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
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
Quantum Phase and Discrete Space A Channel-Based Interpretation of Time, Action, and Transport H. Bilgin Ergun, MSc.January 2026 — Bolu / TürkiyeORCID: 0009-0009-4733-4730 Abstract This book presents a unified conceptual framework for interpreting quantum and classical phenomena through discrete space, phase evolution, and channel formation. Rather than introducing new physical laws, it offers a geometrical and phase-based interpretation explaining why established principles such as least action, tunneling, interference, and lossless transport arise so robustly.Space is treated as a discrete phase-supporting structure in which physically meaningful events require completion of coherent phase cycles. Time is not assumed as a continuously flowing parameter, but emerges only after phase closure. Within this framework, transport phenomena are understood as phase-mediated channels rather than energetic violation or predefined trajectories.The approach provides a coherent interpretation of path integrals, tunneling, superconductivity, symmetry relaxation, and observer-induced decoherence, unifying them within a single phase-organized picture compatible with standard quantum formalism. Preface This book does not seek to replace established physical laws. Its purpose is to provide a geometrical and phase-based intuition explaining why those laws operate with such robustness across quantum and classical domains.The ideas presented here have been developed gradually through peer-reviewed articles and DOI-registered preprints. They are brought together in this volume to form a unified narrative accessible to physicists, engineers, and conceptually inclined readers interested in the foundations of physical theory.Author’s prior related work includes: A Phase-Coherence Interpretation of the Jahn–Teller Effect in Discrete Triadic Lattices, Zenodo (H. Bilgin Ergun), Record No: 18289641, Version 1, January 2026. Section 1 — Conceptual Interlude: Time Without Observation In phase-based descriptions, temporal ordering does not precede physical evolution; it emerges only after phase completion. Within a closed system evolving through discrete phase steps, intermediate configurations do not correspond to distinct moments in time but represent pre-temporal phase progressions.If an observer were present at every internal phase step, only the realized outcome would ever be accessible. Section 2 — Phase Selection and the Emergence of Least Action In the path–integral formulation introduced by Feynman, a system formally explores all conceivable trajectories between two configurations. Each path contributes with a phase factor determined by its action. Section 3 — Channel vs Channel-Free Propagation Energy may exist without direction, but direction does not arise without phase coherence. Section 4 — Phase-Guided Tunneling Quantum tunneling represents transport in which energetic transmission is suppressed while phase continuity persists. Section 5 — Collective Phase Locking and Lossless Transport Superconductivity represents the collective limit of phase-guided transport. Closure Note — Observation and Channel Disruption Observation disrupts phase continuity, collapsing channel multiplicity into a single route.
This work introduces the Phase–Lattice Atomic Model, a fundamentally geometric and dynamical reinterpretation of atomic structure. Instead of a point-like nucleus and probabilistic orbital clouds, the model proposes that mass–energy is distributed over a spherical surface through discrete, phase-coherent micro-spheres arranged along quantized spiral pathways. Each micro-sphere carries a triple-phase structure separated by 120°, and the requirement of global phase compatibility over successive Planck-scale steps enforces a natural “phase-selection rule” for propagation. This phase-coherent dynamics generates a quantized surface lattice composed of finite spiral windings, with the total number of phase-carrying nodes bounded by the experimentally observed proton–electron mass ratio (≈1836). The interaction between phase delay accumulation and phase-compatibility constraints produces amplitude envelope modulation, giving rise to a natural mechanism for electronic fine-structure splitting—without invoking continuous orbital wavefunctions. The framework provides:• a geometric foundation for spin, exclusion, and handedness;• a discrete mechanism for fine-structure variation;• a surface-dynamical alternative to point-charge quantum orbitals;• a unifying interpretation of classical and quantum behavior based on minimal phase disturbance and least-action pathways. This preprint consolidates the theoretical structure, graphical representations, derivations, and physical implications of the Phase–Lattice model and is intended to make the framework publicly accessible while formal journal submission is in progress.
This paper introduces a novel theoretical framework that bridges discrete and continuous descriptions in physics through a unified probabilistic approach. At its core, the framework demonstrates how continuous forms naturally emerge from discrete entities via probability distributions, providing fresh insights into phenomena ranging from classical mechanical systems to quantum mechanics. The work develops a rigorous mathematical formalism that includes a geometric interpretation through Riemannian metrics and extends naturally to relativistic systems.What sets this approach apart is its ability to describe transitions between discrete and continuous regimes using a single mathematical structure, while maintaining compatibility with both classical and quantum mechanical descriptions. The framework introduces a continuity probability function that characterizes systems across all scales, offering new perspectives on wave-particle duality and the emergence of continuous forms in nature. By providing a unified mathematical language for describing such phenomena, this work opens up new possibilities for understanding the relationship between discrete and continuous aspects of physical reality.
Abstract This work presents a unified geometric framework for quantum reality through four interconnected papers. It proposes that the coherent, non-separable correlations described by Hilbert space originate from an unobservable Energy Space, a fundamental substrate beyond spacetime that preserves perfect coherence and all conservation laws, thereby providing a geometric interpretation of quantum entanglement. Within this framework, the relation E = hf is interpreted as an encoding relation rather than a statement of physical energy actualization. During measurement, structural branching may occur, but Energy Space ensures that only one geometrically valid branch undergoes physical localization. Spacetime emerges from Energy Space as a passive geometric medium with intrinsic dynamic capabilities, giving rise to quantum objects and their interactions. Quantum objects are interpreted as dynamic geometric patterns of spacetime possessing an encoded geometric identity. Their physical properties, including mass, charge, spin, momentum, energy, wavelength, and phase, are fundamentally encoded in Energy Space and become physically actualized according to the interaction context and the degree of coherence or decoherence. The stability, transformation, and propagation of quantum objects are determined by their geometric compatibility with spacetime and with other quantum geometries. Electromagnetic, weak, and strong interactions are interpreted as direct interactions between compatible quantum-object geometries, whereas gravity is regarded as an indirect geometric interaction mediated through spacetime geometry. Geometric interactions may produce superposition, transformation into new quantum-object geometries, or the formation of larger composite geometric structures, providing a unified geometric interpretation of interactions, confinement, and composite systems. Within this geometric framework, a recursive geometric scaling parameter satisfying the invariant relation is proposed. Based on this hierarchy, phenomenological recursive scaling relations are developed for the lepton and quark families, suggesting a possible underlying geometric structure governing fermion masses, generational hierarchy, and relative stability. Finally, the Peak-Coupling Theory proposes that quantum localization and decoherence occur through discrete peak-coupling events between interacting quantum geometries at oscillatory extrema within a quantum wave packet. The wave envelope and phase continuously modulate the distribution of possible coupling events, while observable interaction probabilities may emerge from the squared magnitude of local coupling amplitudes, providing a possible geometric route toward the emergence of Born-rule probabilities Together, these four papers present a unified conceptual framework in which Energy Space, spacetime, quantum objects, physical interactions, particle hierarchies, quantum measurement, and localization are interpreted as interconnected manifestations of an underlying geometric reality. These ideas are developed across four papers: Paper 1: Energy Space and Geometric Nature of Quantum Objects and SpacetimePaper 2: Quantum GeometryPaper 3: Lepton and Quark Generational Phenomenological Patterns; and Paper 4: Peak-Coupling Theory of Quantum Interaction
This work proposes a structural theory of wave dynamics in which quantum, statistical, and cosmological phenomena emerge from a single underlying principle: whether a wave process achieves phase closure or remains phase-open. Within a discrete conservative framework, wave evolution is shown to admit two qualitatively distinct regimes. Phase-closed processes generate stationary normal modes and localized particle-like states, whereas phase-open processes produce dispersive envelope dynamics and persistent background fluctuations. In this framework, Schrödinger-type evolution is not postulated as a fundamental law but arises universally as the effective continuum description of structurally incomplete (phase-open) wave processes. A central result of this paper is that Heisenberg-type uncertainty relations emerge as a structural consequence of phase openness rather than measurement postulates or operator non-commutativity. Persistent background fluctuations, including vacuum noise and cosmological background phenomena, are likewise interpreted as unavoidable residuals of incomplete phase closure in conservative wave systems. The theory further introduces a probabilistic structural law governing phase closure, predicting that particle-like states are rare events in a dominantly phase-open universe. This leads to falsifiable scaling relations connecting microscopic phase dynamics to macroscopic cosmological matter fractions. The framework is integrated with the JS–SH discrete geometry and the SRCD ratio coordinate, providing a unified structural interpretation of quantum mechanics, particle formation, and cosmic background structure. Unlike conventional approaches, this work does not modify quantum mechanics by additional axioms or stochastic assumptions. Instead, it derives quantum and cosmological phenomena from structural properties of discrete wave dynamics, offering a unified conceptual and mathematical foundation linking Schrödinger evolution, uncertainty, and cosmic background fluctuations.
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.