In canonical quantum mechanics and quantum field theory on curved spacetimes, gravitation is traditionally incorporated either as an external classical potential introduced into the Schr¨odinger or Dirac equations, or via perturbative coupling to an unquantized background metric. In both paradigms, the temporal parameter is postulated as an isotropic, scalar coordinate flowing uniformly in all spatial directions, which strictly dictates that the spatial dispersion of free wave packets remains isotropic (spherically symmetric). In this work, we propose a geometric framework wherein quantum particles are not zero-dimensional mathematical singularities, but possess a finite intrinsic temporal span (∆τ p ), and gravitational acceleration is fundamentally governed not by an external attractive pull, but directly by the local proper time gradient (∇τ). In the weak-field regime, the transverse gradient vanishes identically along spherical equipotential surfaces parallel to the Earth’s surface (isochrons, ∇ ⊥ τ ≈ 0), whereas it is continuous and maximal along the radial vertical axis (∇ ∥ τ = g/c 2 ). When the particle’s internal phase—driven by its Compton frequency (ω C = mc 2 /ℏ)—intersects these vertical proper time steps, differential clock rates induce severe phase mixing (dephasing), squeezing and narrowing the vertical coherence length (σ ∥ ). Conversely, because phase coherence is rigorously preserved across the horizontal equipotential plane, the wavefunction disperses freely and broadly (σ ⊥ ≫ σ ∥ ). The resulting oblate (pancake-shaped) anisotropy is not merely a passive geometric deformation; via the directional quantum stress tensor quantum accumulated in the vertical axis (T zz ≫ T xx , T yy ), it reactively bends surrounding equipotential surfaces inward, constituting the microscopic quantum source of gravitational curvature itself. This single ontological mechanism accounts for the vertical quantization and horizontal classical spreading of ultra-cold neutrons at ILL Grenoble, the unavoidable intrinsic decoherence floor encountered by vertical baselines in atom interferometry, and the spontaneous relaxation of wave packets into spherical isotropy in the Bremen Drop Tower and MAIUS microgravity experiments. Finally, a falsifiable experimental protocol is formulated to directly test this anisotropy via single-photon or cold-atom scattering in a vacuum tower.
In canonical quantum mechanics and quantum field theory on curved spacetimes, gravitation is traditionally incorporated either as an external classical potential introduced into the Schr¨odinger or Dirac equations, or via perturbative coupling to an unquantized background metric. In both paradigms, the temporal parameter is postulated as an isotropic, scalar coordinate flowing uniformly in all spatial directions, which strictly dictates that the spatial dispersion of free wave packets remains isotropic (spherically symmetric). In this work, we propose a geometric framework wherein quantum particles are not zero-dimensional mathematical singularities, but possess a finite intrinsic temporal span (∆τ p ), and gravitational acceleration is fundamentally governed not by an external attractive pull, but directly by the local proper time gradient (∇τ). In the weak-field regime, the transverse gradient vanishes identically along spherical equipotential surfaces parallel to the Earth’s surface (isochrons, ∇ ⊥ τ ≈ 0), whereas it is continuous and maximal along the radial vertical axis (∇ ∥ τ = g/c 2 ). When the particle’s internal phase—driven by its Compton frequency (ω C = mc 2 /ℏ)—intersects these vertical proper time steps, differential clock rates induce severe phase mixing (dephasing), squeezing and narrowing the vertical coherence length (σ ∥ ). Conversely, because phase coherence is rigorously preserved across the horizontal equipotential plane, the wavefunction disperses freely and broadly (σ ⊥ ≫ σ ∥ ). The resulting oblate (pancake-shaped) anisotropy is not merely a passive geometric deformation; via the directional quantum stress tensor quantum accumulated in the vertical axis (T zz ≫ T xx , T yy ), it reactively bends surrounding equipotential surfaces inward, constituting the microscopic quantum source of gravitational curvature itself. This single ontological mechanism accounts for the vertical quantization and horizontal classical spreading of ultra-cold neutrons at ILL Grenoble, the unavoidable intrinsic decoherence floor encountered by vertical baselines in atom interferometry, and the spontaneous relaxation of wave packets into spherical isotropy in the Bremen Drop Tower and MAIUS microgravity experiments. Finally, a falsifiable experimental protocol is formulated to directly test this anisotropy via single-photon or cold-atom scattering in a vacuum tower.
Gravity is traditionally understood either as geometric curvature (general relativity) or as an external classical field acting on quantum systems. This paper develops a unified alternative: gravity arises from spatial variation in the temporal coherence window τ(x), the finite interval over which quantum systems can sustain coherent phase relations before collapse. Building on experimental evidence that decoherence rates in laboratory systems obey an empirical κ/τ law, I show that gravitational self-energy constrains coherence time according to τgrav ∝ 1/√(Gρ). Three independent derivations—via a modified Lindblad equation, an effective potential Veff = A/τ, and spectral-overlap analysis—converge on the same dynamical law: a(x) = −∇[1/τ(x)], identifying gravitational acceleration as coherence-gradient descent. In this view, mass is condensed temporal capacity, curvature is the geometric imprint of temporal structure, and falling is the drift of quantum evolution toward regions where coherence collapses most rapidly. I extend this framework to show that gravity is engineerable: any spatially structured decoherence environment producing an artificial coherence profile τart(x) generates a gravitational-like acceleration agen(x) = −κart ∇[1/τart(x)], indistinguishable from natural gravitation insofar as their coherence-gradient profiles match. I provide explicit recipes for realizing such gradients using noise-shaping, optical scattering, dissipative optical lattices, and superconducting cavity engineering, along with quantitative acceleration estimates (10⁻⁷–10⁻³ m/s²) and full experimental protocols for cold atoms, matter-wave interferometry, and superconducting qubits. Finally, the framework offers a microphysical account of gravitational time dilation, predicts non-universal response in highly coherent systems, suggests achievable tabletop tests, and points toward a future τ-field theory capable of reproducing general relativity in the macroscopic limit. The result is a falsifiable, coherence-based foundation for gravitation and the first principled pathway to artificial gravity via engineered temporal coherence.
Modern gravitational experiments are fundamentally measurements of clock rates. Atomic clocks in terrestrial laboratories and satellite navigation systems demonstrate that gravitational environments manifest operationally through variations in the rate at which physical time accumulates. In this work gravity is interpreted as a scalar timing field θ(x,t) relating coordinate time to proper time. Spatial gradients of this timing field generate classical gravitational acceleration (Alpha-C), while accumulated proper time along a trajectory governs quantum phase evolution (Alpha-Q). Classical trajectories and quantum phase shifts therefore become complementary probes of a common timing structure governing clock synchronization across 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.
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.
It has been suggested that the nonlinear Schrödinger–Newton equation might approximate the coupling of quantum mechanics with gravitation, particularly in the context of the Møller–Rosenfeld semiclassical theory. Numerical results for the spherically symmetric, time-dependent, single-particle case are presented, clarifying and extending previous work on the subject. It is found that, for a particle mass greater than 1.14(ℏ 2 /( G σ)) 1/3 , a wave packet of width σ partially 'collapses' to a groundstate solution found by Moroz, Penrose and Tod, with excess probability dispersing away. However, for a mass less than 1.14(ℏ 2 /( G σ)) 1/3 , the entire wave packet appears to spread like a free particle, albeit more slowly. It is argued that, on some scales (lower than the Planck scale), this theory predicts significant deviation from conventional (linear) quantum mechanics. However, owing to the difficulty of controlling quantum coherence on one hand, and the weakness of gravity on the other, definitive experimental falsification poses a technologically formidable challenge.
If gravity and entanglement share a common origin in the temporal flow rate field τ(x), then gravitational tidal fields should produce measurable decoherence of entanglement. This paper derives the first quantitative prediction for this effect. We construct the dynamics of a Non-Separable Temporal Bubble (NSTB) — the shared temporal configuration of two entangled particles — in a Schwarzschild gravitational background. The bubble's internal coherence field satisfies a wave equation with a tidal potential proportional to the second derivative of the background τ-field. Linearization yields a visibility reduction for entanglement: ΔV = GM d² / (c² r³ f_intrinsic) where d is the spatial extent of the bubble (the separation between entangled particles), r the distance from the gravitating mass, and f_intrinsic the internal frequency set by the fractal-temporal hierarchy. The key signature is the tidal scaling ∝ d²/r³, which uniquely distinguishes NSTB from competing gravitational decoherence proposals: Penrose-Diósi predicts mass-dependent decoherence (different observable), Ralph-Pienaar predicts gradient scaling ∝ d/r² (different power law), and standard QFT in curved spacetime predicts no decoherence at all (zero). Any observed gravitational decoherence of entanglement with d²/r³ scaling would therefore constitute direct evidence for a shared origin of gravity and quantum correlations. For Earth-orbit experiments with optical photons (d ~ 400 km, f ~ 10¹⁴ Hz), the predicted effect is ΔV ~ 10⁻²⁷ — far below current sensitivity. Near a neutron star with microwave-frequency entanglement (d ~ 100 km, f ~ 10¹⁰ Hz), the effect grows to ~ 10⁻¹⁰, within conceivable reach of future space-based quantum networks. Three enhancement strategies are identified: stronger tidal fields, larger bubble separations, and lower-frequency entangled states. The prediction closes an open parameter problem from the companion entanglement paper (κ = 1, f_bubble = f_photon) and establishes a concrete, falsifiable target for the emerging field of gravitational quantum experiments.