Abstract This paper introduces Existential Relativity (ER) as a context-indexed mathematical framework for physical existence and change. ER asserts that existence is not a context-free property of objects, fields, or excitations within an external container, but a locally defined in/out distinction generated by an internally specified basis-set, ruler, constraint system, and complement. Static existence is defined as a distinction that is a nontrivial partition of a context. Dynamic change is formalized as a lawful, interaction-conditioned transition from one context-indexed distinction to another. Transitions are generally not isolated, as they may be conditioned by many factors, such as static distinctions, boundaries, fields, apparatus settings, background structures, or simultaneous transitions of other contexts. Cause and effect are not considered primitive assumptions in ER, but as derived features of lawful transition when one distinction directionally conditions another relative to a selected ordering basis. Derivation and recovery constraints for the major models of physics are presented in this paper. Classical Hamiltonian mechanics is recovered through symplectic, interaction-conditioned transitions. Born-rule probability is motivated through normalization, additivity over exclusive distinctions, and context-consistency in Hilbert-space event structures. Schrödinger evolution follows from reversible transitions preserving quantum distinguishability, while entanglement corresponds to nonfactorizable joint transition. Quantum field theory is incorporated by treating fields as context-indexed operator structures and particles as excitation distinctions. Lorentzian signature, general relativity, gauge connections, the Standard Model gauge group, and conservation laws are treated as context-specific recoveries. The paper proposes empirical programs to test whether context-boundary residuals associated with ER can improve existing physical explanations.
Abstract This paper introduces Existential Relativity (ER) as a context-indexed mathematical framework for physical existence and change. ER asserts that existence is not a context-free property of objects, fields, or excitations within an external container, but a locally defined in/out distinction generated by an internally specified basis-set, ruler, constraint system, and complement. Static existence is defined as a distinction that is a nontrivial partition of a context. Dynamic change is formalized as a lawful, interaction-conditioned transition from one context-indexed distinction to another. Transitions are generally not isolated, as they may be conditioned by many factors, such as static distinctions, boundaries, fields, apparatus settings, background structures, or simultaneous transitions of other contexts. Cause and effect are not considered primitive assumptions in ER, but as derived features of lawful transition when one distinction directionally conditions another relative to a selected ordering basis. Derivation and recovery constraints for the major models of physics are presented in this paper. Classical Hamiltonian mechanics is recovered through symplectic, interaction-conditioned transitions. Born-rule probability is motivated through normalization, additivity over exclusive distinctions, and context-consistency in Hilbert-space event structures. Schrödinger evolution follows from reversible transitions preserving quantum distinguishability, while entanglement corresponds to nonfactorizable joint transition. Quantum field theory is incorporated by treating fields as context-indexed operator structures and particles as excitation distinctions. Lorentzian signature, general relativity, gauge connections, the Standard Model gauge group, and conservation laws are treated as context-specific recoveries. The paper proposes empirical programs to test whether context-boundary residuals associated with ER can improve existing physical explanations.
Abstract This paper introduces Existential Relativity (ER) as a context-indexed mathematical framework for physical existence and change. ER asserts that existence is not a context-free property of objects, fields, or excitations within an external container, but a locally defined in/out distinction generated by an internally specified basis-set, ruler, constraint system, complement, admissible transformation class, and boundary structure. Static existence is defined as a distinction that is a nontrivial partition of a context. Dynamic change is formalized as a lawful, interaction-conditioned transition from one context-indexed distinction to another. Transitions are generally not isolated, as they may be conditioned by static distinctions, boundaries, fields, apparatus settings, background structures, or simultaneous transitions of other contexts. Derivation, recovery, and reinterpretation constraints for the major models of physics are presented. Classical Hamiltonian mechanics and quantum field theory are recovered as special context structures. Born-rule probability, continuous Schrödinger evolution, Lorentzian signature, and gauge connection result from conditional derivations under stated auxiliary assumptions. General relativity is developed in greater depth through the Proposition of Metric-Stress-Energy Co-Admissibility, in which diffeomorphism covariance, shared variational closure, boundary consistency, covariant balance, and local second-order metric dynamics constrain the admissible coupling between a metric-ruler context and a matter context to the Einstein form within the declared regime. The paper also specifies admissibility conditions for contexts and transitions and proposes micro-to-macro emergence as the primary empirical application.
We challenge the common view that relativity and quantum formalisms compel a static block-universe ontology. Instead, we show that Existential Realism (ER) – can be formulated as an ontological extension of the specific physical models studied here, leaving empirical predictions unchanged so long as the added ER structure remains empirically idle. First, we clarify that the mathematical formalism of physics is neutral: one can impose a preferred foliation or an existence predicate without changing the equations. Second, we explicitly construct ER-compatible models for Minkowski spacetime (special relativity) and a finite-dimensional quantum system. In these Minkowski-spacetime and finite-dimensional quantum toy models, we show that the standard relativistic dynamical laws, Born-rule calculations, and unitary evolution between measurements are preserved, while the ER additions remain extra ontological structure. More precisely, we have constructed models that are empirically equivalent and dynamically identical while differing in their ontological assignments, thereby demonstrating underdetermination in a model-theoretic sense. We conclude that relativity and quantum theory, in the model presented here, do not logically force eternalism, leaving ER as a viable alternative ontology.
This paper introduces the Relativity of Information Frames (RIF), a foundational framework that precedes and constrains dynamical theories. RIF treats information frames—σ-algebras of distinguishable events—as the fundamental objects of physical description, and formulates interaction as the joint realization of such frames subject to a symmetry principle: no information frame may be privileged over another. From this principle alone, the framework derives a canonical restriction on joint event structures. We prove the existence of a distinguished σ-algebra—the pointer algebra—which is the unique maximal event algebra compatible with perspectival symmetry and the existence of consistent probability assignments. Any empirical model admits a global probability measure on this algebra, while any strict extension generically fails to do so, reintroducing contextuality. These results impose non-trivial structural constraints that any admissible dynamics must respect. The framework is applied to quantum theory, not by postulating dynamics, but by showing how its core structures arise necessarily from informational consistency. Observables appear as perspectival maps, state update corresponds to interaction-induced coarse-graining, the Born rule follows from a martingale structure on the induced σ-algebra filtrations, Wigner-type scenarios are consistent, and unitary evolution is reinterpreted as gauge freedom in joint descriptions rather than ontic time evolution. RIF does not replace dynamical theories; it delimits them. It identifies which event structures, probability assignments, and symmetries are admissible prior to dynamics, and therefore clarifies what features of quantum theory are structural necessities rather than contingent dynamical postulates. The framework further implies intrinsic irreversibility, a relational notion of locality, and constraints on emergent geometric structure, which any subsequent dynamical formulation must accommodate.
Standard quantum descriptions treat interference, entanglement, measurement, and no signaling as separate operational rules, yet their shared structural features point to a deeper geometric origin. In this work we identify that origin by developing the analytic exterior: a non‑spatiotemporal analytic domain specified intrinsically by a single analytic direction, a compatibility condition, and a singularity–residue geometry. A relational bundle then supplies the curvature and boundary projections that generate the operational structure of the amplitude calculus. This intrinsic specification requires neither explicit analytic functions nor global coordinates. Within this analytic framework, familiar quantum structures emerge naturally as boundary effects. The Hilbert‑space inner product appears as the boundary pairing induced by residue geometry; analytic flow along the distinguished direction reveals the Schrödinger‑type evolution already encoded in analytic displacement; and boundary evaluation combined with normalization invariance yields the Born rule as the unique probability assignment compatible with the analytic exterior. Interference, entanglement, measurement, and no signaling thus arise not as independent postulates but as geometric consequences of singularities, curvature, and contextual transport. The relational object introduced in [6] is recovered as the boundary value of an analytic‑exterior amplitude kernel, exposing the analytic origin of its interference and measurement properties. The analytic exterior therefore provides a unified, non‑spatiotemporal foundation in which amplitudes, probabilities, and correlations are boundary manifestations of a single underlying analytic geometry. Quantum mechanics emerges as the boundary theory of this analytic structure, offering a unified and conceptually coherent reformulation parallel in spirit to the relational architecture developed in our earlier work. Version 1.1. This revision adds a new subsection clarifying the ontological divergence between the analytic–exterior framework and the standard Lorentzian manifold ontology. The update explains why the analytic exterior cannot arise within the classical spacetime model and introduces the notion of mathematical ontology as a representational constraint. No mathematical results or definitions have been changed.
We develop a pregeometric reconstruction framework in which quantum mechanics, gauge symmetry, probabilistic structure, matter, Lorentzian spacetime geometry, gravitation, and physical constants emerge from recursively stabilized coherent relational transport organization. The framework begins from a primitive causal-relational substrate consisting only of fluctuating accessibility relations and compositional transport structure. No background spacetime manifold, metric geometry, particle ontology, or external temporal parameter is assumed fundamentally. The theory further proposes that the preconditions underlying Einsteinian physics must already exist at the pre-geometric level as deeper relational consistency principles. Lorentz invariance, causal structure, covariance, conservation laws, and gravitational equivalence are interpreted as emergent macroscopic expressions of more primitive coherent accessibility constraints. A generalized spectral transport operator governs coherent relational evolution and generates stable eigensectors corresponding to persistent physical structure. Quantum mechanics emerges from coherent compositional consistency and norm-preserving recursive transport flow. Gauge symmetry emerges as local redundancy of coherent transport representation. Classical mechanics emerges through stationary coherent transport stabilization. A reconstruction of the Born rule is proposed in which quadratic probability amplitudes arise from multiplicative persistence consistency under independent coherent composition. Lorentzian spacetime geometry emerges statistically from stabilized causal accessibility organization, while gravitation emerges thermodynamically as equilibrium relaxation of coherent accessibility geometry. The framework further proposes that physical constants correspond to frozen stability invariants selected during primordial coherent transport evolution. In particular, the fine-structure constant is interpreted as a stable surviving coherent phase-accessibility ratio associated with recursive phase closure. The theory therefore attempts not merely to reproduce known equations, but to explain why physical reality universally organizes itself through Hilbert structure, gauge redundancy, localization, Lorentzian geometry, and thermodynamic gravitational dynamics. In particular, the framework proposes that Einsteinian spacetime physics emerges from deeper pre-Einsteinian coherent relational conditions governing recursive transport accessibility before spacetime itself exists.
This record presents a review and synthesis of a five-part research series devoted to clarifying the domain of validity of quantum descriptions. The work introduces an explicit process–event framework, distinguishing between continuous quantum processes described by the formalism and their irreversible realization as physical events. Rather than proposing new dynamics or modifying quantum theory, the synthesis operates at a meta-level, making explicit the conditions under which standard quantum concepts—such as Planck’s relation, Born’s rule, conservation laws, entanglement, and Bell-type constraints—acquire physical meaning. A minimal realization criterion, expressed schematically as a resonant event threshold, delineates when a quantum description corresponds to an empirically accessible event rather than a purely formal process. By consistently maintaining the process–event distinction, the framework resolves longstanding conceptual tensions surrounding measurement, nonlocality, conservation laws, and information without altering the mathematical structure or empirical predictions of quantum mechanics.