The original article The Global Entropic Consistency Principle (GEC): A Strictly Physical Axiomatic Framework formulated GEC as a physical principle governingclosed quantum systems through global entropic invariance and compensatory informational flux. This essay argues that the same axioms that define GEC physically alsopossess a deeper mathematical–ontological status: they express necessary conditions for any reality that is mathematically representable. Under this interpretation, GEC acquires a dual character. It remains a physical principle describing the informational dynamics of closed quantum systems, yet simultaneously functions as a meta-principle of mathematical reality, constraining the structure of any world that can be mathematically formulated. The three axioms ofGEC—distinguishability, boundedness (derived from the existence of a horizon with finite entropy at a given moment), and global–local consistency—are therefore not onlyphysical requirements but also mathematical necessities. The essay thus positions GEC as a bridge between ontology and epistemology: a principle that governs both what can exist and what can be known.
The original article The Global Entropic Consistency Principle (GEC): A Strictly Physical Axiomatic Framework formulated GEC as a physical principle governingclosed quantum systems through global entropic invariance and compensatory informational flux. This essay argues that the same axioms that define GEC physically alsopossess a deeper mathematical–ontological status: they express necessary conditions for any reality that is mathematically representable. Under this interpretation, GEC acquires a dual character. It remains a physical principle describing the informational dynamics of closed quantum systems, yet simultaneously functions as a meta-principle of mathematical reality, constraining the structure of any world that can be mathematically formulated. The three axioms ofGEC—distinguishability, boundedness (derived from the existence of a horizon with finite entropy at a given moment), and global–local consistency—are therefore not onlyphysical requirements but also mathematical necessities. The essay thus positions GEC as a bridge between ontology and epistemology: a principle that governs both what can exist and what can be known.
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.
The emergence of an objective reality in line with the laws of the microscopic world has been the focus of longstanding debates. Recent approaches seem to have reached a consensus at least with respect to one aspect, namely, that the encoding of information about a given observable in a physical degree freedom is a necessary condition for such an observable to become an element of the physical reality. Taking this as a fundamental premise and inspired by quantum information theory, here we build an axiomatization for quantum realism---a notion of realism compatible with quantum theory. Our strategy consists of listing some physically motivated principles able to characterize quantum realism in a ``metric'' independent manner. We introduce some criteria defining monotones and measures of realism and then search for potential candidates within some celebrated information theories---those induced by the von Neumann, R\'enyi, and Tsallis entropies. We explicitly construct some classes of entropic quantifiers, among which some are shown to satisfy all the proposed axioms and hence can be taken as faithful estimates for the degree of reality (or definiteness) of a given physical observable. Hopefully, our framework may offer a formal ground for further discussions on foundational aspects of quantum mechanics.
This paper introduces the Total Entropic Quantity (TEQ) framework, a structural reformulation of quantum theory grounded in two foundational axioms. Axiom 0 posits entropy as a generative constraint: a geometric principle that determines which configurations can stably distinguish themselves, independent of space, time, or dynamics. Here, entropy is defined as a curvature-functional over distinguishability configurations, preserving only those patterns that remain stable under finite informational resolution---that is, structures not dissolved by coarse-graining or limited observability. Axiom 1, the Minimal Principle (MP), selects from these structures those that are maximally stable under entropy-weighted variation. From this entropic foundation, core elements of quantum theory---including the Born rule, quantization, and Schrödinger dynamics---emerge as special cases of entropy-stabilized geometry. The framework derives an entropy-weighted path integral and introduces a corrected Schrödinger equation that governs evolution in regimes of finite entropy curvature. In the high-resolution limit (β→∞), TEQ reduces to standard unitary quantum mechanics; in more general regimes, entropy flow deforms canonical dynamics, linking decoherence, dissipation, and gravitational curvature. TEQ reinterprets physical law as emergent structure within the geometry of distinguishability, rather than as imposed dynamics on a fixed spacetime background.
This paper introduces the Total Entropic Quantity (TEQ) framework, a structural reformulation of quantum theory grounded in two foundational axioms. Axiom 0 posits entropy as a generative constraint: a geometric principle that determines which configurations can stably distinguish themselves, independent of space, time, or dynamics. Here, entropy is defined as a curvature-functional over distinguishability configurations, preserving only those patterns that remain stable under finite informational resolution---that is, structures not dissolved by coarse-graining or limited observability. Axiom 1, the Minimal Principle (MP), selects from these structures those that are maximally stable under entropy-weighted variation. From this entropic foundation, core elements of quantum theory---including the Born rule, quantization, and Schrödinger dynamics---emerge as special cases of entropy-stabilized geometry. The framework derives an entropy-weighted path integral and introduces a corrected Schrödinger equation that governs evolution in regimes of finite entropy curvature. In the high-resolution limit (β→∞), TEQ reduces to standard unitary quantum mechanics; in more general regimes, entropy flow deforms canonical dynamics, linking decoherence, dissipation, and gravitational curvature. TEQ reinterprets physical law as emergent structure within the geometry of distinguishability, rather than as imposed dynamics on a fixed spacetime background.
Beyond Causality: Temporal Geometry, Informational Consistency, and the Foundations of Physical Time What if the deepest mystery of time is not whether the past can be reached, but whether causality itself is more fundamental than the physical laws through which we describe it? For more than a century, modern physics has transformed our understanding of space, time, matter, and information. General relativity revealed that temporal order is inseparable from spacetime geometry. Quantum theory challenged classical intuitions about measurement, correlations, and physical reality. Information theory provided a mathematical language for describing what can be known, transmitted, and recovered. Yet a profound question remains: must every physically consistent universe possess a globally ordered sequence of causes and effects? Beyond Causality investigates this question through an extended mathematical and conceptual study of temporal geometry, informational dependence, retrocausal feedback, and global consistency. Organized into six interconnected parts, this 430-page research monograph develops a framework for examining causal structures beyond conventional temporal ordering. It brings together established results from general relativity, quantum information, causal modeling, and fixed-point theory, while exploring additional mathematical constructions designed to clarify the conditions under which temporally nonstandard information networks can remain internally consistent. Particular attention is devoted to distinguishing mathematical self-consistency from physical realizability, statistical correlation from controllable communication, and unconventional temporal descriptions from genuine violations of operational causality. Among its principal investigations are the geometric and energetic constraints associated with localized chronology-violating spacetime models, the existence and stability of globally consistent informational feedback networks, the behavior of finite stochastic systems under intervention, and the relationship between quantum causal structures and hypothetical retrocausal channels. The work also extends the theoretical research program introduced in Eon Reverser: Toward Temporal Bubble Radio Communication, examining what additional mathematical, physical, and experimental conditions would be required before communication with an earlier receiver record could be considered a meaningful scientific possibility. Analytical derivations, formal propositions, computational examples, and reproducibility materials accompany the discussion. The proposed constructions are explicitly distinguished from established physical results, and no experimental evidence for backward-in-time communication is claimed. The central ambition of this monograph is neither to declare that causality can be violated nor to assume that temporal paradoxes admit a universal resolution. It is to ask a more precise question: what mathematical structures, consistency principles, and observable constraints would a physical theory have to satisfy if causal order were not universally fixed? The possibility that time, information, and causality may possess a deeper relationship than our present formulations reveal remains an open intellectual frontier. Exploring that frontier requires imagination disciplined by mathematics, speculation constrained by physical principles, and theoretical proposals that remain accountable to observation. Beyond Causality is offered as a contribution to that exploration: an attempt to extend the questions we can rigorously formulate, identify the limits of existing models, and provide a foundation for further investigation into the nature of physical time. Keywords: Causality; Temporal Geometry; General Relativity; Retrocausality; Closed Timelike Curves; Quantum Causal Structures; Information Theory; Global Consistency; Fixed-Point Theory; Chronology Protection; Advanced Electromagnetic Response; Eon Reverser.
This paper introduces the Total Entropic Quantity (TEQ) framework, a structural reformulation of quantum theory grounded in two foundational axioms. Axiom 0 posits entropy as a generative constraint: a geometric principle that determines which configurations can stably distinguish themselves, independent of space, time, or dynamics. Here, entropy refers to a curvature-functional over distinguishability configurations, maintaining only those structural patterns that remain stable or well-posed under finite informational resolution—that is, structures that are not destroyed or dissolved by coarse-graining or limited observability. Axiom 1, the Minimal Principle (MP), selects from these configurations those that remain maximally resolvable under finite entropy resolution. From this entropic foundation, core features of quantum theory—including the Born rule, Schrödinger dynamics, quantization, and gravitational structure—emerge as consequences of variation within an entropy-curved geometry. TEQ unifies quantum coherence, classical emergence, and spacetime curvature under a single informational principle, replacing conventional postulates with entropy-stabilized structure. The framework predicts deviations in high-curvature regimes and reinterprets physical law as the geometry of distinguishability rather than imposed dynamics.