This publication presents an extended axiomatic revision of the Probability-Space Axiomatic Foundation. The original minimal logical core (K1–K4), governing realization, temporal asymmetry, and constrained selection among unrealized possibilities, is preserved verbatim and unchanged. This revision introduces an Extended Core (v2.0) consisting of three additional axioms (K5–K7) that are additive rather than revisionary. These axioms are required to support observer-dependent projection of observables, non-signaling correlation via shared collapse ancestry (entanglement), and the emergence of persistent relational deformation interpreted as effective curvature. The extended axioms do not modify the original logical foundation; instead, they constrain how realized structure is accessed, correlated, and stabilized when instantiated as a physical system. The work is structured as a strict in-place extension of the original manuscript. All original text, numbering, and logical development are preserved word-for-word. New material is inserted only where logically required, and is explicitly labeled as part of the Extended Core. No experimental claims are made. No force-based or field-first primitives are introduced. Physical quantities such as mass, energy, or spacetime curvature are not assumed at the axiomatic level. This axiomatic framework is intended to function as a constraint layer for physical theories built on Probability-Space concepts, ensuring compatibility with observer locality, non-signaling correlation, and emergent large-scale structure without altering the minimal logical basis. The framework is falsifiable in principle: any physical realization must recover standard quantum statistics and empirically tested gravitational behavior in appropriate limits. This record supersedes and extends the author’s prior Zenodo publication by providing a formally defined Extended Core (v2.0), while maintaining full continuity with the original axiomatic foundation.
This publication presents an extended axiomatic revision of the Probability-Space Axiomatic Foundation. The original minimal logical core (K1–K4), governing realization, temporal asymmetry, and constrained selection among unrealized possibilities, is preserved verbatim and unchanged. This revision introduces an Extended Core (v2.0) consisting of three additional axioms (K5–K7) that are additive rather than revisionary. These axioms are required to support observer-dependent projection of observables, non-signaling correlation via shared collapse ancestry (entanglement), and the emergence of persistent relational deformation interpreted as effective curvature. The extended axioms do not modify the original logical foundation; instead, they constrain how realized structure is accessed, correlated, and stabilized when instantiated as a physical system. The work is structured as a strict in-place extension of the original manuscript. All original text, numbering, and logical development are preserved word-for-word. New material is inserted only where logically required, and is explicitly labeled as part of the Extended Core. No experimental claims are made. No force-based or field-first primitives are introduced. Physical quantities such as mass, energy, or spacetime curvature are not assumed at the axiomatic level. This axiomatic framework is intended to function as a constraint layer for physical theories built on Probability-Space concepts, ensuring compatibility with observer locality, non-signaling correlation, and emergent large-scale structure without altering the minimal logical basis. The framework is falsifiable in principle: any physical realization must recover standard quantum statistics and empirically tested gravitational behavior in appropriate limits. This record supersedes and extends the author’s prior Zenodo publication by providing a formally defined Extended Core (v2.0), while maintaining full continuity with the original axiomatic foundation.
This paper develops a theoretical framework that seeks to unify the foundational principles of quantum mechanics, general relativity, and thermodynamics by extending spatial geometry to include a compactified fourth spatial dimension. The central proposal is that many counterintuitive features of quantum systems—such as wave function collapse, superposition, entanglement, tunneling, and decoherence—emerge as phenomena from the projection of four-dimensional quantum states into observable three-dimensional space. Within this formulation, apparent quantum randomness is reinterpreted as a consequence of observing only a lower-dimensional slice of a higher-dimensional structure. A key innovation of the framework is the introduction of a scalar degree of freedom, termed the entropion field, which governs decoherence and encodes the thermodynamic arrow of time. The entropion field couples directly to both quantum fields and spacetime curvature, leading to modified Einstein field equations and an entropic extension of quantum field dynamics. This mechanism provides a consistent account of classicality emerging from quantum substrates, links entropy growth to projection dynamics, and clarifies how spacetime geometry constrains quantum evolution. The theory is presented through a structured progression of conceptual foundations, mathematical formalism, physical interpretation, and predictive consequences. Particular emphasis is placed on testable deviations from standard theories, including altered interference signatures in 4D-projected systems, entropion-modulated decoherence rates, and revised mechanisms of tunneling and entanglement. Broader implications are explored for quantum information theory, cosmology, condensed matter, and computational theory. Collectively, these results establish a geometrically grounded unification scheme that integrates the three major pillars of modern physics into a consistent and falsifiable framework.
This volume is the foundational and mathematical entry point of the global-realism theory tower. Exactly three physical axioms are retained: microscopic ontic definiteness with finite localization, physical reality of a dynamical spacetime–vacuum substrate, and persistent causal retarded source–response coupling. Wave functions, Hilbert and Fock spaces, Born probabilities, gauge groups, Einstein equations, entropy, temperature, particle species, chemical bonds, life, information, and complexity are not additional physical axioms. They enter only as representations, conditional theorems, controlled limits, effective models, computations, observations, or downstream organizational levels. The volume establishes a many-sorted formal language, an anti-confusion type discipline, a theory-layer category, conservative import maps, an acyclic dependency graph, state and parameter certificates, and universal uncertainty and rejection rules. Later parts connect this common spine to finite topological matter, causal historical dynamics, gravitation, quantum representation, statistical reduction, macroscopic projection, observation, and the specialized physics, chemistry, biology, Earth-system, astronomical, and complex-system volumes. These interfaces authorize downstream inputs but do not replace the full calculations owned by those volumes. All nonstandard claims remain conditional on existence, stability, causal realization, independent calibration, standard-theory subtraction, and held-out tests. The purpose is internal architectural closure and empirical accountability, not a claim that three axioms already compute every law or that nature has been shown to realize the proposed history and finite-core sectors. Keywords **Global realism; three physical axioms; finite topological matter; physical spacetime vacuum; causal historical dynamics; quantum representation; gravitation; statistical reduction; acyclic theory tower; uncertainty quantification; falsifiability.** Note on the Two Versions **This paper is available in two versions. Readers interested in the original ideas and the development of the manuscript are encouraged to consult the original version. For a more systematic presentation and a deeper understanding of the complete theoretical framework, we recommend reading both versions.**
Emergent Reality Architecture: Probability, Gravitation, and Physical Regimes This paper introduces Emergent Reality Architecture (ERA), an ontological and structural framework aimed at clarifying why modern physics contains three persistent puzzles that are typically treated separately: quantum phenomena that resist classical intuition, massless propagation (e.g., light) whose trajectories carry no proper time (null structure), and gravitation that appears as curvature rather than a conventional force. Rather than proposing new equations or modifying established dynamics, ERA examines representational assumptions that are often implicit in contemporary theory—specifically the widespread assumption that spacetime geometry is fundamental and that time admits arbitrarily fine resolution. ERA argues that these assumptions are not directly empirically mandated and that several foundational tensions arise when they are treated as universally valid outside the regimes in which they succeed. At the core of ERA is a constraint–freedom engine in which physical behavior depends on the relationship between imposed constraints and finite representational capacity. Within this framework, probability arises as residual freedom among admissible configurations; determinism corresponds to representational saturation; and emergence is forced when lawful behavior can no longer be coherently represented within a given regime. ERA identifies four representational regimes—configuration (Regime I), distinguishability (Regime II), ordering (Regime III), and metric closure (Regime IV)—each introduced to resolve specific structural failures of the one below it. Quantum phenomena arise naturally in regimes lacking metric closure; massless propagation originates in a regime that supports relational distinction without internal temporal ordering; and gravitation is interpreted as the geometric instantiation of ordering constraints once metric closure is enforced. In this view, stable orbital motion can be understood as the metric-closure encoding of temporal persistence (“temporal rest”) when time-relational stability must be expressed within spacetime. ERA is offered as an explanatory framework, not a competing dynamical theory. Its contribution lies in clarifying why probability, gravitation, and regime-dependent physical behavior—including quantum contextuality, null propagation, and orbital persistence—can be structurally unavoidable features of physical description, while preserving the empirical validity of quantum mechanics and general relativity. Related work: Two complementary conceptual clarifications within standard general relativity are developed separately. Orbits as Inertial States: Rethinking Rest in General Relativity (Zenodo) isolates the distinction between inertial rest (geodesic motion) and spatial fixation (non-geodesic constraint) in curved spacetime. Geodesics as Regimes of Persistence (Zenodo) unpacks how the geodesic classification (timelike/null/spacelike), via the sign of ds², encodes distinct modes of physical realizability—persistence with proper time, persistence without proper time, and geometric relations without physical worldlines. Revision note (5 Feb 2026): Deepened the dark-matter analysis by extending its functional role to galactic scales, clarifying how dark matter halos act as distributed geometric buffers that stabilize increasing ordering demand without particle-level rendering. Integrated supermassive black holes into the same constraint-management framework, describing them as localized rupture boundaries that arise when buffering capacity is exceeded, rather than as independent gravitational anomalies. Provided a unified structural explanation for observed halo–black hole scaling relations, including the M–σ correlation, as necessary outcomes of balanced buffering and rupture within a single representational closure. Clarified that galaxies are treated as coherent representational systems, in which extended dark matter curvature and central singularities jointly delimit the operational bounds of deterministic metric closure. No new forces, particles, or dynamical equations are introduced; all additions remain architectural extensions consistent with general relativity and ΛCDM phenomenology. Correspondence: Peter Nowicki — peternowicki@proton.me
This work presents an axiomatic and structural reconstruction of core elements of quantum mechanics. Starting from minimal principles — symmetry under vanishing preference, normalization, consistency of probability assignments, and coherence-preserving dynamics — we derive several central features of the quantum formalism rather than postulating them. Key results include: A geometric derivation of the constants 1/21/\sqrt{2}1/2 and 1/21/21/2 from symmetry and normalization. A theorem-level derivation of the Born rule (including the qubit case) from noncontextuality and additivity. A reconstruction of Schrödinger dynamics from reversible norm-preserving structure. A derivation of the tensor-product structure for composite systems from composition axioms and local tomography, with entanglement emerging as a necessary consequence. Formal treatment of Bell–CHSH nonlocality, Tsirelson’s bound, and no-signalling. A conditional reconstruction of complex Hilbert space structure from intrinsic phase dynamics and compositional consistency. The manuscript is self-contained and framed in standard mathematical-physics language. It does not propose modifications to quantum mechanics, but instead clarifies why many of its defining structures arise inevitably from deeper structural constraints. Prior computational and model-based work by the authors (including diagnostic toy models exploring phase locking, coherence stabilization, and recursive-time dynamics) is acknowledged but intentionally not reproduced here, in order to keep the present work focused on axiomatic structure rather than model-specific architecture. This upload is intended as a foundations and reconstruction contribution, suitable for readers interested in the mathematical and conceptual structure of quantum theory.
Modern theoretical physics rests on two highly successful but conceptually distinct frameworks: quantum mechanics and general relativity. While both theories are experimentally confirmed to high precision within their respective domains, they rely on fundamentally different starting points. General relativity takes spacetime as a primitive geometric structure, whereas quantum mechanics is formulated in terms of abstract state spaces without intrinsic spacetime meaning. Most approaches to quantum gravity attempt to reconcile this tension by modifying, quantizing, or discretizing spacetime itself. Even in approaches where spacetime is said to be “emergent,” it typically remains the primary conceptual backdrop on which physical processes are defined. Despite extensive efforts, there is no consensus on whether spacetime should be regarded as fundamental or derivative. In this work, a more radical starting point is explored. Rather than modifying spacetime or its geometry, we ask whether spacetime can be excluded entirely from the fundamental layer of the theory and recovered only at a later, operational stage. The central question is not how spacetime behaves, but whether the notion of “what lies between physical objects” must be spatial or temporal at the most fundamental level. We propose a framework—referred to here as Super Relativity (SR)—based on a single pre-geometric postulate: the existence of a monotonically expanding set of possible quantum configurations, referred to as the flux. Formally, this flux is represented as a monotone, σ-finite family of capacity measures on a common configuration space (introduced in Section 2). This postulate deliberately refrains from assuming spacetime, time ordering, metric structure, causality, or dynamics. Within this pre-geometric core, two derived, dimensionless notions are introduced: utilization, describing the realization of configurations, and saturation, defined as the ratio between utilized and available configurations. A central structural element of SR is the strict separation between a core layer and an interface layer. In the core layer, all quantities are pre-geometric and dimensionless, and no reference is made to space, time, motion, energy, or interaction. Only at the interface layer are operational notions introduced, including clocks, rulers, and signal propagation. Spacetime, in this construction, is not a dynamical entity but an effective bookkeeping structure that encodes relative rates of change once a calibration to physical units is performed. Within this framework, gravitational phenomena do not originate from spacetime curvature taken as fundamental. Instead, they arise from variations in saturation that, at the interface level, manifest as uniform rescalings of physical processes. When expressed in geometric language, these rescalings reproduce the standard predictions of general relativity, including gravitational time dilation and the equivalence between gravitation and acceleration. The invariant local speed of light is not postulated but follows as a derived consequence, since both clock rates and signal propagation are affected identically by the same underlying saturation mechanism. The aim of this paper is not to introduce new empirical predictions beyond those of general relativity, nor to present a complete theory of quantum gravity. Rather, the objective is foundational: to demonstrate that the mathematical structure of general relativity can be reconstructed from a single pre-geometric postulate without assuming spacetime as part of the fundamental ontology. In this sense, SR should be understood as a reconstruction and reinterpretation of known physics, rather than as a competing dynamical theory. An extended and fully explicit formulation of the framework, including all intermediate steps, is available in a companion preprint (version V12) deposited on Zenodo. The present paper restricts itself to the minimal conceptual and mathematical structure required to establish logical consistency and to demonstrate the emergence of general-relativistic behavior at the interface level.
This paper introduces Axiom 0, a minimal foundational principle for physical reality: the impossibility of any globally closed description of the total correlational structure. Rather than postulating space, time, dynamics, locality, or physical laws as primitive, the framework assumes only: (i) the existence of a correlational structure, (ii) the structural impossibility of complete self-closure, and (iii) consistency under partial comparison. From these ingredients, the paper shows how: physical laws emerge as stabilizing regularities of incomplete descriptions, time, dynamics, and geometry arise as effective, regime-dependent structures, irreversibility follows from projection and information loss, and why no description can be both exact and globally complete. Non-closure is treated as an ontological constraint, not as epistemic ignorance or observer dependence. Physical reality exists precisely because complete closure is impossible, independently of observation or modeling. The paper does not attempt to replace existing physical theories or derive numerical constants. Instead, it provides a structural foundation within which effective physical theories (quantum, classical, relativistic, and open-system regimes) can be consistently understood as emergent and domain-limited. This work is intended as a conceptual and structural foundation for correlational and relational approaches to fundamental physics, clarifying the origin of laws, dynamics, and physical regularity without invoking additional ontological postulates.