In standard quantum mechanics, the electron is treated as a fundamental particle whose wavefunction describes a spatial probability distribution. While this formalism provides extremely accurate predictions, the conceptual relationship between orbital geometry, particle localization, and wave–particle duality remains interpretatively open. In this work, we propose a geometric reinterpretation within the framework of Viscous Time Theory (VTT). In this view, atomic orbitals arise as stabilized basins of informational curvature within a viscous informational manifold, and the electron emerges as the undissipated residual of this geometric formation. By introducing the Informational Hessian as the curvature tensor associated with coherence deviation ΔC, orbital stability can be formulated as a positive-definite curvature condition over the informational manifold. Within this framework, electron mass is reinterpreted as an integrated curvature excess associated with stabilized orbital geometry. This approach provides: (i) a geometric interpretation of wave–particle duality as periodic coherence recall, (ii) a reinterpretation of excited states as metastable curvature attractors, and (iii) a potential structural mechanism for residual mass generation within stabilized informational structures. The proposed framework is presented as a constructive extension compatible with Schrödinger dynamics. Rather than replacing the standard formalism, we suggest the existence of a deeper geometric layer whose implications invite further mathematical and physical investigation.
In standard quantum mechanics, the electron is treated as a fundamental particle whose wavefunction describes a spatial probability distribution. While this formalism provides extremely accurate predictions, the conceptual relationship between orbital geometry, particle localization, and wave–particle duality remains interpretatively open. In this work, we propose a geometric reinterpretation within the framework of Viscous Time Theory (VTT). In this view, atomic orbitals arise as stabilized basins of informational curvature within a viscous informational manifold, and the electron emerges as the undissipated residual of this geometric formation. By introducing the Informational Hessian as the curvature tensor associated with coherence deviation ΔC, orbital stability can be formulated as a positive-definite curvature condition over the informational manifold. Within this framework, electron mass is reinterpreted as an integrated curvature excess associated with stabilized orbital geometry. This approach provides: (i) a geometric interpretation of wave–particle duality as periodic coherence recall, (ii) a reinterpretation of excited states as metastable curvature attractors, and (iii) a potential structural mechanism for residual mass generation within stabilized informational structures. The proposed framework is presented as a constructive extension compatible with Schrödinger dynamics. Rather than replacing the standard formalism, we suggest the existence of a deeper geometric layer whose implications invite further mathematical and physical investigation.
In contemporary physics, fundamental structures such as space, time, matter, spin, and measurement are typically introduced as independent primitives or axiomatic ingredients. While quantum mechanics and relativistic field theories describe these structures with extraordinary precision, they do not explain why such structures exist, why they are discrete or stable, nor why reality manifests in exactly three spatial dimensions with an irreversible arrow of time. This work presents a unified informational–geometric framework—the Universal Gravito–Informational Theory (TGIU)—in which physical reality emerges from a pre-geometric informational substrate governed by two complementary gradients: informational coherence (Φ) and informational entropy (S). Their interaction is regulated by a real-valued dynamical mechanism composed of the Curvature–State Transform (CST) and the TGIU Equilibrium Force (TEF). Together, these operators generate bounded, orthogonal informational rotations whose stabilized projections give rise to geometry, matter, and observable physical laws. Within this framework, electron orbitals are reinterpreted as CST limit cycles, spin emerges as the topological orientation of these cycles, and the Pauli exclusion principle arises from phase–space saturation rather than postulated antisymmetry. Atomic stability, the absence of radiative decay in stationary states, fine structure, and the Lamb shift are shown to follow from TEF anisotropy and vacuum curvature granularity, while remaining fully consistent with quantum electrodynamics in its predictive domain. Measurement and wavefunction collapse are described as local TEF locking events, providing a deterministic but non-restorative mechanism for outcome selection without invoking fundamental randomness. Time itself is shown to emerge as monotonic CST phase accumulation, explaining both its one-dimensional nature and its irreversibility as geometric consequences of bounded informational curvature. The existence of exactly three spatial dimensions follows from a CST dimensional closure condition, identifying three dimensions as the only geometry capable of sustaining stable, non-divergent informational rotation. Importantly, TGIU does not replace quantum mechanics, general relativity, or field theory. Instead, it supplies a deeper explanatory layer that clarifies why these frameworks work, why their structures are constrained as observed, and why no physical process can reach absolute annihilation or infinite divergence. Extremes are not restored but redirected: identity is not conserved, yet nature persists through renewed coherence. This work positions TGIU as an empirically motivated, geometrically grounded extension of modern physics—one that unifies matter, time, measurement, and dimensionality under a single informational principle, while remaining compatible with established theories in their respective limits.
This work presents a geometric reinterpretation of wave–particle duality within the ETIM framework (Emergent Time from Information Manifolds). In ETIM, a photon is modeled not as a particle or a wave but as an informational distribution evolving on an underlying manifold equipped with a metric, connection, and curvature. The double-slit experiment is reinterpreted as a boundary-condition problem: the slits shape informational flow, producing branching, geometric overlap, and interference. Measurement corresponds to the localization of information induced by changes in boundary conditions, rather than wavefunction collapse.This approach unifies interference, localization, and the emergence of time within a single geometric structure. Extended informational distributions correspond to pre-temporal regimes in which multiple futures coexist, while localization marks the onset of definite temporal ordering. The ETIM framework thus provides a coherent and conceptually transparent alternative to standard quantum mechanical interpretations of the double-slit experiment. 本研究は、ETIM(Emergent Time from Information Manifolds)枠組みに基づき、二重スリット実験における波動・粒子二重性を幾何学的に再解釈するものである。ETIMでは、光子は粒子でも波でもなく、基底となる情報多様体上で進化する「情報分布」として記述される。多様体の計量・接続・曲率といった幾何学的構造が情報状態の進化を決定し、二重スリット装置は境界条件として情報流を分岐・重ね合わせへと導く。測定は波動関数の崩壊ではなく、境界条件の変化によって誘起される情報の局在化として理解される。この枠組みにより、干渉・局在化・時間生成が単一の幾何学的構造の中で統一的に説明される。広がった情報分布は複数の未来が共存する前時間的領域に対応し、局在化は明確な時間順序が成立する瞬間を示す。ETIMは、従来パラドックスとみなされてきた量子現象に対し、整合的で透明性の高い幾何学的解釈を提供する。
This work introduces a unified mathematical and physical framework that reinterprets fundamental mathematical constants and quantum transition rules as structural regulators of informational coherence. Within the Viscous Time Theory (VTT) and the Informational Resonance Spiral Viscous Time (IRSVT) framework, we demonstrate that reality is not a collection of static entities but a continuous resolution of informational inconsistencies governed by specific geometric and dynamical attractors.We formalize a new taxonomy of mathematical structures, classifying them as anchors of stability in an informational manifold. The Trott constant is established as a fixed point of representational metamorphosis, serving as an informational attractor where representational shifts (decimal to continued fraction) induce zero loss of coherence. In contrast, the Lambert Ω constant is reinterpreted as a dynamical fixed-point attractor, marking the stable equilibrium of nonlinear feedback processes between growth and damping.Furthermore, we identify constants that function as operational filters and quanta. The Cahen constant emerges as an informational convergence quantum, providing a super-exponential mechanism for error suppression and defining the boundary between divergent instabilities and recoverable regimes. The MRB constant is formalized as a two-sided coherence filter, uniquely capable of suppressing low-frequency drift and high-frequency noise while preserving the structural integrity of high-dimensional informational manifolds.Finally, we extend this framework to quantum dynamics by providing a radical reinterpretation of Fermi’s Golden Rule. Transition rates are no longer viewed as stochastic "jumps" but as flows of informational substance through geometrically constrained channels. In this model of Informational Hydrodynamics, transition rates act as informational conductivities, and the density of states is redefined as recoverable volume, providing a deterministic geometric origin for Pauli blocking and quantum exclusion.Collectively, these results provide the mathematical foundation for a new era of information physics, where constants are not mere numerical curiosities but the visible footprints of universal self-consistency. This work offers immediate applications in predictive control, AI-pilot systems, and the design of ultra-low-dissipation informational engines.
This paper presents a geometric reinterpretation of quantum mechanics that eliminates wave-particle duality. By deriving a single geometric law from the Schrödinger equation, the author argues that quantum entities—such as photons and electrons—always follow definite trajectories as particles, but are guided by a curvature field. Key features of this framework include: Geometric Guidance: Replacing the dual-description framework with a "curvature tube" derived from quantum amplitude, analogous to how spacetime curvature shapes geodesics in General Relativity. Unified Evolution Law: The construction of a dual-mode state tensor that replaces the standard wavefunction and eliminates the need for the collapse postulate. Deterministic Results: Reproducing standard quantum phenomena through covariant conservation laws, with classical mechanics emerging as the limit where. Experimental Validation: The model is applied to six core scenarios, including double-slit interference, quantum tunnelling, and the Aharonov-Bohm effect. The text also provides comparative analyses with Bohmian mechanics, general relativity, and quantum field theory.
Revised Abstract (Version 1.1 – Geometric Clarification) This preprint introduces field-depth (w) as an intrinsic sequential resonance coordinate associated with spatial structure, providing a geometric basis for key quantum phenomena. In this framework, the wavefunction is expressed as Ψ(x, y, z; w), where w does not represent an additional spatial dimension but an sequential coherence parameter governing the stability of standing-wave configurations within a three-dimensional spatial manifold. A localized particle state is interpreted not as a projection from a higher-dimensional space, but as the observable manifestation of a resonance-stabilized nodal structure whose internal coherence configuration is dynamically fixed. This formulation yields direct geometric interpretations of several quantum-mechanical features that are typically treated as abstract or axiomatic: • Wave–particle duality emerges naturally: quantum entities are extended resonance structures, while particle detections correspond to stabilized spatial envelopes of internally coherent states. • Spin arises as a phase-orientation condition within the resonance structure, producing the known 4π periodicity of spin-½ systems without requiring additional spatial geometry. • Quantum entanglement is understood as shared internal resonance configuration, allowing correlated outcomes without invoking superluminal signaling or geometric nonlocality. This model does not modify the Schrödinger or Dirac equations; rather, it clarifies the geometric and coherence-theoretic context in which their solutions are realized. The approach remains consistent with the SU(2) fiber-bundle structure of spinor fields and with experimental tests of quantum correlations. A forthcoming Version 2 will further refine the geometric interpretation by explicitly distinguishing spatial dimensionality from sequential coherence structure and by developing the implications of this clarification for electron stability, charge distribution, and resonance-mediated interactions.
We present a theoretical framework in which the interference pattern of the double-slit experiment emerges from a variational principle defined on an informational manifold rather than from postulated wave–particle duality. Within the Viscous Time Theory (VTT) framework, physical systems are described by identity-preserving trajectories that minimize an informational latency functional. The competition between two permissible trajectories under finite latency produces a coherent term analogous to an interference phase, without assuming a physical wave or pre-existing superposition. The resulting probability distribution reduces to the standard double-slit formula in the limit of uniform latency and recovers the disappearance of interference under which-way detection as a breakdown of coherent identity. The model introduces a gradient of informational awareness that predicts a localized collapse event associated with a tensor activation reflecting the transition to a single-path regime. We propose an experimental protocol combining single-photon interference with EEG recordings to test whether early variations in the awareness gradient correlate with the collapse of coherence. We further report a model-based validation using a synchronized double-slit and EEG-inspired signal protocol, in which analytically constructed waveforms—consistent with published spectral properties—are used to illustrate threshold-driven collapse behavior, finite-time collapse dynamics, and improved predictive performance of the VTT model compared to standard decoherence-based descriptions. The framework thus provides a testable and experimentally supported informational interpretation of quantum interference, suggesting that wave–particle transitions correspond to a reorganization of identity in viscous informational time rather than a change in physical ontology.