-lock at the end of each coherence interval. The Collapse Boundary is thus a physically meaningful event horizon, and if energy or configuration offload is required, a Quantum Emission Opportunity (QEO) occurs. This framework preserves all predictive results of QM/QFT while offering a physically causal explanation for collapse timing, wavefunction termination, and entanglement. It resolves the quantum time asymmetry paradox by distinguishing between internal evolution (experienced in +t) and external observation (reconstructed in −t). By reinterpreting Planck constants as causal boundary conditions rather than universal abstractions, this model provides a substrate-based foundation beneath conventional quantum dynamics—one in which measurement, correlation, and irreversibility arise from finite structural support, not observer-induced discontinuity.
The Theory of Temporal Relativity proposes a unified theoretical framework that extends Special and General Relativity into the complex domain, integrating aspects of Quantum Mechanics within a single geometrical structure. The theory introduces a generalized Hilbert-space geometry and interprets quantum states as observer-dependent, arising from complex temporal relations between reference frames. Theory of Temporal Relativity is a theoretical framework proposing a unified extension of Special and General Relativity into the complex domain, with the goal of incorporating aspects of Quantum Mechanics within a consistent geometrical model. The theory generalizes Hilbert-space geometry and relativistic invariance to complex coordinates, introducing observer-dependent descriptions of physical quantities and a reinterpretation of quantum states as complex-phase relations between reference frames. Within this model, fundamental constants such as c, G, and h are not strictly universal but can exhibit apparent local variations arising from the observer’s position in the complex spacetime manifold. These variations preserve global covariance and CPT symmetry while reconciling quantum non-locality with relativistic kinematics. The framework predicts experimentally testable effects, including measurable phase shifts in interferometric experiments, possible frequency modulations in non-inertial systems, and small local deviations of physical constants detectable in condensed-matter and gravitational contexts. The supplementary work, “Quantum Uncertainty, Planck’s Constant, and Ontological Insights from Complex Spacetime Geometry and Local Metric Deformations”, develops the principle of Temporal Relativity as a foundational element of the theory. It formalizes the connection between quantum uncertainty, metric deformations, and complex temporal structures, within an alternative logical framework (AU). This extension provides both an ontological interpretation of the wavefunction and a basis for the emergence of quantum indeterminacy from geometric causes. Together, these works present a coherent attempt to unify the relativistic and quantum domains under a single complex-geometric view of spacetime, maintaining mathematical rigor while providing clear experimental pathways for empirical validation.