Classical physics implicitly assumes instantaneous state evolution. This paper demonstrates that this assumption is neither necessary nor correct. We reformulate both quantum and classical dynamics as history-dependent processes using retarded kernels defined on information-geometric spaces. Time evolution is no longer local and instantaneous, but emerges from integral propagation over past states encoded as geometric information flow. Within this framework, effective mass, effective potential, and large-scale gravitational behavior arise naturally from retarded information propagation alone. No dark matter, no dark energy components, and no additional exotic fields are required. Flat galactic rotation curves, long-range gravitational anomalies, and apparent nonlocal effects emerge as consequences of delayed dynamics, not as evidence for unseen matter. This is not an extension of standard theory. It replaces the instantaneous-time paradigm itself, and removes the need for dark matter as a fundamental entity. 1. Introduction2. Failure of Instantaneous Dynamics3. Distance-Based State Space4. Retarded Kernel Dynamics5. Unitary Evolution and Continuity6. Emergence of the Schrödinger Equation7. Probability Density and the Born Rule8. Information Geometry and Fisher Structure9. Fubini–Study Distance Limit10. Density Matrix and Mixed States11. Classical Limit and Hamilton–Jacobi Theory12. Relativistic Extension13. Effective Gravitational Dynamics14. Information-Induced Curvature15. Galactic Rotation Curves16. SPARC Relation and Acceleration Scale17. Cosmological Limit (FLRW Dynamics)18. Unified Limit Correspondence19. Minimal Axiomatic Formulation20. Discussion21. Conclusion
Classical physics implicitly assumes instantaneous state evolution. This paper demonstrates that this assumption is neither necessary nor correct. We reformulate both quantum and classical dynamics as history-dependent processes using retarded kernels defined on information-geometric spaces. Time evolution is no longer local and instantaneous, but emerges from integral propagation over past states encoded as geometric information flow. Within this framework, effective mass, effective potential, and large-scale gravitational behavior arise naturally from retarded information propagation alone. No dark matter, no dark energy components, and no additional exotic fields are required. Flat galactic rotation curves, long-range gravitational anomalies, and apparent nonlocal effects emerge as consequences of delayed dynamics, not as evidence for unseen matter. This is not an extension of standard theory. It replaces the instantaneous-time paradigm itself, and removes the need for dark matter as a fundamental entity. 1. Introduction2. Failure of Instantaneous Dynamics3. Distance-Based State Space4. Retarded Kernel Dynamics5. Unitary Evolution and Continuity6. Emergence of the Schrödinger Equation7. Probability Density and the Born Rule8. Information Geometry and Fisher Structure9. Fubini–Study Distance Limit10. Density Matrix and Mixed States11. Classical Limit and Hamilton–Jacobi Theory12. Relativistic Extension13. Effective Gravitational Dynamics14. Information-Induced Curvature15. Galactic Rotation Curves16. SPARC Relation and Acceleration Scale17. Cosmological Limit (FLRW Dynamics)18. Unified Limit Correspondence19. Minimal Axiomatic Formulation20. Discussion21. Conclusion
This work provides a conceptual foundation for physics by identifying and removing a hidden assumption shared by classical and quantum theories: instantaneity. Modern physical theories are typically formulated in terms of instantaneous states that evolve through local-in-time update rules. This paper argues that such an assumption is neither empirically required nor conceptually fundamental. Instead, physical reality is reformulated in terms of history bundles: weighted ensembles of temporally extended, globally consistent histories. Within this framework, time evolution emerges from consistency constraints imposed on entire histories rather than from differential equations acting on instantaneous states. Quantum probability arises as a geometric and combinatorial measure over admissible histories, yielding the Born rule without postulating measurement axioms, collapse, or observer-dependent rules. Apparent quantum nonlocality is reinterpreted as a temporal selection effect, not as instantaneous spatial influence. At cosmological scales, causal horizons progressively restrict the set of extendable histories. This irreversible contraction of the history bundle induces an effective negative pressure, providing a natural interpretation of late-time cosmic acceleration without introducing scalar fields, vacuum energy, or ad hoc modifications of gravity. The resulting effective equation of state approaches −1 at late times while remaining non-phantom, and leads to observationally distinguishable signatures. Rather than proposing a new phenomenological model, this paper reorganizes the conceptual structure underlying quantum mechanics, statistical physics, and cosmology. By relaxing a single modeling assumption—instantaneity—it reveals a unified structural explanation for probability, nonlocal correlations, irreversibility, and cosmic acceleration. The work is foundational and conceptual in scope. It is intended as a basis for future numerical studies, observational tests, and extensions toward quantum gravity and information theory.
This work presents a unified reinterpretation framework for quantum phenomena based on Unitary Retarded Probability Dynamics (URPD). URPD replaces instantaneous time evolution and measurement-induced wavefunction collapse with a structure grounded in temporal delay, informational distance, and probabilistic weighting. Quantum dynamics emerge from retarded probabilistic averaging over informationally separated reference states. Within this framework, standard quantum phenomena—including double-slit interference, the quantum Zeno effect, weak measurement and weak values, quantum entanglement, and effective temporal discreteness—arise naturally without introducing additional axioms. Standard quantum mechanics is recovered as a limiting case where delay fluctuations vanish. URPD preserves relativistic causality by constraining delayed informational contributions and reinterprets the invariance of the speed of light as a consequence of shared informational geometry rather than a fundamental postulate. A more general and foundational formulation of URPD itself is developed in *Classical Science Assumes Instantaneity — and That Assumption Is Wrong*, where the framework is presented in a fully unified form beyond the quantum sector. https://doi.org/10.5281/zenodo.17987215
This work introduces a quantum extension of Retarded Consistency Field Theory (RCFT), a framework in which the present is not assumed as a primitive instantaneous object but emerges through the resolution of delayed consistency across prior history. Instead of starting from local time evolution alone, the theory treats causal memory and history dependence as foundational and formulates quantum dynamics on a history space rather than on an instantaneous state space only. The paper develops a retarded consistency action, a history-weighted path integral, and a history-space Schrödinger formulation for non-Markovian quantum dynamics. In the short-delay limit, the framework reduces to ordinary local mechanics and standard quantum theory, while finite-delay effects generate controlled corrections governed by the moments of a causal memory kernel. The formalism also shows how inertial motion and geodesic structure can appear as local limits of the same delayed consistency principle. Conceptually, the theory proposes that quantum reality is organized not by a pre-given temporal present but by interference among possible histories weighted by delayed consistency. In this picture, the physically realized present is an emergent endpoint of constructive consistency selection. The work positions RCFT as a unified foundation for rethinking time, inertia, and gravitational structure within a quantum history-based framework.
This framework preserves the empirical success of existing physical theories while proposing an alternative set of foundational assumptions from which their standard formulations emerge as effective limits. Abstract — Key Innovative Points Discrete Updating FabricThe theory postulates a fundamental discrete fabric whose elementary constituents evolve through local update processes, replacing continuous fields and background spacetime as primary entities. Irreversible Local Dynamics as FundamentalUnlike standard approaches based on unitary or reversible evolution, irreversibility is taken as ontological. Physical law emerges from irreversible local updates rather than from imposed symmetries or variational principles. Emergent Time and SpacetimeTime is not assumed as a fundamental parameter but arises from the counting of update events. Spacetime geometry emerges as a coarse-grained description of update activity across the fabric. Quantum Probability from Microstate CountingQuantum probabilities, including the Born rule, emerge from combinatorial counting of compatible microstates of the fabric, rather than being postulated axiomatically. Gravity as Update-Rate ModulationGravitational phenomena are interpreted as variations in local update rates, leading to effective curvature, time dilation, and relativistic behavior at macroscopic scales. Mass as Resistance to UpdateMass and inertia arise from stable topological structures within the fabric that resist updates, providing a dynamical origin of mass without introducing fundamental mass parameters. Fundamental Dissipation and IrreversibilityDissipation is intrinsic to the fabric dynamics and not an emergent statistical effect. The arrow of time follows directly from the irreversible nature of local updates. Extension Beyond Fundamental PhysicsThe same discrete framework accounts for macroscopic dissipative phenomena—such as friction, stick–slip dynamics, superlubricity, growth, and self-organization—linking fundamental physics and material behavior within a single process-based model. iversality Without Fundamental SymmetryLarge-scale physical laws emerge as dynamical attractors of the updating fabric, arising through elimination of unstable configurations rather than enforcement of fundamental symmetries. Emergent Rules Beyond the Born Rule in the Unified Fabric Framework The same discrete-fabric + local-update + coarse-graining structure generates multiple quantum rules without postulation. 1. Schrödinger Dynamics as an Emergent Long-Wavelength Limit Local deterministic updates on a discrete fabric admit spectral modes.In the long-wavelength limit, their evolution converges to a Schrödinger-type equation. No quantum dynamics is postulated.Only update rules and spectral structure are assumed. 2. Superposition from Coarse-Grained Microstate Counting Macroscopic amplitudes arise as sums over compatible microstates.Linearity follows from additive contributions at the amplitude level. Superposition is therefore emergent.It reflects coarse-graining, not a fundamental axiom. 3. Interference as Cross-Terms in Microstate Combinatorics Probabilities are quadratic because amplitudes sum before squaring.Cross-terms correspond exactly to interference effects. Interference is not assumed.It is a combinatorial consequence of microstate superposition. 4. Tensor Product Structure and the Origin of Entanglement Composite systems correspond to composite regions of the fabric.Global microstates factorize only if compatibility constraints separate. Entanglement arises when constraints couple subsystems.It is structural, not mysterious. 5. Decoherence from Phase Inaccessibility Observers access only coarse-grained variables.Rapidly varying microstate phases average out. Off-diagonal terms are dynamically suppressed.Decoherence emerges without postulation. 6. Measurement Collapse as Constraint Reduction Measurement is an interaction that reduces compatible microstates.The effective state updates accordingly. Collapse is not a new law.It is constraint updating under coarse-graining. 7. The Arrow of Time from Asymmetric State Counting Entropy is defined as the logarithm of compatible microstates.Local updates generically move toward larger compatible sets. Irreversibility is structural.It does not rely on subjective ignorance. 8. Coulomb Friction from Discrete Event Statistics Friction equals dissipated update energy per unit distance.The Coulomb law emerges from counting active interfacial events. The friction coefficient is not fundamental.It decomposes into microscopic event parameters. 9. Superlubricity as the Event-Free Limit Superlubricity occurs when locking events are suppressed.Dissipation is rare, not forbidden. This is a limit regime, not an exception.It confirms friction as emergent. 11. Conservation Laws from Update Invariance If the update rule is invariant under local transformations,conserved quantities emerge automatically. Noether’s theorem becomes emergent.Symmetry is a property of the update, not an axiom. 12. Classical Determinism from Phase Averaging At large scales, phase information becomes inaccessible.Only expectation values survive. Classical trajectories emerge statistically.Determinism is an effective limit. 13. Locality from Finite Update Propagation Updates propagate only through neighboring fabric nodes.Information speed is bounded. Causality is structural.Nonlocality is only apparent at coarse scales. 14. Emergent Speed Limit (c) The maximum update rate defines a universal speed.No signal can exceed it. The speed of light is not fundamental.It is a fabric update bound. 15. Metric Geometry from Update Delays Spatial curvature corresponds to spatially varying update rates.Time dilation is an update slowdown. Geometry is dynamical.The metric is emergent. 16. Gravity from Update Resistance Mass corresponds to structures resisting updates.Nearby updates slow down in response. Gravitational attraction emerges.No force field is postulated. 17. Equivalence Principle as a Structural Identity All stable update-resisting structures slow updates identically.Their response is universal. Inertial and gravitational mass coincide.Equivalence is automatic. 18. Quantization from Discrete Spectrum A finite update lattice admits discrete eigenmodes.Energy levels are quantized. Quantization is not imposed.Continuum is an approximation. 19. Noise Spectra (1/f) from Avalanche Dynamics Update cascades produce scale-free event statistics.Long-range correlations appear. 1/f noise is generic.It signals discrete underlying dynamics. 20. Criticality without Tuning The fabric naturally operates near instability thresholds.Small perturbations trigger cascades. Self-organized criticality emerges.No parameter tuning is required. 21. Thermodynamic Laws as Counting Theorems Temperature measures update activity density.Heat is disordered update flow. Thermodynamics is not independent.It is bookkeeping of updates. 22. Growth and Morphogenesis from Update Bias Directional update biases produce structured growth.Forms emerge without templates. Morphogenesis is dynamical.Shape follows update flow. 23. Fine-structure value and other unknow meaning The fine-structure value (~137) corresponds to the effective degeneracyof coherently contributing update configurations in an elementary coupling process.Proton–electron mass ratio the number of internal update cycles required to stabilize a topological vortex (proton), and a simple oscillatory update mode (electron). Mass measures cumulative resistance to updates. Lepton mass hierarchy Different stability thresholds of the same update pattern. Each mass corresponds to a different coherence regime.→ Families are metastable realizations of one structure. Reduced Planck constant Energy × time associated with one elementary update event. → ħ is the discrete unit of updating. Speed of light Maximum update propagation speed across the fabric. → c is the causal limit of the fabric. Bekenstein–Hawking entropy Number of blocked or saturated update configurations at the horizon. → An event horizon is an informational saturation boundary. Universal critical exponents They arise from the topology of update avalanches,independent of microscopic details. → Criticality is a natural fabric regime. Explanations Rarely Given in Existing Theories 1. Why probabilities are quadratic and not cubic or linear Most theories postulate P=∣ψ∣2P=|\psi|^2P=∣ψ∣2.Here it follows from coherent counting plus phase cancellation. The square is not a choice.It is the minimal stable coarse-graining. 2. Why quantum phases are physically unobservable but indispensable Phases affect interference but not outcomes directly.They label micro-configurations, not macrostates. Phase is structural memory.Measurement erases access to it. 3. Why constants are dimensionless and few Only ratios of update counts survive coarse-graining.Dimensional parameters wash out. Dimensionless constants are structural.They encode geometry, not dynamics. 4. Why “free parameters” cluster around simple numbers Many constants are order-one ratios or small inverses.They reflect combinatorial suppression. Fine tuning is apparent.It is state counting in disguise. 5. Why quantum randomness is stable and reproducible Randomness is not noise.It is deterministic micro-dynamics seen through coarse-graining. Statistics are invariant.Details are inaccessible. 6. Why identical particles are truly identical Microstates differ, macrostates do not.Labels are erased by update symmetry. Indistinguishability is enforced.It is not a postulate. 7. Why spin is quantized and half-integer values exist Spin counts topological winding in update cycles.Only discrete windings are stable. Half-integer spin reflects double-cover topology.No mystery remains. 8. Why gauge free
This work presents a reconstruction of quantum mechanics in which Schrödinger-type dynamics emerges from reversible probabilistic evolution rather than being postulated. Starting from a normalized probability density, we impose reversible probability dynamics, Fisher information geometry, and classical correspondence. These compatibility conditions yield coupled real equations equivalent to the continuity equation and the Hamilton–Jacobi equation with an additional information curvature (quantum potential) term. By combining density and phase into a complex amplitude, the Schrödinger equation appears as a compact encoding of reversible statistical flow. The result is mathematically equivalent to the Madelung hydrodynamic formulation and structurally connected to Bohmian mechanics, but derived without assuming Hilbert space, operator axioms, or measurement postulates. The work can therefore be viewed as an information-geometric derivation of quantum dynamics: quantum theory arises as the unique consistent representation of reversible probability flow. Keywords: quantum foundations, quantum reconstruction, emergent quantum mechanics, derivation of the Schrödinger equation, information geometry, Fisher information, Hamilton–Jacobi theory, Madelung formulation, Bohmian mechanics, reversible probability dynamics
The series Time as Phase Flow (Papers I–IV) established that time is not fundamental but emerges from the geometric phase flow of quantum information, providing a unified account of dynamically generated cosmological constants, informational temporal viscosity, and the suppression of large-scale structure. Despite these successes, a fundamental mechanism explaining why a single, stable observable reality emerges from the space of quantum informational states has remained unresolved. In this work, we introduce the framework of Information-Geometric Spacetime (IGS), in which spacetime itself emerges from the geometry of quantum information, entanglement, and modular flow. Within IGS, we define an Actualization Operator that mediates between quantum informational states and observable spacetime geometry. Derived from first principles, the operator combines entropy-based suppression with modular evolution, governed by a universal geometric constant β = 1/(π√3) ≈ 0.1837 fixed by the geometry of causal diamonds and the associated modular Hamiltonian. We show that actualization preserves information conservation and quantum unitarity, acting as a structural filter that selectively stabilizes informational states capable of forming consistent geometric reality, in close analogy with decoherence-driven classical emergence. Under this mechanism, previously identified cosmological effects—most notably the suppression of the matter power spectrum and the S_8 tension—are reinterpreted as observational consequences of information actualization rather than modifications of gravity or exotic matter. This framework also offers a geometric reformulation of the quantum measurement problem, in which the observer is not an external agent but an emergent process associated with modular structure and entanglement thermodynamics. The theory yields testable predictions in controlled quantum systems and forthcoming cosmological surveys, providing a concrete pathway toward empirical tests of spacetime emergence from quantum information.