We develop a staged research framework in which physical time is treated not as a primitive external parameter, but as an emergent quantity generated by the quantum dynamical structure of matter-energy configurations. The central working hypothesis is that a physically meaningful temporal increment exists only when state-change distinguishability is both relationally accessible and supported by stable physical records. On this basis, we formulate a Relational Chronometric Principle (RCP) and construct a local chronometric field χℓ(x) from two standard quantum-information-theoretic ingredients: quantum Fisher information and a record-stability factor derived from relative-entropy loss under a calibrated noisy channel (Braunstein & Caves, 1994; Page & Wootters, 1983). The present paper has four limited but explicit goals. First, we formulate the RCP as a minimal axiom set and derive an existence result for a bounded chronometric order parameter, together with a restricted uniqueness result. Second, we introduce a micro-operational definition of χℓ(x), specify the admissible class of coarse-graining maps Cℓ from which it is constructed, and establish a set of core properties for the field including non-negativity, boundedness, and convergence of the operational estimator in the Markovian-Gaussian limit. Third, we analyse the minimal low-energy covariant completion compatible with chronometric universality and show that a scalar-tensor effective field theory provides a controlled representation of emergent proper-time dressing and weak-field gravitational corrections. Fourth, we identify an operational metrology package with full uncertainty propagation and explicit sensitivity targets, a systematic budget for the primary experimental channel, and a three-channel experimental hierarchy based on co-located optical clocks, vertical clock comparisons, and atom interferometry. The framework is deliberately not presented as a final unification theory. It does not provide a UV completion, it does not derive the chronometric coarse-graining map from a fundamental quantum-gravity architecture, and it does not derive the Standard Model gauge sector. Instead, it is advanced as a disciplined low-energy programme that connects three normally separate domains: relational quantum dynamics, weak-field gravity, and precision chronometric observables. Within that restricted scope, the theory yields a falsifiable screened scalar sector, controlled weak-field limits, concrete sensitivity targets, and a cross-channel falsifiability architecture. Keywords: emergent time; relational dynamics; chronometric scalar; quantum Fisher information; scalar-tensor EFT; optical clocks; atom interferometry; screened gravity; coarse-graining maps; record stability
We develop a staged research framework in which physical time is treated not as a primitive external parameter, but as an emergent quantity generated by the quantum dynamical structure of matter-energy configurations. The central working hypothesis is that a physically meaningful temporal increment exists only when state-change distinguishability is both relationally accessible and supported by stable physical records. On this basis, we formulate a Relational Chronometric Principle (RCP) and construct a local chronometric field χℓ(x) from two standard quantum-information-theoretic ingredients: quantum Fisher information and a record-stability factor derived from relative-entropy loss under a calibrated noisy channel (Braunstein & Caves, 1994; Page & Wootters, 1983). The present paper has four limited but explicit goals. First, we formulate the RCP as a minimal axiom set and derive an existence result for a bounded chronometric order parameter, together with a restricted uniqueness result. Second, we introduce a micro-operational definition of χℓ(x), specify the admissible class of coarse-graining maps Cℓ from which it is constructed, and establish a set of core properties for the field including non-negativity, boundedness, and convergence of the operational estimator in the Markovian-Gaussian limit. Third, we analyse the minimal low-energy covariant completion compatible with chronometric universality and show that a scalar-tensor effective field theory provides a controlled representation of emergent proper-time dressing and weak-field gravitational corrections. Fourth, we identify an operational metrology package with full uncertainty propagation and explicit sensitivity targets, a systematic budget for the primary experimental channel, and a three-channel experimental hierarchy based on co-located optical clocks, vertical clock comparisons, and atom interferometry. The framework is deliberately not presented as a final unification theory. It does not provide a UV completion, it does not derive the chronometric coarse-graining map from a fundamental quantum-gravity architecture, and it does not derive the Standard Model gauge sector. Instead, it is advanced as a disciplined low-energy programme that connects three normally separate domains: relational quantum dynamics, weak-field gravity, and precision chronometric observables. Within that restricted scope, the theory yields a falsifiable screened scalar sector, controlled weak-field limits, concrete sensitivity targets, and a cross-channel falsifiability architecture. Keywords: emergent time; relational dynamics; chronometric scalar; quantum Fisher information; scalar-tensor EFT; optical clocks; atom interferometry; screened gravity; coarse-graining maps; record stability
This work introduces the Generative Principle of the Universal Correlational Lattice (UCL), a pre-geometric theoretical framework in which physical reality is described as an evolving network of correlational sites, rather than as fields defined on a pre-existing spacetime background. In the UCL framework, spacetime, dynamics, quantum uncertainty, and effective physical observables emerge from structured correlations encoded in a universal kernel. The theory does not postulate spacetime, wavefunctions, or classical fields as fundamental objects. Instead, it treats them as effective constructs arising from coarse-grained correlational dynamics. A central element of the framework is the introduction of internal times associated with correlational sites, whose relational synchronization generates an emergent external time only at the effective level. Temporal evolution is therefore defined intrinsically, without requiring a fundamental global clock or background metric. The Generative Principle specifies: how admissible correlational configurations are formed, how dynamical evolution arises as a one-parameter flow in correlational space, and how stable, observable regimes emerge through functional selection and decoherence-like processes intrinsic to the lattice. Importantly, the framework provides a well-defined notion of observables as emergent, operational quantities derived from correlational averages, spectral properties of the kernel, and effective coarse-graining procedures. These observables are not postulated ad hoc, but arise naturally from the internal structure of the lattice and its generative dynamics. Quantum uncertainty is interpreted as emergent and contextual, reflecting partial access to the full correlational state rather than a fundamental indeterminism. In principle, the framework allows deterministic underlying dynamics while reproducing effective probabilistic behavior at observable scales. The UCL is constructed to be compatible with known physical theories in appropriate limits, while remaining ontologically independent from both classical spacetime and traditional quantum mechanical foundations. It provides a unified conceptual basis for addressing quantum theory, gravity, and cosmology within a single correlational framework. This paper focuses on the foundational and generative aspects of the UCL. Specific phenomenological models and numerical predictions are deferred to subsequent works, where concrete kernels and parameter regimes are explored.
Quantum mechanics, general relativity, and statistical mechanics employ notably different temporal parameters: external or relational clock time, geometric proper time, and modular or thermal time. This paper proposes that their agreement is not primitive but a finite-resource relation. Each temporal level is represented by an update system, and two levels share time over an interval only when an order-preserving translation map between them can be implemented with bounded error and cost below the certification budget of a finite observer. The admissibility ratio η_T = K_c / (ω* T) is a dimensionless control parameter for temporal agreement, with ω* < ∞ established both by a resource-envelope bound and by a self-contained quantum-plus-gravitational frame argument with a unique positive minimum. A canonical local cost ansatz, the lowest-order separable representative compatible with reparametrization invariance, clock-scale additivity, and interface and action monotonicity, supplies four channels with protocol-class floors from the Margolus–Levitin and Mandelstam–Tamm bounds. A weak-field proper-time worked example shows that ordinary clock comparison sits orders of magnitude below threshold, with the coefficients acting as calibration constants of the comparison architecture rather than free parameters. Known time concepts are recovered as low-η_T limits; breakdowns are classified as four admissibility failures (cost threshold, domain collapse, non-invertibility, and resolution error). Applied to the problem of time in quantum gravity, the criterion identifies when a finite-cost map Φ₁₃ between quantum phase time and geometric proper time exists. A Bianchi IX sketch shows the failure mechanisms; the natural next quantitative test is evaluation of η_T[Φ₁₃] for an isotropic loop quantum cosmology bounce, where three operationally distinct outcomes are possible and none is predetermined by the formalism. --- Keywords: problem of time; quantum gravity; temporal translation; finite observers; finite-resource theory; temporal admissibility; clock synchronization; proper time; modular time; relational time; Page–Wootters mechanism; quantum reference frames; loop quantum cosmology; Bianchi IX cosmology; quantum clocks
This document presents the Universal Correlational Lattice (UCL) as a general theoretical framework for constructing physical models directly from correlational structures, without assuming spacetime, fields, or quantum states as fundamental entities. The UCL formalism is built around a universal correlational kernel defined over relational sites, from which effective notions of dynamics, observables, uncertainty, and emergent geometry arise through explicit variational and coarse-graining procedures. Rather than postulating equations of motion or quantization rules a priori, the framework provides a model-building methodology: physical laws appear as effective descriptions of stable correlational configurations. This document is not a phenomenological fit nor a proposal of a specific new particle or interaction. Instead, it serves as a theoretical construction manual, showing how to: Define correlational degrees of freedom and their internal parameters, Construct effective observables from correlational averages, Derive emergent dynamics through functional variation, Identify classical, quantum-like, and geometric regimes as limits of the same underlying structure, Build toy models and progressively refine them toward empirical applicability. Uncertainty, probabilistic behavior, and apparent quantum effects are treated as emergent properties of incomplete access to correlational information, not as fundamental axioms. Likewise, time is introduced through internal correlational evolution and synchronization, rather than assumed as an external background parameter. The goal of the UCL framework is to provide a unified, internally consistent base from which models relevant to particle physics, gravity, and cosmology can be constructed and compared with existing theories such as Quantum Field Theory and General Relativity, while remaining agnostic about their ultimate empirical success. This work is intended for researchers interested in: Foundations of physics, Emergent spacetime and dynamics, Alternative formulations of quantum theory, Correlational and relational approaches to physical law. Empirical validation is not claimed at this stage; instead, the emphasis is placed on conceptual completeness, internal consistency, and explicit model-building capability.
In this thesis, we lay out the goal, and a broad outline, for a program that takes quantum mechanics in its minimal form to be the fundamental ontology of the universe. Everything else, including features like space-time, matter and gravity associated with classical reality, are emergent from these minimal quantum elements. We argue that the Hilbert space of quantum gravity is locally finite-dimensional, in sharp contrast to that of conventional field theory, which could have observable consequences for gravity. We also treat time and space on an equal footing in Hilbert space in a reparametrization invariant setting and show how symmetry transformations, both global and local, can be treated as unitary basis changes. Motivated by the finite-dimensional context, we use Generalized Pauli Operators as finite-dimensional conjugate variables and define a purely Hilbert space notion of locality based on the spread induced by conjugate operators which we call "Operator Collimation." We study deviations in the spectrum of physical theories, particularly the quantum harmonic oscillator, induced by finite-dimensional effects, and show that by including a black hole-based bound in a lattice field theory, the quantum contribution to the vacuum energy can be suppressed by multiple orders of magnitude. We then show how one can recover subsystem structure in Hilbert space which exhibits emergent quasi-classical dynamics. We explicitly connect classical features (such as pointer states of the system being relatively robust to entanglement production under environmental monitoring and the existence of approximately classical trajectories) with features of the Hamiltonian. We develop an in-principle algorithm based on extremization of an entropic quantity that can sift through different factorizations of Hilbert space to pick out the one with manifest classical dynamics. This discussion is then extended to include direct sum decompositions and their compatibility with Hamiltonian evolution. Following this, we study quantum coarse-graining and state-reduction maps in a broad context. In addition to developing a first-principle quantum coarse-graining algorithm based on principle component analysis, we construct more general state-reduction maps specified by a restricted set of observables which do not span the full algebra (as could be the case of limited access in a laboratory or in various situations in quantum gravity). We also present a general, not inherently numeric, algorithm for finding irreducible representations of matrix algebras. Throughout the thesis, we discuss implications of our work in the broader goal of understanding quantum gravity from minimal elements in quantum mechanics.
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.