This paper proposes a conceptual and mathematical framework connecting quantum decoherence andgravity through the language of motivic geometry and the motivic Galois group. The central idea is that quantumsuperpositions correspond to mixed motivic structures, while gravitational interaction induces a flow towardpure motives via the suppression of extension classes. In this picture, divergences in quantum path integrals arereinterpreted as artifacts of non-admissible motivic weights, and classical spacetime geometry—governed byEinstein’s equations— emerges as a stable fixed point under the combined action of gravitational dynamics andthe motivic Galois group. It is presented explicit toy numerical examples illustrating (i) the resolution ofquantum infinities via motivic periods and (ii) the emergence of classical reality through gravitationally inducedmotivic decoherence. Finally, It is discussed the advantages of this approach relative to existing methods inquantum gravity and decoherence theory.
This paper proposes a conceptual and mathematical framework connecting quantum decoherence andgravity through the language of motivic geometry and the motivic Galois group. The central idea is that quantumsuperpositions correspond to mixed motivic structures, while gravitational interaction induces a flow towardpure motives via the suppression of extension classes. In this picture, divergences in quantum path integrals arereinterpreted as artifacts of non-admissible motivic weights, and classical spacetime geometry—governed byEinstein’s equations— emerges as a stable fixed point under the combined action of gravitational dynamics andthe motivic Galois group. It is presented explicit toy numerical examples illustrating (i) the resolution ofquantum infinities via motivic periods and (ii) the emergence of classical reality through gravitationally inducedmotivic decoherence. Finally, It is discussed the advantages of this approach relative to existing methods inquantum gravity and decoherence theory.
The gravitational decoherence field studies the suppression of coherence in quantum systems caused by effects rooted in the gravitational interaction. This models are not just important to yield interesting ideas about the search, in regimes others than the Planck scale, for the interplay between quantum mechanics and general relativity, but also from a theoretical point of view. The fact that the gravitational field can not be shielded opens the question of how strong will the gravitational ‘environment’ decohere a quantum system? and if this decoherence can somehow explain the absence of macroscopical super- positions? This thesis studies in depth the ‘Classical Channel Gravity’ (CCG) model, a recent proposal of gravitational decoherence that assumes that the gravitational interac- tion is always accompanied with an intrinsic decoherence mechanism which ensures that there is no transmission of quantum information between the parties involved. This model can be understood a series of weak continuous quantum measurements accompanied with a feedback term produced by some underlying hidden gravitational degrees of freedom. We first study all the possible emergent dynamics from collisional Markovian dynamics; these ones range from exact unitary to arbitrary fast decoherence (Zeno effect). The second part of the thesis is devoted to study the Newtonian and post Newtonian limits of the CCG model, with particular focus on the testability features of CCG. In particular, we apply this model to coupled clocks and find that the amount of decoherence predicted by CCG is the same as the decoherence that an ‘environment of clocks’ will imprint in a single clock in the context of unitary evolution. On the other hand, we find that this effect is far from being detectable with the current achieved time accuracy. However, CCG as a model for multi partite systems and two systems with very different masses seems to yield an amount of decoherence that is not only able to be detectable with current experiments but also seems to indicate that this model is ruled out. Nevertheless, we also mention potential caveats with our assumptions and discuss other physically motivated directions to further study this result. Finally, we also explore the extension of CCG for the cosmological scenario. In this context the scale factor is being decohered by test particles ‘sitting’ on spacetime. We find that this decoherence will be seen by an observer unaware of the CCG fundamental mechanism as an emergent form of dark energy filling the universe.
We develop an effective gravitational framework for the quantum–classical transition based on the dynamical stability of historical information. Building on previous analyses of gravitational temporal decoherence and the emergence of classical time, the present work addresses the subsequent problem of how classical histories become stable, persistent, and objectively accessible. The framework is formulated as a non-relativistic, semiclassical open-system dynamics in which gravity induces structurally constrained dissipative effects of Lindblad type. Within this setting, we introduce a stability functional that operationally characterizes which quantum states can support robust historical records and which are dynamically suppressed. The quantum–classical transition is described as a smooth, scale-dependent crossover controlled by physically meaningful parameters, rather than as a sharp boundary or interpretational postulate. The emergence of a unique classical past is shown to arise from dynamical selection: while multiple quantum histories are formally allowed, only those supported by stable physical records persist under gravitationally induced dissipation. The framework is explicitly effective in scope and does not rely on a microscopic derivation or full relativistic covariance. Instead, it identifies universal structural features that any viable fundamental theory must reproduce in the appropriate semiclassical regime. This work complements earlier studies on the emergence of classical time by providing a dynamical account of historical stability, thereby contributing to a coherent program for understanding the physical origin of classical reality.
We propose a novel operator-based formulation of quantum gravity grounded in two foundational principles: a discrete causal lattice and algebraic microcausality. Departing from traditional continuum approaches and wavefunction-based quantum mechanics, this framework models spacetime and matter as emergent phenomena arising from the algebraic structure of displacement operators. In this first part of a two-part series, we construct the foundational framework and demonstrate how key features of quantum mechanics—such as the uncertainty principle, de Broglie relations, and entanglement—emerge naturally without invoking wavefunctions, path integrals, or metric-based geometry. Operator non-commutativity on the causal lattice gives rise to a self-consistent quantum structure with natural ultraviolet finiteness, intrinsic time directionality, and a microcausal interpretation of measurement. This foundational part lays the groundwork for gravitational dynamics, cosmology, and the grand unification principles of gravity and the Standard Model to be explored in the sequel to quantum gravity part II.
Contact Jonathan.duchesne@hotmail.com 418-953-0596 This thesis presents Time–Decoherence Gravity (TDG), a unified theoretical framework in which spacetime geometry, gravitation, and the physical flow of time arise from fundamental quantum decoherence. Rather than treating decoherence as an environmental or effective process, TDG builds on a covariant extension of the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation, where four directional Lindblad operators encode intrinsic, irreversible information loss. These operators define a “decoherence tensor,” which acts both as a memory of quantum irreversibility and as the generator of emergent spacetime geometry through a nonlinear constitutive relation. The theory provides a coherent gravitational collapse mechanism based on the incompatibility of decoherence patterns across quantum branches. This leads to an intrinsic “decoherence energy,” whose magnitude determines the collapse timescale, extending and generalizing the well-known Penrose–Diósi models. TDG predicts a smooth transition from persistent microscopic coherence to rapid macroscopic collapse. At cosmological scales, a homogeneous decoherence tensor naturally generates modified Friedmann dynamics, early-universe stiff-fluid behavior, and late-time acceleration without requiring a fine-tuned cosmological constant. Black-hole entropy emerges as a saturation of decoherence memory at the horizon, while Hawking radiation appears as the dissipative relaxation of this saturation. The theory also predicts short-range deviations from Newtonian gravity and a universal spectrum of fundamental gravitational noise. Finally, TDG offers several experimentally testable signatures involving optical clocks, mesoscopic interferometry, short-range force measurements, and correlated phase noise in global timing networks. The framework is internally consistent, falsifiable, and provides a novel and unified approach to the relationship between quantum mechanics, gravity, and the arrow of time.
AbstractThis 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 probabilitiesTogether, 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 Spacetime Paper 2: Quantum Geometry Paper 3: Lepton and Quark Generational Phenomenological Patterns; and Paper 4: Peak-Coupling Theory of Quantum Interaction
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.