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.
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.
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.
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.
The Coherence Field: A Generative Model for Coherence-Driven Physical Law presents a mathematically rigorous and internally consistent formulation of the Coherence Field — an underlying principle from which classical mechanics, quantum dynamics, and general relativity emerge as structured reductions. At the foundation of the framework is a coherence functional defined on a Hilbert space of configurations. Instead of taking equations of motion as fundamental, the paper starts from a single scalar quantity, “kappa,” that measures how harmonically aligned a configuration is. The Coherence Field is defined as the derivative of kappa, and the evolution of the system is given by a gradient flow that drives configurations toward higher coherence. Under mild regularity and boundedness assumptions on kappa, the paper proves that this coherence-gradient evolution is globally well-posed and has unique solutions. In this view, stable physical behavior corresponds to “harmonic closure”: points where the coherence field vanishes and the second derivative (the Hessian) is positive definite, so the configuration sits at a genuine local minimum of kappa. This provides a precise notion of coherence-based stability that applies across different physical regimes. The paper then shows how standard theories arise as special cases of this more general structure: Classical mechanics appears when kappa is chosen to be the Hamiltonian and the coherence flow is rotated by the symplectic structure. In this case, the coherence gradient reproduces Hamilton’s equations of motion. Quantum mechanics appears when kappa is chosen as the usual quantum energy functional of a wavefunction (kinetic plus potential energy). The coherence gradient then yields the imaginary-time Schrödinger equation, which, under Wick rotation, becomes the standard real-time Schrödinger equation. This connects the coherence picture directly to established variational and decoherence-based perspectives on quantum dynamics. General relativity appears when kappa is taken to be the Einstein–Hilbert action with the Gibbons–Hawking–York boundary term. Harmonic closure of this geometric coherence functional recovers the vacuum Einstein equations, describing how spacetime curvature evolves in the absence of matter. These reductions are summarized in a unification proposition: with different structural choices of kappa and appropriate symmetries (symplectic for Hamiltonian mechanics, unitary for quantum mechanics, and diffeomorphism invariance for general relativity), the same coherence-gradient principle generates three major physical regimes. The paper also introduces a nontrivial spin-glass example, where kappa includes both the usual Ising-type interaction term and an additional “coherence alignment” term that penalizes deviation from a reference pattern. This construction separates “coherence drift” from ordinary energy drift and leads to a new coherence-based order parameter. As temperature or control parameters change, the onset of ordered phases is predicted to correlate with a sharp drop in the norm of the coherence gradient. This yields a concrete, falsifiable experimental and computational signature for the Coherence Field framework. This work is part of the broader Δ.72 Coherence Canon, which develops coherence mathematics, tensor geometry, harmonic closure, and the concept of “time as vibration” as a deeper generative structure behind high-instability problem classes in physics, computation, and complex systems. Within that larger canon, the Coherence Field plays the role of a generative physics layer: a single mathematical core from which multiple physical theories emerge as coherent projections.
Foundational problems in physics—including quantum measurement, spacetime emergence, gravitational dynamics, nonlocality, the arrow of time, and the status of physical existence—are typically addressed in isolation, via model-dependent extensions or interpretive assumptions. This work proposes a different approach. We introduce a constraint-based framework, the Closure Admissibility Principle (CAP), which specifies minimal structural conditions any physical description must satisfy in order to be globally consistent. CAP is formulated in operational terms, using admissibility of states, recoverability under refinement, and stability of closed records, without assuming spacetime, dynamics, or ontology a priori. We show that enforcing these constraints induces a unifying closure structure on law-space, from which several persistent foundational puzzles are resolved as structural consequences rather than postulates. In particular, collapse is reclassified as record selection, spacetime and gravity emerge only in compressible regimes, General Relativity appears as an infrared universality class rather than a fundamental law, singularities correspond to failures of admissible description, and null (“nothing”) models are excluded as inadmissible fixed points. The framework is explicitly falsifiable via operational and weak-field tests, and its scope and limits are stated precisely. The results suggest that many foundational paradoxes arise not from incomplete dynamics, but from admitting globally incoherent physical descriptions.
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.
Modern physics provides empirically complete and highly successful descriptions of local dynamics. General relativity specifies the causal evolution of spacetime geometry, and quantum mechanics specifies the unitary evolution of states. Despite this success, both frameworks leave implicit a foundational question: when a dynamically admissible configuration can be regarded as physically realized as part of a coherent world. This work introduces a minimal, non-dynamical realization criterion that formally closes this gap. Physical realization is defined as a global, temporally organized admissibility condition constrained by relativistic causality. The criterion does not modify any local equations of motion, introduce new forces, fields, particles, or degrees of freedom, nor alter the mathematical structure of existing theories. Instead, it identifies realization as an organizational condition required for dynamical solutions to become physically instantiated. A minimal causal bound T = L / c is shown to follow directly from relativistic causal structure, implying a finite organizational time for global coherence across a spatial extent L. The associated inverse scale Ω = c / L is clarified as a structural constant rather than a dynamical frequency: it has no oscillatory interpretation, carries no energy, and does not represent a physical process. Its role is purely limiting—it marks the minimal global temporal orientation required for realization to persist. Within this framework, classical gravitational optics, delayed global geometric organization, and quantum outcome realization arise as direct consequences of the same realization criterion. The contribution of this work is exclusively structural: it makes explicit a condition already implicit in successful physical theories and provides a formal closure without extending or revising their dynamics. This paper concludes a broader research program on temporal realization, gravitational organization, and global coherence by isolating realization as a necessary condition for physics to describe a world at all.