Abstract Event-State Theory (EST) proposes a pre-geometric, cost-based explanatory framework for why variational structures arise so broadly in physics. EST does not claim to replace General Relativity (GR) or Quantum Mechanics (QM). Instead, it frames both as effective descriptions emerging from different uses of a single additive, real-valued history cost functional. The classical (GR-compatible) regime is characterized by dominance of extremal-cost histories (minimization), while the quantum regime is characterized by interference between many admissible histories, which requires a unitary representation of the additive cost as a complex phase. This paper is a programmatic bridge: it cleanly separates core postulates from auxiliary assumptions, identifies the precise boundary where purely positive weighting fails to generate interference, and states the minimal conditions under which complex amplitudes of the form \(\exp(iS/\hbar)\) are forced. We outline a research program: (I) mathematical sharpening of the cost functional on discrete causal substrates, (II) derivation of continuum variational limits (GR-side), (III) derivation of unitary amplitude propagation (QM-side), and (IV) empirical diagnostics where deviations from standard models may arise.
Abstract Event-State Theory (EST) proposes a pre-geometric, cost-based explanatory framework for why variational structures arise so broadly in physics. EST does not claim to replace General Relativity (GR) or Quantum Mechanics (QM). Instead, it frames both as effective descriptions emerging from different uses of a single additive, real-valued history cost functional. The classical (GR-compatible) regime is characterized by dominance of extremal-cost histories (minimization), while the quantum regime is characterized by interference between many admissible histories, which requires a unitary representation of the additive cost as a complex phase. This paper is a programmatic bridge: it cleanly separates core postulates from auxiliary assumptions, identifies the precise boundary where purely positive weighting fails to generate interference, and states the minimal conditions under which complex amplitudes of the form (\exp(iS/\hbar)) are forced. We outline a research program: (I) mathematical sharpening of the cost functional on discrete causal substrates, (II) derivation of continuum variational limits (GR-side), (III) derivation of unitary amplitude propagation (QM-side), and (IV) empirical diagnostics where deviations from standard models may arise.
Derivative Continuum: An Event-Based Framework for Quantum Mechanics and Emergent Spacetime Geometry We present a theoretical framework called Derivative Continuum, in which physical reality is composed of discrete events and their mutual complex relation amplitudes, rather than continuous fields or point particles. A reproducing kernel Hilbert space (RKHS) is constructed from a positive-definite kernel that maps the discrete event configuration into a continuous derived field Ψ(x). Within this structure: The Schrödinger equation arises from unitary evolution of event amplitudes in the RKHS projection. The Born rule is derived from the reproducing inner product, not assumed. The Einstein field equations emerge as a self-consistency condition when the kernel depends on spacetime geometry. The framework contains a single free parameter ℓ₀, a fundamental relation scale. When ℓ₀ → 0 and event density becomes infinite, standard quantum mechanics and classical general relativity are fully recovered. At finite ℓ₀, corrections appear. As a concrete example, we compute the leading deviation in the double-slit experiment: a suppression of interference visibility and a non-sinusoidal envelope distortion, both scaling as (ℓ₀/d)² where d is the slit separation. This work does not claim to replace existing theories. It offers a candidate pre-paradigm language that re-derives known results from fewer assumptions and opens a new path toward quantum gravity. Comments, criticism, and collaboration are welcome.
General relativity (GR) is naturally organized around spacetime events and their causal order, whereas quantum field theory (QFT) is formulated in terms of states, operators, and unitary evolution, without an intrinsic criterion for when a quantum process becomes a definite spacetime fact. We propose an event-centered framework in which events are locally irreversible records generated by quantum-environment interactions and serve as an interface between quantum dynamics and relativistic spacetime structure. Event anchoring is characterized operationally by three jointly sufficient conditions: local classicalization, redundant environmental recording, and irreversibility against recovery. Their joint satisfaction defines local generative freezing. We realize these criteria in an explicit repeated-collision open-system model. The model is illustrative rather than a derivation from relativistic QFT, but it remains globally unitary and yields the freezing time in closed form. For all admissible tolerances, local classicalization is certified no later than channel-level irrecoverability, and generically earlier. Full anchoring occurs only when both irrecoverability and the required record redundancy have been reached, producing irrecoverability-limited and redundancy-limited regimes. At the level of anchored records, physical history is therefore represented as a partially ordered causal skeleton of frozen events on which effective field-theoretic descriptions operate. The framework addresses event anchoring--when a candidate outcome becomes a stable spacetime fact--while remaining compatible with standard QFT and relativistic causality. It does not derive the Born rule or solve single-outcome selection, which belong to the separate problem of event generation.
Abstract We derive the formalism of Quantum Mechanics from the axioms of Event-State Theory (EST). While Paper VI established General Relativity as the deterministic limit of computational optimization, this work addresses the stochastic limit where the computational temperature λ is non-negligible. We demonstrate that the "Field of Potential" Ω functions as a phase space of possible next-frames, governed by a Boltzmann-like selection rule. By identifying matter not as point particles but as topological defects ("twists") in the causal graph, we show that the cost function acquires an oscillatory phase component to satisfy lattice continuity. This creates interference effects in the selection probability, reproducing the Feynman Path Integral and the Schrödinger equation. Thus, Quantum Mechanics is identified not as a fundamental framework, but as the statistical mechanics of causal exploration.
This paper develops the structural modeling core of a global realization approach to quantum interference. Building on prior work that established the possibility of non-propagational descriptions, the present study addresses a more precise question: how quantum interference can be explicitly modeled once local propagation, trajectories, and in-transit dynamics are excluded. The model introduces realization admissibility functionals defined over the complete experimental configuration, including source, apertures, and absorbing boundaries. These functionals are non-dynamical and non-ontic; they do not represent physical fields or evolving states, but encode global compatibility conditions that govern where detection events can coherently close. Detection probabilities emerge through statistical closure at the absorbing boundary, reproducing standard interference patterns without invoking wave superposition in space. A minimal geometric formulation is presented to demonstrate how slit configurations generate admissibility structures that yield conventional interference statistics. Within this framework, interference minima arise naturally as forbidden realizations rather than as products of destructive interaction between propagating entities. The model preserves full empirical equivalence with standard quantum mechanics while clarifying the physical status of interference as an organizational, rather than dynamical, phenomenon. This work does not modify quantum dynamics or introduce additional degrees of freedom. Its contribution is structural: it sharpens the distinction between quantum dynamical states and realization, delineates the limits of local modeling, and provides a concrete, explicit framework for modeling interference at the level where empirical outcomes occur. The paper serves as the modeling core of a broader global realization program, situated between conceptual foundations and empirical analysis.
Why do local actions and exponential Euclidean weights arise so universally in classical, statistical, and quantum theories? We offer a structural explanation from minimal constraints on finite descriptions of admissible histories. Assume that histories admit finite, self-delimiting (prefix-free) generative codes that can be decoded sequentially in a single forward pass. These purely syntactic requirements define a minimal descriptive cost, interpretable as a smoothed minimal program length, that is additive over local segments. First, any continuous local additive cost whose stationary sector coincides with the empirically identified classical variational sector is forced into a unique Euler--Lagrange equivalence class. Hence the universal form of an action is fixed by descriptional structure alone, while the specific microscopic Lagrangian and couplings remain system-dependent semantic input. Second, independently of microscopic stochasticity, finite prefix-free languages exhibit exponential redundancy: many distinct programs encode the same coarse history, and this redundancy induces a universal exponential multiplicity weight on histories. Requiring this weight to be real and bounded below selects a real Euclidean representative for stable local bosonic systems, yielding the standard Euclidean path-integral form. When Osterwalder--Schrader reflection positivity holds, the Euclidean measure reconstructs a unitary Lorentzian amplitude.
We present a conceptual and partially formalized framework in which general relativity (GR) and quantum mechanics (QM) are viewed not as competing theories, but as descriptions of different phases of a single causal-informational process. GR describes actualized geometric reality (the space of effects E), while QM describes the emergence of this reality from a pre-geometric domain of potentials (the space of causes C). The key element is a map Φ : C → E that preserves information but breaks time symmetry. For the first time, we propose a rigorous mathematical framework fully verified in the Lean 4 proof assistant, including bridges between spectral dimension, algebraic nuclei, and Čech topological obstructions. This synthesis resolves the measurement problem, the continuum limit problem, and Zeno's paradox, and yields testable predictions for the primordial perturbation spectrum, gravitational wave dispersion, and variation of the fine-structure constant. Published by The Institute for Applied Ontological Mathematics.