This paper develops a reciprocity‑based account of observation that treats interfaces as primary objects and links informational and geometric structure via a dimensionless reciprocity constant Ξ. On the informational side, a measuring instrument is modeled by a Fisher or Bures / quantum Fisher metric on a statistical manifold, from which an intrinsic scalar curvature ℛ[g_I] is constructed. On the geometric side, the Raychaudhuri equation is packaged into a focusing bracket ℬ, normalized to a dimensionless quantity ℬ̃. The central principle, Observation as Mutual Curvature (OMC), states that for a fixed instrument class operated in a stationary regime, a linear combination of informational curvature and focusing curvature is approximately invariant under reciprocity‑equivalent implementations of the same instrument. This motivates an operational reciprocity constant Ξ, obtained by regressing changes in ℛ[g_I] against changes in ℬ̃ across calibrated configurations. The framework is “interface‑first”: a Noether‑type balance theorem for moving boundaries yields a cut‑independent boundary ledger that tracks fluxes of energy, helicity, and information at photonic interfaces. Combining these elements, the paper defines Ξ‑light, a reciprocal dark–luminous architecture that employs quasi–bound states in the continuum, coherent‑perfect absorption, anapole modes, and time‑modulated media, together with a trap–meter–release protocol for estimating Ξ. A cosmological roadmap based on weak gravitational lensing is outlined, and the interpretive implications for objectivity and the role of information in physics are discussed. No new microphysics is assumed; all novel structures appear as balance principles, definitions, or falsifiable conjectures built on standard general relativity, quantum theory, and electromagnetism. Keywords: observation; information geometry; Fisher information; quantum Fisher information; Raychaudhuri equation; Noether charges; interfaces; metasurfaces; bound states in the continuum; anapole modes; coherent perfect absorption; photonic time crystals; weak gravitational lensing; reciprocity constant; Ξ‑light.
This paper develops a reciprocity‑based account of observation that treats interfaces as primary objects and links informational and geometric structure via a dimensionless reciprocity constant Ξ. On the informational side, a measuring instrument is modeled by a Fisher or Bures / quantum Fisher metric on a statistical manifold, from which an intrinsic scalar curvature ℛ[g_I] is constructed. On the geometric side, the Raychaudhuri equation is packaged into a focusing bracket ℬ, normalized to a dimensionless quantity ℬ̃. The central principle, Observation as Mutual Curvature (OMC), states that for a fixed instrument class operated in a stationary regime, a linear combination of informational curvature and focusing curvature is approximately invariant under reciprocity‑equivalent implementations of the same instrument. This motivates an operational reciprocity constant Ξ, obtained by regressing changes in ℛ[g_I] against changes in ℬ̃ across calibrated configurations. The framework is “interface‑first”: a Noether‑type balance theorem for moving boundaries yields a cut‑independent boundary ledger that tracks fluxes of energy, helicity, and information at photonic interfaces. Combining these elements, the paper defines Ξ‑light, a reciprocal dark–luminous architecture that employs quasi–bound states in the continuum, coherent‑perfect absorption, anapole modes, and time‑modulated media, together with a trap–meter–release protocol for estimating Ξ. A cosmological roadmap based on weak gravitational lensing is outlined, and the interpretive implications for objectivity and the role of information in physics are discussed. No new microphysics is assumed; all novel structures appear as balance principles, definitions, or falsifiable conjectures built on standard general relativity, quantum theory, and electromagnetism. Keywords: observation; information geometry; Fisher information; quantum Fisher information; Raychaudhuri equation; Noether charges; interfaces; metasurfaces; bound states in the continuum; anapole modes; coherent perfect absorption; photonic time crystals; weak gravitational lensing; reciprocity constant; Ξ‑light.
The Fisher information of a binary quantum measurement with visibility V is I(V) = 1/(1-V²) = γ²(V), the squared Lorentz factor from special relativity. This identity, proven in the companion anchor preprint, holds only for qubits: for N≥3 quantum systems, the Weyl curvature tensor obstructs the conformal equivalence between the Bures metric of quantum state space and the Beltrami-Klein metric of hyperbolic/relativistic geometry. Five independent research programs—in quantum optics, condensed matter, stochastic thermodynamics, holography, and quantum measurement theory—have converged on this same γ² structure over the past decade. This document is the interpretive companion to the anchor preprint. It traces the implications of the identity from fundamental physics (a deductive chain through five published theorems connecting γ² to Einstein's equations) through cosmology (dark energy, dark matter, fine-tuning as Fisher optimality), consciousness (entropy production as the measurement process experienced from inside), biology (evolution, aging, cancer as Fisher information dynamics), and computation (transformer attention as Fisher-Rao geometry). It introduces the concepts of "beautiful change" (structured, self-organized entropy production as the distinguishing feature of rich consciousness) and the "downprojection hypothesis" (experienced spacetime as a conformal restriction of a higher-dimensional information-geometric manifold). All claims are explicitly labeled by epistemic status across four tiers: proven mathematical identity, published theorems by independent groups, strong circumstantial evidence, and conjecture. Falsifiable predictions are provided, two already experimentally confirmed. The proven mathematics stands independently of the interpretive framework built upon it.
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.
Complementarity-First Foundational Release III develops reciprocal phase architecture, conditional gauge and incidence geometry, finite Lorentzian connection selection, and relational quantum-information tasks. This paper synthesizes the eight research preprints and one reproducibility dataset in Waves A–C without transferring theorem ownership or treating their separately admitted carriers as a single derived physical system. The release is organized by four distinctions: structural admission versus conditional selection; geometric covariance versus operational implementation; restricted agreement versus complete identification; and mathematical existence versus a resource-accounted realization. The reciprocal quantum construction separates local inclusion, coherent completion, entanglement, finite projective valuation, and individual outcomes. Its synthetic biphoton companion distinguishes image intensity from phase-sensitive entanglement evidence. The geometric papers distinguish a derived compact phase-frame type from electromagnetic gauge interpretation and constitutive dynamics, anti-linear opposite-weight pairing from same-bundle reversal, an indefinite incidence form from positive records, and geometric-section agreement from independent connection variation. The Wave C papers supply finite addressing classifications, task- and record-relative recovery, encoded-preparation advantages, and exact exchange constructions with trajectory and timing bounds. Cross-wave comparisons locate genuine imported interfaces and identify bridges that remain absent, including the passage from finite Born-form valuation to general instruments and from a recorded group-error model to a physical timing-error model. Analytic proofs, finite calculations, numerical certificates, recorded replays, and scoped Lean verification are assigned distinct evidentiary roles. The contribution is a source-attributed scientific synthesis and an explicit dependency and residual-premise map, not a new primitive derivation of quantum theory, electromagnetism, or gravity.
Mutual Witness Theory (MWT) proposes a unifying physical principle: a system persists only to the extent that its state is continuously verified through reciprocal interaction. This requirement —mutual witness—underlies coherence in quantum mechanics, curvature in general relativity, conservation laws, and thermodynamic behavior. In this paper, I extend the formalism introduced in Papers I and II to show that time, energy, gravitation, entropy, entanglement, and cosmological structure can all be understood as consequences of how well systems sustain relational coherence across interaction. The framework does not modify existing physical equations. Instead, it identifies a deeper invariant beneath them: continuity of witness across all frames. When coherence is stable, relativistic behavior emerges; when coherence is fragmented or intermittently maintained, quantum behavior arises. Time becomes the measurable gradient of coherence adjustment, energy becomes the persistence of relational structure, and entropy becomes the diffusion of witness into wider degrees of freedom. General relativity and quantum mechanics appear as opposite limits of the same relational requirement. Cosmologically, the theory interprets dark matter–like phenomena as the gravitational manifestation of coherence-sourced, non-electromagnetic resonance fields, and dark energy as a large-scale coherence gradient. Black holes are treated not as sites of information loss, but as boundaries where external witness fails while internal relational structure persists. The framework yields testable predictions involving coherence-dependent time rates, gravitational curvature scaling with coherence density, entropy–time coupling, and cosmological signatures linked to the history of large-scale ordering. MWT offers a relational interpretation that preserves all established physics while clarifying the single structural requirement that allows quantum theory, relativity, thermodynamics, and cosmology to coexist: no physical process is one-directional, and no system persists without mutual witness. The resulting structure constitutes a unified description of physical law grounded in coherence, reciprocity, and information-preserving interaction. This work serves as the third installment in the Mutual Witness Theory series, following:(1) Perez (2025), “Mutual Witness, Resonance Tethers, and Coherence Fields: Toward a Quantum-Cosmological Unification of Measurement and Dark Matter”;(2) Perez (2025), “Mutual Witness Dynamics: A Symmetric Lindblad Framework for Dark Sector Resonance Fields.”It consolidates the conceptual, relational, and thermodynamic extensions into a unified framework for time, energy, gravitation, entanglement, and cosmology.
Title: The Invariance of the Interface: Why Fisher Information Reappears in Derivations of Physical Law Description This note addresses a persistent conceptual gap in “information physics” programs that derive familiar dynamical laws by extremizing Fisher-information-based functionals: why Fisher information, rather than some other statistical functional? The proposed answer is meta-explanatory. The observer–world interface is modeled as probabilistic, and “objectivity” is formulated as Observer Equivalence (OE): invariance under reparameterization and monotonicity under coarse-graining (information-loss channels). Under these constraints, Chentsov-type characterization results single out the Fisher information metric as the unique local Riemannian geometry on the space of probability distributions (up to an overall scale). Fisher information is thus treated not as an axiom but as an invariance residue forced by OE at the probabilistic interface. To connect geometry to dynamics, the note introduces an explicit postulate—Informational Inertia—motivated as an information-geometric analogue of least-action/geodesic principles: in the absence of forcing, interface states evolve along paths of minimal statistical resistance (geodesics of the OE-fixed geometry), with physical constraints supplying the remaining “potential” structure. A single exemplar is presented: revisiting the Madelung/Reginatto (Hall–Reginatto) route to the Schrödinger equation, where the “quantum potential” arises as the geometric term associated with the Fisher penalty for reshaping the probability density. The overall scale (and thus ℏ) is explicitly acknowledged as empirical input: OE fixes the form of the geometry, not its scale. Keywords observer equivalence; Fisher information; information geometry; Chentsov theorem; coarse-graining; monotone metrics; Schrödinger equation; Madelung transformation; Reginatto; foundations of physics How to cite Ullman, G. “The Invariance of the Interface: Why Fisher Information Reappears in Derivations of Physical Law.” Zenodo. https://doi.org/10.5281/zenodo.18495542 Notes on AI assistance This manuscript was prepared with assistance from large language models for drafting, editing, and LaTeX formatting. The author takes full responsibility for the technical content, claims, and references.
Tri-Wave Geometry of Quantum Information: Curvature, Reciprocity, and Emergent Structure introduces a unified mathematical framework that links quantum information, quantum field theory, complexity dynamics, and gravitational geometry through three fundamental operators: curvature reciprocity , and log-log emergence. The paper develops these operators from first principles and demonstrates how their interaction gives rise to quantum behavior, information flow, multi-scale structure, and the geometry of spacetime. The Tri-Wave model reframes several core concepts in physics—including entanglement, renormalization, complexity growth, and curvature—as manifestations of a single underlying geometric structure. Applications to quantum computing, QFT, and gravity are explored, along with implications for quantum measurement, superposition, and the informational foundations of physical law. The manuscript was developed through a novel human–AI collaborative methodology, blending human conceptual exploration with AI-assisted mathematical refinement and structural articulation. This work stands as an early example of AI-augmented theoretical research and offers a potential foundation for future inquiry into information-based interpretations of quantum mechanics and geometric unification.