This work reformulates the Time Delay Field (TDF) by promoting the phase τ(x,t)\tau(x,t)τ(x,t) from a scalar to a gauge connection, Aμ=∂μτA_\mu = \partial_\mu \tauAμ=∂μτ, showing that quantum mechanics and gravity emerge from phase transport and curvature. Decoherence is interpreted as fluctuations of this connection, with τc\tau_cτc representing the memory scale of non-Markovian dynamics. The result is a unified gauge-geometric framework linking quantum phase, energy–momentum, and gravity.
This work reformulates the Time Delay Field (TDF) by promoting the phase τ(x,t)\tau(x,t)τ(x,t) from a scalar to a gauge connection, Aμ=∂μτA_\mu = \partial_\mu \tauAμ=∂μτ, showing that quantum mechanics and gravity emerge from phase transport and curvature. Decoherence is interpreted as fluctuations of this connection, with τc\tau_cτc representing the memory scale of non-Markovian dynamics. The result is a unified gauge-geometric framework linking quantum phase, energy–momentum, and gravity.
n the Time Delay Field (TDF) framework, the quantum phase is promoted to a geometric coordi- nate. The scalar field τ represents a fundamental time–phase dimension whose evolution determines observable quantities such as energy and momentum. A key relation connecting energy to the evolution of the phase field is E = ℏ dτ dt . (1) This relation emerges naturally in several formulations of physics, including Schr¨odinger wave mechanics, the Hamilton–Jacobi formulation, and the Feynman path integral. Motivated by this correspondence, we treat τ as an additional geometric coordinate extending spacetime.
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.
This preprint develops a refined TDF-QM formulation within the Time Delay Field (TDF) framework, focusing on the interpretation of quantum phase as a temporal-phase rotation. The central proposal is that the TDF quantum variable (N_t) should be interpreted not as the phase angle itself, but as the local angular rate of temporal-phase rotation, (N_t=\dot{\theta}\tau). Under this definition, the quantum phase becomes (\theta\tau=\int N_t dt), while the standard quantum relation (E=\hbar \omega) is reinterpreted as (E=\hbar N_t). The paper examines how this definition aligns with core structures of nonrelativistic quantum mechanics, including the wavefunction (\psi=\sqrt{\rho}e^{-i\theta_\tau}), Schrödinger phase evolution, de Broglie momentum, interference, decoherence, uncertainty relations, rest mass as internal phase rotation, and entanglement as temporal-phase locking. In this formulation, Planck’s constant is interpreted as the conversion factor between temporal-phase rotation and physical action/energy, with (h=E_qt_q) representing the action associated with one complete fundamental time-phase cycle. The work is intended as a conceptual and mathematical bridge between the broader TDF program and effective quantum mechanics. It does not claim a complete derivation of the Standard Model, spin, charge, or quantum field theory, but identifies which standard QM relations are structurally compatible with the TDF time-phase-rate interpretation and which areas require further development. This work builds on the TDF framework and references the related Zenodo record: https://doi.org/10.5281/zenodo.20633775.
This work presents a focused theoretical extension of the Time-Delay Field (TDF) framework, previously introduced in “A Theory of Everything via the Five-Dimensional Delay Field Model” (Masarrat-Bakhsh, 2025). The present paper applies the TDF approach to the physical interpretation of spin, offering a complementary perspective to the standard Dirac formulation. Within the TDF framework, spacetime is endowed with intrinsic temporal memory, modeled through an effective time-delay field arising from a higher-dimensional (5D) structure. Spin is reinterpreted not as a purely algebraic or intrinsic quantum number, but as an emergent dynamical feature associated with delayed phase responses in non-Markovian field evolution. The characteristic spin-1/2 behavior and 4π rotational periodicity are shown to arise naturally from this delay-induced phase structure. The standard Dirac theory and its successful predictions are fully recovered in the limit of vanishing delay, ensuring consistency with established relativistic quantum mechanics. This work does not propose a replacement of the Dirac framework, but rather provides a causal reinterpretation that may offer deeper insight into the origin of spin and spin–orbit coupling. The paper is intended as a conceptual and foundational contribution, suitable for discussions in theoretical physics, quantum foundations, and spacetime-based interpretations of quantum phenomena.
Abstract We present a covariant extension of the Schrödinger framework in which the quantum phase is promoted to a geometric connection AμA_\muAμ on spacetime. The associated curvature Fμν=∂μAν−∂νAμF_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\muFμν=∂μAν−∂νAμ encodes local deviations from flat phase geometry and manifests as measurable spectral shifts and uncertainty modulation. This formulation unifies geometric and probabilistic interpretations of quantum mechanics by identifying phase curvature with the internal concave curvature of the quantum domain. Two minimal, testable models—a one-dimensional ring (Aharonov–Bohm type) and a two-dimensional constant-curvature plane (Landau-type quantization)—demonstrate how phase curvature translates into observable level spacing. The framework preserves probability conservation in admissible gauges and recovers standard quantum mechanics in the flat-phase limit.
Geometric Derivation of Quantum Mechanics from a 5D Time-Delay Manifold This paper introduces the "Time-Delay Field" (TDF) theory, a novel geometric framework that derives the fundamental equations of quantum mechanics from a deterministic five-dimensional spacetime structure. By treating the fifth dimension as an intrinsic "delay" coordinate (τ), we demonstrate that quantum behaviors—such as superposition and interference—are projections of continuous 5D null geodesics onto our 4D reality. Abstract:We present a geometric derivation of quantum mechanics based on the TDF theory. Extending the spacetime manifold to five dimensions (M4×S1), where the fifth dimension τ represents an intrinsic time delay, we postulate that all fundamental particles travel on null geodesics in the 5D bulk. We demonstrate that the rest mass of a particle arises from its momentum component in the delay dimension, leading to a helical trajectory. The quantum wave function ψ(x,t) is derived not as a probability amplitude, but as the Fourier projection of this 5D trajectory onto the 4D hypersurface. This framework rigorously recovers the Klein-Gordon and Schrödinger equations and provides a deterministic, geometric explanation for quantum interference and wave-particle duality. Furthermore, we address the measurement problem as a momentum transfer in the τ-dimension and discuss consistency with recent experimental observations of symmetry-dependent quantum timing [Guo et al., 2026]. Key Contributions: Derivation of the Schrödinger Equation: Proves that the non-relativistic wave equation emerges naturally from the projection of 5D null paths. Resolution of Wave-Particle Duality: Explains wave-like interference as a topological phase accumulation (Moiré pattern) of helical trajectories. Objective Collapse Mechanism: Defines "measurement" as a momentum transfer in the delay dimension, eliminating the need for an observer. Mass-Dependent Decoherence: Introduces the "Quantumness Factor" (Q), predicting an intrinsic transition from quantum to classical behavior for macroscopic masses. Experimental Alignment: Consistent with recent findings on geometry-dependent time delays in attosecond physics. Keywords: Quantum Foundations, Time-Delay Field, 5D Spacetime, Null Geodesics, Kaluza-Klein Theory, Measurement Problem, Emergent Quantum Mechanics, Geometric Phase.