We propose a theoretical framework in which time is described as a physical field charac- terized by a time-density field ν. In this formulation, the local flow of time is determined by ν, and gravitational acceleration arises from its spatial gradient. The theory reproduces New- tonian gravity in the weak-field limit and provides a consistent relativistic formulation through a ν-dependent metric.. By extending ν to a complex scalar field, key structures of quantum mechanics emerge naturally, including probability density, momentum, and uncertainty. Fur- thermore, the path integral formulation is interpreted as arising from the phase structure of the time-density field. The quantum potential is derived from the amplitude of ν, providing a direct mechanism for quantum phenomena such as wave packet spreading, quantization, and tunneling. These results suggest that gravity and quantum behavior may originate from a com- mon underlying structure associated with time itself. While the present formulation is not yet a complete quantum theory, it offers a unified perspective that connects classical gravity and quantum mechanics within a single framework. This version includes a minor typographical correction in the mathematical expressions. In the previous version, the exponential function was mistakenly written as "exp!" in several equations. I have corrected this to the proper notation "exp(...)". This correction does not affect the theoretical results or conclusions of the work.
We propose a theoretical framework in which time is described as a physical field charac- terized by a time-density field ν. In this formulation, the local flow of time is determined by ν, and gravitational acceleration arises from its spatial gradient. The theory reproduces New- tonian gravity in the weak-field limit and provides a consistent relativistic formulation through a ν-dependent metric.. By extending ν to a complex scalar field, key structures of quantum mechanics emerge naturally, including probability density, momentum, and uncertainty. Fur- thermore, the path integral formulation is interpreted as arising from the phase structure of the time-density field. The quantum potential is derived from the amplitude of ν, providing a direct mechanism for quantum phenomena such as wave packet spreading, quantization, and tunneling. These results suggest that gravity and quantum behavior may originate from a com- mon underlying structure associated with time itself. While the present formulation is not yet a complete quantum theory, it offers a unified perspective that connects classical gravity and quantum mechanics within a single framework. This version includes a minor typographical correction in the mathematical expressions. In the previous version, the exponential function was mistakenly written as "exp!" in several equations. I have corrected this to the proper notation "exp(...)". This correction does not affect the theoretical results or conclusions of the work.
This work proposes a fundamental scalar field, denoted , as the underlying structure from which quantum mechanics emerges. In this framework, particles are interpreted as stable localized excitations of the temporal field rather than fundamental point-like entities. Starting from a classical Lagrangian field theory, wave dynamics naturally arise in the low-energy limit, leading to the emergence of the Schrödinger equation. The probabilistic interpretation of quantum mechanics is derived from the energy density of the field, yielding the Born rule . Furthermore, the Fourier structure of field excitations leads directly to the Heisenberg uncertainty principle as a consequence of wave localization. By extending the relativistic structure of the field, a linear factorization of the energy-momentum relation produces the Dirac equation and the associated spinor structure. In this approach, quantum mechanics is not fundamental but emerges as an effective description of deeper dynamics governed by the temporal field . The model suggests that vacuum structure, particle properties, and quantum uncertainty originate from the underlying behavior of this field
Contact: Jonathan.duchesne@hotmail.com FinalTDG: Full Mathematical proposition. AddTDG22: Natural Add-ons TDGStressTest: Stress Test results TDGEX: Experimental Protocol TDGpaper: Abstract Temporal Decoherence Geometry (TDG) is a conservative theoretical framework that systematically explores a possible connection between quantum decoherence, weak-field gravity, and an emergent notion of time, while remaining strictly within a GKSL (Lindblad) open quantum dynamics, i.e. Markovian and completely positive, with no ad hoc collapse mechanism. The central idea of TDG is to take seriously the structure of decoherence of an open quantum system and promote it to an effective geometric object: a decoherence tensor Gamma_{mu nu}, constructed from a Lindblad generator, is introduced as the primary source of a weak-field gravitational potential and an emergent time defined from local decoherence rates. The framework is deliberately minimalist in its assumptions: weak-field regime, standard quantum mechanics (no modification of the Schrödinger equation or the GKSL structure), no exotic measurement postulates. This new “DOI version” collects and organises the following elements: A mathematical core in which Gamma_{mu nu} is derived from a GKSL generator (Lindbladian), a gradient-flow–type evolution drives Gamma_{mu nu} towards a quantity proportional to the usual energy-momentum tensor T_{mu nu}, an emergent time scalar T(x) is defined from the local decoherence rate lambda(x), under explicit integrability conditions, an effective weak-field gravitational potential Phi_TDG is associated with this decoherence structure. The analysis of static, spherically symmetric compact configurations, obtained from a simple “decoherence-energy” functional E[gamma], which: have a regular, non-singular core, exhibit a Yukawa-type tail, reproduce a Newtonian / Schwarzschild-like exterior over a given radial interval, while avoiding central singularities. A phenomenological layer in which TDG induces decoherence-dependent corrections to gravitational redshift, encoded in an effective parameter epsilon_TDG. This parameter is, in principle, falsifiable with state-of-the-art optical clocks, providing a clear experimental handle: TDG is not only a formal construction, but a framework that can be constrained or ruled out by precision redshift measurements. A key feature of this revised version is the inclusion of a set of analytical stress tests explicitly designed to challenge the model within the regime it claims to describe (weak-field, GKSL, Markovian): regular-core compact configurations, extreme parameter limits (diffusion, screening length scales, etc.), dynamical behaviour of the decoherence tensor, analysis of the absence of finite-time collapse in the GKSL setting. These stress tests show that, under the stated assumptions and within the weak-field regime, the TDG framework remains regular, well-posed, and consistent with its own domain of validity. The Zenodo deposit therefore gathers both a main TDG manuscript (model structure + weak-field applications) and a technical stress-test note, enabling readers to assess not only the construction itself, but also its internal robustness and phenomenological viability. This deposit is intended to serve as a stable reference for the current version of TDG: it provides the complete description of the framework together with the technical ingredients needed to evaluate its mathematical consistency, its compatibility with weak-field gravity, and its falsifiability through decoherence-sensitive redshift tests with optical clocks.
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.
Abstract Quantum mechanics and relativity are extraordinarily successful mathematical theories, yet their conventional physical interpretations rely on substantially different conceptual frameworks. The Theory of Space (TS) proposes a fourth dimension defined by the Planck-related interval, with interpreted as a longitudinal dimension associated with energy (cτ), rather than as the conventional Minkowski spacetime interval. This fourth dimension does not coexist continuously with the observable three spatial dimensions as a conventional four-dimensional manifold. Instead, TS proposes an oscillatory existence between observable 3D presence and a non-observable fourth-dimensional phase. Through this oscillation, the quantum system undergoes repeated dimensional projection into observable 3D, with individual eigenstates manifested probabilistically while the underlying quantum state continues to evolve. Within this framework, phenomena including measurement, the Born rule, the arrow of time, entropy, entanglement, tunneling, and Bell-type correlations acquire a common physical interpretation. Heisenberg uncertainty and non-commutativity are interpreted as consequences of physical parameters associated with different phases of the dimensional oscillation and therefore not simultaneously manifested within the same 3D instance. TS further distinguishes between the quantum system’s spatial component and its compact physical entity. Their coexistence within the complete system provides a proposed physical basis for quantum interference and phase-dependent phenomena, including the double-slit experiment and the path-integral description of quantum evolution. As an extension of the model, TS proposes that the periodic displacement and replacement of quantum space generate a pulsed inward spatial flow. This mechanism provides a possible basis for a quantized gravitational interaction and suggests that gravitational energy may be represented by a positive contribution. Related developments, including spiral spatial flows, follow naturally from the same dimensional-oscillation mechanism. The Theory of Space therefore seeks to provide a common conceptual framework for quantum, relativistic, and gravitational phenomena without replacing the established mathematical equations that successfully reproduce experimental observations. The present work develops this framework and invites critical examination of its assumptions, physical implications, and potential experimental consequences. Keywords: relativity; Lorentz transformation; quantum superposition; quantum superposition; collapse; entanglement; quantum gravity
This work presents a minimal and unified formulation of physical reality based on a single coupled system of two scalar fields: a phase S(x) and a realization density ρ(x). The dynamics is completely determined by two principles: conservation of a realization current and a geometric constraint linking the norm of the phase gradient to the structure of the density field. Together, these relations form a closed system with no additional dynamical assumptions. From this system, all major physical regimes emerge as limiting cases. When the density is uniform, propagation is null and describes lightlike behavior. When the geometric constraint reduces to a constant, the system reproduces classical Hamilton–Jacobi dynamics for massive particles. When the density varies significantly, the coupled system yields quantum behavior, including the Schrödinger equation in the appropriate limit. In this framework, the wave function is not a fundamental entity but an emergent representation of the underlying geometric structure of realization. Interference arises from phase consistency, and quantum behavior reflects the nontrivial structure of the realization density rather than intrinsic indeterminism. The theory also naturally incorporates gravitation by promoting the spacetime metric to a dynamical field. In the appropriate limit, the stress–energy tensor reduces to that of classical matter, and Einstein’s field equations are recovered. Regions where the realization density approaches zero define a geometric boundary where timelike realization ceases, corresponding to horizon-like structures. The central result is that a single coupled equation governs propagation, mass, quantum behavior, and gravitational structure. Physical reality is determined by global consistency of realization rather than by selection among multiple possibilities. This formulation provides a minimal geometric unification of light, matter, quantum phenomena, and gravity within a single coherent framework.
We propose a self-consistent axiomatic framework that unifies quantum unitary evolution, thermal dissipation, and spacetime geometry based on three fundamental principles: the \emph{complex-time principle}, the \emph{information-geometry equivalence principle}, and the \emph{maximal entropy gradient principle}. Starting from these axioms, we rigorously derive three core equations: a complex-time quantum-thermal master equation, an information-induced gravitational field equation, and a unified gradient-flow dynamics that couples quantum states, thermodynamics, and curvature. From these, we further derive four key derived equations: a generalized Einstein field equation in the low-energy limit, a quantum-thermodynamic uncertainty relation, a relation between entropy production and curvature scalar, and a conservation law for quantum information current. The framework naturally recovers standard quantum mechanics, thermodynamics, and general relativity in appropriate limits, while offering new predictions about the relation between quantum entanglement and spacetime structure. All derivations are carried out in full mathematical detail, and the resulting equations are original, closed-form, and internally consistent.