The Theory of Entropicity (ToE) Living Review Letters ID: The Entropic Seesaw Model (ESSM) of the Theory of Entropicity (ToE) — A Complete Entropic Theory of Quantum Entanglement, the Attosecond Formation-Time Evidence, and the Resolution of Einstein's EPR Paradox and the Maldacena-Susskind ER=EPR Conjecture — Living Review Letters Series. Letter ID
Abstract The present Letter — Letter ID in the Theory of Entropicity (ToE) Living Review Letters Series — introduces and fully formalizes the Entropic Seesaw Model (ESSM) as a self-contained, mathematically complete entropic theory of quantum entanglement. ESSM is developed within the broader framework of the Theory of Entropicity, an entropy-first program that posits the entropic field as the ontological ground of physical reality. The model is constructed in two conceptually distinct but mathematically unified stages. First, a formation stage, in which two previously independent entropic sectors — each described by a local entropic field configuration on its own manifold — undergo a local, finite-time, topological merger into a single shared entropic manifold. This merger is not an instantaneous kinematic fact but a genuine dynamical process requiring finite entropic resources and finite time, governed by a formation drive equation with a well-defined threshold-crossing time. Second, a persistence stage, in which the shared manifold is maintained under arbitrary spatial separation of the subsystems without the transport of any signal — the correlations survive not because information travels but because the two subsystems remain structurally identical to one entropic object, and the entropic distance between them remains near zero even as their spatial distance grows without bound. ESSM resolves the Einstein-Podolsky-Rosen paradox at the ontological level by introducing a rigorous distinction between spatial distance and entropic distance. The core of the EPR argument is the assumption that spatial separation implies ontological separation. ESSM denies this premise: once the shared manifold M_AB has crystallized, the subsystems A and B remain entropically local (d_E(A,B) ≈ 0) regardless of their spatial distance (d_space(A,B) ≫ 0). Correlations measured at spacelike separation are therefore not "spooky action at a distance" but local facts in entropic geometry, apprehended from the standpoint of spatial geometry as nonlocal. This resolution preserves Bell's theorem, preserves the no-signaling principle, and requires no hidden variables — it simply relocates the locus of the relational fact from spacetime geometry to the entropic manifold. The Letter further reinterprets the Maldacena-Susskind ER=EPR conjecture [23] as an entropic bridge rather than a literal spacetime wormhole. ESSM defines a bridge order parameter Ξ_AB whose nonzero expectation value signals the "turning on" of the entropic bridge, and derives a bridge length functional L_AB that shortens toward zero at maximal entanglement and diverges at decoherence. The relationship between ER bridges and entropic bridges is shown to be one of geometric shadow: in special gravitational regimes, the entropic bridge may admit a representation in Einstein-Rosen bridge language, but the ESSM bridge is the more general and more physically transparent object. ESSM thereby completes the ER=EPR conjecture by supplying the dynamical content — formation dynamics, coherence strength, threshold breakdown — that the original conjecture leaves unspecified. The empirical grounding of ESSM is provided by the rapidly advancing attosecond photoionization literature [33]. Jiang et al. (2024, Physical Review Letters 133, 163201) [27] demonstrated, through numerical solution of the full-dimensional time-dependent Schrödinger equation for helium, that photoionization time delays can serve as an attosecond probe of interelectronic coherence and entanglement. The widely cited figure of roughly 232 attoseconds is reported in institutional summaries — notably the TU Wien news release of October 2024 [34] — as the timescale for entanglement development in the helium system; however, the present Letter emphasizes that the primary 2024 PRL paper by Jiang et al. is a numerical and theoretical attosecond chronoscopy study, and the “232 attoseconds” figure appears in news summaries rather than as a directly measured coincidence result in the primary paper. Subsequent experimental works provide increasingly direct attosecond-scale evidence: Shobeiry et al. (2024, Scientific Reports 14, 19630) [28] demonstrated direct control of emission direction of entangled photoelectrons in dissociative H₂ ionization; Stenquist and Dahlström (2025, Physical Review Research 7, 013270) [29] showed how time-symmetry can be harnessed to alter entanglement in photoionization; Makos et al. (2025, Nature Communications 16, 8554) [30] revealed ionic coupling effects on attosecond time delays through entanglement in CO₂ photoionization; and Koll et al. (2026, Nature 652, 82–88) [31] provided the most direct experimental demonstration to date that ion–photoelectron entanglement influences electronic coherence in attosecond molecular photoionization of H₂. These experiments collectively demonstrate that entanglement formation is a finite-time, channel-dependent, dynamically rich process — precisely as ESSM predicts.The mathematical architecture developed in this Letter includes: the ESSM two-sector effective action in symmetric and antisymmetric entropic mode variables; the bridge order parameter and its symmetry-breaking potential; the coherence strength functional Γ_AB; the equation of motion for the antisymmetric mode S₋; the formation drive equation and its analytic solution; the seesaw collapse criterion and decoherence rate decomposition; the entropic bridge length functional; and the entropic formation functional connecting ESSM formation to the Obidi Action's variational philosophy. This Letter — Letter ID in the ToE Living Review Letters Series — builds upon the foundational materials established in Letter I [1] (ontological primacy of entropy), Letter IA [2] (the Haller correspondence), Letter IB [3] (the Haller-Obidi Action and Lagrangian), and Letter IC [4] (the Alemoh-Obidi Correspondence). The present Letter gives the reader a veritable expose on the synthesis of the ToE formal proposals on the Entropic Seesaw Model (ESSM).Letter ID thus establishes the Entropic Seesaw Model (ESSM) of the Theory of Entropicity (ToE) as a rigorously formulated, experimentally falsifiable, and physically motivated entropic framework for quantum entanglement — one that takes the entanglement problem seriously as a question about the physical world and provides, for the first time within any entropic program, the mathematical apparatus to answer it. Keywords: Theory of Entropicity (ToE); Entropic Seesaw Model (ESSM); Quantum Entanglement; Entropic Field; Obidi Action; Entropic Manifold; Entropic Distance; Entropic Bridge; Coherence Strength Functional; Attosecond Entanglement Formation Time; Einstein-Podolsky-Rosen (EPR); ER=EPR; Maldacena-Susskind Conjecture; No-Rush Theorem; Entropic Time Limit; Entropic Decoherence; Measurement Threshold; Seesaw Collapse Criterion; Photoionization Entanglement; Attosecond Chronoscopy; Bell Inequality; Entropic Nonlocality; Formation-Persistence Distinction; Environmental Torque (EnvT); Entropic Torque (ET) General Introduction Quantum entanglement is, by broad consensus, the most profoundly non-classical feature of modern physics. Since its identification by Einstein, Podolsky, and Rosen in 1935 [20] and its christening by Schrödinger [43] in the same year, entanglement has migrated from the margins of interpretive debate to the center of theoretical and experimental physics. It underwrites quantum computation, quantum cryptography, quantum teleportation, and the emerging consensus that spacetime itself may be stitched together by entanglement [24]. And yet, despite nearly a century of investigation, the foundational theory of entanglement remains strangely incomplete. Standard quantum mechanics treats entanglement as a kinematic feature of Hilbert space — a non-factorizability of the state vector — but offers no dynamical account of how entanglement forms, why it persists under arbitrary spatial separation, or what physical process governs its breakdown under measurement or decoherence. The present Letter addresses this deficit head-on. The Einstein-Podolsky-Rosen paradox remains, at its philosophical core, unresolved. Bell's theorem [22] demonstrated that no local hidden-variable theory can reproduce the quantum predictions, and decades of experimental confirmation — from Aspect's [38] pioneering tests through the loophole-free demonstrations of the 2010s — have established that quantum correlations violate Bell inequalities. But establishing that entanglement is real and nonlocal is not the same as explaining what it is. The EPR argument relies on the premise that spatial separation guarantees ontological independence; this premise is denied by entanglement but never replaced by a positive account of what structure underwrites the correlations. The Copenhagen tradition declares the question meaningless; the many-worlds interpretation distributes the correlations across branching worlds; Bohmian mechanics [44] introduces a pilot wave that is explicitly nonlocal. None of these provides a dynamical ontology for the relational structure of entanglement itself. A striking development from the high-energy and quantum-gravity community is the ER=EPR conjecture of Maldacena and Susskind [23], which proposes that entangled systems are connected by Einstein-Rosen bridges [21] — spacetime wormholes. This conjecture, elaborated by Van Raamsdonk's spacetime-from-entanglement program [24] and more recently by the "ER for typical EPR" analysis of Magán, Sasieta, and Swingle [25], has the great merit of treating entanglement as a structural, geometric fact rather than a mere correlation. But ER=EPR, in its original form, is a conjecture framed within AdS/CFT duality and black-hole thermodynamics; it does not specify the dynamical mechanism by which the bridge forms, nor does it apply straightforwardly to the laboratory Bell pairs and photoionization entanglements of atomic p
Abstract The present Letter — Letter ID in the Theory of Entropicity (ToE) Living Review Letters Series — introduces and fully formalizes the Entropic Seesaw Model (ESSM) as a self-contained, mathematically complete entropic theory of quantum entanglement. ESSM is developed within the broader framework of the Theory of Entropicity, an entropy-first program that posits the entropic field as the ontological ground of physical reality. The model is constructed in two conceptually distinct but mathematically unified stages. First, a formation stage, in which two previously independent entropic sectors — each described by a local entropic field configuration on its own manifold — undergo a local, finite-time, topological merger into a single shared entropic manifold. This merger is not an instantaneous kinematic fact but a genuine dynamical process requiring finite entropic resources and finite time, governed by a formation drive equation with a well-defined threshold-crossing time. Second, a persistence stage, in which the shared manifold is maintained under arbitrary spatial separation of the subsystems without the transport of any signal — the correlations survive not because information travels but because the two subsystems remain structurally identical to one entropic object, and the entropic distance between them remains near zero even as their spatial distance grows without bound. ESSM resolves the Einstein-Podolsky-Rosen paradox at the ontological level by introducing a rigorous distinction between spatial distance and entropic distance. The core of the EPR argument is the assumption that spatial separation implies ontological separation. ESSM denies this premise: once the shared manifold M_AB has crystallized, the subsystems A and B remain entropically local (d_E(A,B) ≈ 0) regardless of their spatial distance (d_space(A,B) ≫ 0). Correlations measured at spacelike separation are therefore not "spooky action at a distance" but local facts in entropic geometry, apprehended from the standpoint of spatial geometry as nonlocal. This resolution preserves Bell's theorem, preserves the no-signaling principle, and requires no hidden variables — it simply relocates the locus of the relational fact from spacetime geometry to the entropic manifold. The Letter further reinterprets the Maldacena-Susskind ER=EPR conjecture [23] as an entropic bridge rather than a literal spacetime wormhole. ESSM defines a bridge order parameter Ξ_AB whose nonzero expectation value signals the "turning on" of the entropic bridge, and derives a bridge length functional L_AB that shortens toward zero at maximal entanglement and diverges at decoherence. The relationship between ER bridges and entropic bridges is shown to be one of geometric shadow: in special gravitational regimes, the entropic bridge may admit a representation in Einstein-Rosen bridge language, but the ESSM bridge is the more general and more physically transparent object. ESSM thereby completes the ER=EPR conjecture by supplying the dynamical content — formation dynamics, coherence strength, threshold breakdown — that the original conjecture leaves unspecified. The empirical grounding of ESSM is provided by the rapidly advancing attosecond photoionization literature [33]. Jiang et al. (2024, Physical Review Letters 133, 163201) [27] demonstrated, through numerical solution of the full-dimensional time-dependent Schrödinger equation for helium, that photoionization time delays can serve as an attosecond probe of interelectronic coherence and entanglement. The widely cited figure of roughly 232 attoseconds is reported in institutional summaries — notably the TU Wien news release of October 2024 [34] — as the timescale for entanglement development in the helium system; however, the present Letter emphasizes that the primary 2024 PRL paper by Jiang et al. is a numerical and theoretical attosecond chronoscopy study, and the “232 attoseconds” figure appears in news summaries rather than as a directly measured coincidence result in the primary paper. Subsequent experimental works provide increasingly direct attosecond-scale evidence: Shobeiry et al. (2024, Scientific Reports 14, 19630) [28] demonstrated direct control of emission direction of entangled photoelectrons in dissociative H₂ ionization; Stenquist and Dahlström (2025, Physical Review Research 7, 013270) [29] showed how time-symmetry can be harnessed to alter entanglement in photoionization; Makos et al. (2025, Nature Communications 16, 8554) [30] revealed ionic coupling effects on attosecond time delays through entanglement in CO₂ photoionization; and Koll et al. (2026, Nature 652, 82–88) [31] provided the most direct experimental demonstration to date that ion–photoelectron entanglement influences electronic coherence in attosecond molecular photoionization of H₂. These experiments collectively demonstrate that entanglement formation is a finite-time, channel-dependent, dynamically rich process — precisely as ESSM predicts.The mathematical architecture developed in this Letter includes: the ESSM two-sector effective action in symmetric and antisymmetric entropic mode variables; the bridge order parameter and its symmetry-breaking potential; the coherence strength functional Γ_AB; the equation of motion for the antisymmetric mode S₋; the formation drive equation and its analytic solution; the seesaw collapse criterion and decoherence rate decomposition; the entropic bridge length functional; and the entropic formation functional connecting ESSM formation to the Obidi Action's variational philosophy. This Letter — Letter ID in the ToE Living Review Letters Series — builds upon the foundational materials established in Letter I [1] (ontological primacy of entropy), Letter IA [2] (the Haller correspondence), Letter IB [3] (the Haller-Obidi Action and Lagrangian), and Letter IC [4] (the Alemoh-Obidi Correspondence). The present Letter gives the reader a veritable expose on the synthesis of the ToE formal proposals on the Entropic Seesaw Model (ESSM).Letter ID thus establishes the Entropic Seesaw Model (ESSM) of the Theory of Entropicity (ToE) as a rigorously formulated, experimentally falsifiable, and physically motivated entropic framework for quantum entanglement — one that takes the entanglement problem seriously as a question about the physical world and provides, for the first time within any entropic program, the mathematical apparatus to answer it. Keywords: Theory of Entropicity (ToE); Entropic Seesaw Model (ESSM); Quantum Entanglement; Entropic Field; Obidi Action; Entropic Manifold; Entropic Distance; Entropic Bridge; Coherence Strength Functional; Attosecond Entanglement Formation Time; Einstein-Podolsky-Rosen (EPR); ER=EPR; Maldacena-Susskind Conjecture; No-Rush Theorem; Entropic Time Limit; Entropic Decoherence; Measurement Threshold; Seesaw Collapse Criterion; Photoionization Entanglement; Attosecond Chronoscopy; Bell Inequality; Entropic Nonlocality; Formation-Persistence Distinction; Environmental Torque (EnvT); Entropic Torque (ET) General Introduction Quantum entanglement is, by broad consensus, the most profoundly non-classical feature of modern physics. Since its identification by Einstein, Podolsky, and Rosen in 1935 [20] and its christening by Schrödinger [43] in the same year, entanglement has migrated from the margins of interpretive debate to the center of theoretical and experimental physics. It underwrites quantum computation, quantum cryptography, quantum teleportation, and the emerging consensus that spacetime itself may be stitched together by entanglement [24]. And yet, despite nearly a century of investigation, the foundational theory of entanglement remains strangely incomplete. Standard quantum mechanics treats entanglement as a kinematic feature of Hilbert space — a non-factorizability of the state vector — but offers no dynamical account of how entanglement forms, why it persists under arbitrary spatial separation, or what physical process governs its breakdown under measurement or decoherence. The present Letter addresses this deficit head-on. The Einstein-Podolsky-Rosen paradox remains, at its philosophical core, unresolved. Bell's theorem [22] demonstrated that no local hidden-variable theory can reproduce the quantum predictions, and decades of experimental confirmation — from Aspect's [38] pioneering tests through the loophole-free demonstrations of the 2010s — have established that quantum correlations violate Bell inequalities. But establishing that entanglement is real and nonlocal is not the same as explaining what it is. The EPR argument relies on the premise that spatial separation guarantees ontological independence; this premise is denied by entanglement but never replaced by a positive account of what structure underwrites the correlations. The Copenhagen tradition declares the question meaningless; the many-worlds interpretation distributes the correlations across branching worlds; Bohmian mechanics [44] introduces a pilot wave that is explicitly nonlocal. None of these provides a dynamical ontology for the relational structure of entanglement itself. A striking development from the high-energy and quantum-gravity community is the ER=EPR conjecture of Maldacena and Susskind [23], which proposes that entangled systems are connected by Einstein-Rosen bridges [21] — spacetime wormholes. This conjecture, elaborated by Van Raamsdonk's spacetime-from-entanglement program [24] and more recently by the "ER for typical EPR" analysis of Magán, Sasieta, and Swingle [25], has the great merit of treating entanglement as a structural, geometric fact rather than a mere correlation. But ER=EPR, in its original form, is a conjecture framed within AdS/CFT duality and black-hole thermodynamics; it does not specify the dynamical mechanism by which the bridge forms, nor does it apply straightforwardly to the laboratory Bell pairs and photoionization entanglements of atomic p
Abstract The present Letter — Letter ID in the Theory of Entropicity (ToE) Living Review Letters Series — introduces and fully formalizes the Entropic Seesaw Model (ESSM) as a self-contained, mathematically complete entropic theory of quantum entanglement. ESSM is developed within the broader framework of the Theory of Entropicity, an entropy-first program that posits the entropic field as the ontological ground of physical reality. The model is constructed in two conceptually distinct but mathematically unified stages. First, a formation stage, in which two previously independent entropic sectors — each described by a local entropic field configuration on its own manifold — undergo a local, finite-time, topological merger into a single shared entropic manifold. This merger is not an instantaneous kinematic fact but a genuine dynamical process requiring finite entropic resources and finite time, governed by a formation drive equation with a well-defined threshold-crossing time. Second, a persistence stage, in which the shared manifold is maintained under arbitrary spatial separation of the subsystems without the transport of any signal — the correlations survive not because information travels but because the two subsystems remain structurally identical to one entropic object, and the entropic distance between them remains near zero even as their spatial distance grows without bound. ESSM resolves the Einstein-Podolsky-Rosen paradox at the ontological level by introducing a rigorous distinction between spatial distance and entropic distance. The core of the EPR argument is the assumption that spatial separation implies ontological separation. ESSM denies this premise: once the shared manifold M_AB has crystallized, the subsystems A and B remain entropically local (d_E(A,B) ≈ 0) regardless of their spatial distance (d_space(A,B) ≫ 0). Correlations measured at spacelike separation are therefore not "spooky action at a distance" but local facts in entropic geometry, apprehended from the standpoint of spatial geometry as nonlocal. This resolution preserves Bell's theorem, preserves the no-signaling principle, and requires no hidden variables — it simply relocates the locus of the relational fact from spacetime geometry to the entropic manifold. The Letter further reinterprets the Maldacena-Susskind ER=EPR conjecture [23] as an entropic bridge rather than a literal spacetime wormhole. ESSM defines a bridge order parameter Ξ_AB whose nonzero expectation value signals the "turning on" of the entropic bridge, and derives a bridge length functional L_AB that shortens toward zero at maximal entanglement and diverges at decoherence. The relationship between ER bridges and entropic bridges is shown to be one of geometric shadow: in special gravitational regimes, the entropic bridge may admit a representation in Einstein-Rosen bridge language, but the ESSM bridge is the more general and more physically transparent object. ESSM thereby completes the ER=EPR conjecture by supplying the dynamical content — formation dynamics, coherence strength, threshold breakdown — that the original conjecture leaves unspecified. The empirical grounding of ESSM is provided by the rapidly advancing attosecond photoionization literature [33]. Jiang et al. (2024, Physical Review Letters 133, 163201) [27] demonstrated, through numerical solution of the full-dimensional time-dependent Schrödinger equation for helium, that photoionization time delays can serve as an attosecond probe of interelectronic coherence and entanglement. The widely cited figure of roughly 232 attoseconds is reported in institutional summaries — notably the TU Wien news release of October 2024 [34] — as the timescale for entanglement development in the helium system; however, the present Letter emphasizes that the primary 2024 PRL paper by Jiang et al. is a numerical and theoretical attosecond chronoscopy study, and the “232 attoseconds” figure appears in news summaries rather than as a directly measured coincidence result in the primary paper. Subsequent experimental works provide increasingly direct attosecond-scale evidence: Shobeiry et al. (2024, Scientific Reports 14, 19630) [28] demonstrated direct control of emission direction of entangled photoelectrons in dissociative H₂ ionization; Stenquist and Dahlström (2025, Physical Review Research 7, 013270) [29] showed how time-symmetry can be harnessed to alter entanglement in photoionization; Makos et al. (2025, Nature Communications 16, 8554) [30] revealed ionic coupling effects on attosecond time delays through entanglement in CO₂ photoionization; and Koll et al. (2026, Nature 652, 82–88) [31] provided the most direct experimental demonstration to date that ion–photoelectron entanglement influences electronic coherence in attosecond molecular photoionization of H₂. These experiments collectively demonstrate that entanglement formation is a finite-time, channel-dependent, dynamically rich process — precisely as ESSM predicts. The mathematical architecture developed in this Letter includes: the ESSM two-sector effective action in symmetric and antisymmetric entropic mode variables; the bridge order parameter and its symmetry-breaking potential; the coherence strength functional Γ_AB; the equation of motion for the antisymmetric mode S₋; the formation drive equation and its analytic solution; the seesaw collapse criterion and decoherence rate decomposition; the entropic bridge length functional; and the entropic formation functional connecting ESSM formation to the Obidi Action's variational philosophy. This Letter — Letter ID in the ToE Living Review Letters Series — builds upon the foundational materials established in Letter I [1] (ontological primacy of entropy), Letter IA [2] (the Haller correspondence), Letter IB [3] (the Haller-Obidi Action and Lagrangian), and Letter IC [4] (the Alemoh-Obidi Correspondence). The present Letter gives the reader a veritable expose on the synthesis of the ToE formal proposals on the Entropic Seesaw Model (ESSM). Letter ID thus establishes the Entropic Seesaw Model (ESSM) of the Theory of Entropicity (ToE) as a rigorously formulated, experimentally falsifiable, and physically motivated entropic framework for quantum entanglement — one that takes the entanglement problem seriously as a question about the physical world and provides, for the first time within any entropic program, the mathematical apparatus to answer it. # General Introduction Quantum entanglement is, by broad consensus, the most profoundly non-classical feature of modern physics. Since its identification by Einstein, Podolsky, and Rosen in 1935 [20] and its christening by Schrödinger [43] in the same year, entanglement has migrated from the margins of interpretive debate to the center of theoretical and experimental physics. It underwrites quantum computation, quantum cryptography, quantum teleportation, and the emerging consensus that spacetime itself may be stitched together by entanglement [24]. And yet, despite nearly a century of investigation, the foundational theory of entanglement remains strangely incomplete. Standard quantum mechanics treats entanglement as a kinematic feature of Hilbert space — a non-factorizability of the state vector — but offers no dynamical account of how entanglement forms, why it persists under arbitrary spatial separation, or what physical process governs its breakdown under measurement or decoherence. The present Letter addresses this deficit head-on. The Einstein-Podolsky-Rosen paradox remains, at its philosophical core, unresolved. Bell's theorem [22] demonstrated that no local hidden-variable theory can reproduce the quantum predictions, and decades of experimental confirmation — from Aspect's [38] pioneering tests through the loophole-free demonstrations of the 2010s — have established that quantum correlations violate Bell inequalities. But establishing that entanglement is real and nonlocal is not the same as explaining what it is. The EPR argument relies on the premise that spatial separation guarantees ontological independence; this premise is denied by entanglement but never replaced by a positive account of what structure underwrites the correlations. The Copenhagen tradition declares the question meaningless; the many-worlds interpretation distributes the correlations across branching worlds; Bohmian mechanics [44] introduces a pilot wave that is explicitly nonlocal. None of these provides a dynamical ontology for the relational structure of entanglement itself. A striking development from the high-energy and quantum-gravity community is the ER=EPR conjecture of Maldacena and Susskind [23], which proposes that entangled systems are connected by Einstein-Rosen bridges [21] — spacetime wormholes. This conjecture, elaborated by Van Raamsdonk's spacetime-from-entanglement program [24] and more recently by the "ER for typical EPR" analysis of Magán, Sasieta, and Swingle [25], has the great merit of treating entanglement as a structural, geometric fact rather than a mere correlation. But ER=EPR, in its original form, is a conjecture framed within AdS/CFT duality and black-hole thermodynamics; it does not specify the dynamical mechanism by which the bridge forms, nor does it apply straightforwardly to the laboratory Bell pairs and photoionization entanglements of atomic physics. The conjecture names the connection but does not build it. Meanwhile, the experimental landscape has been transformed by the attosecond revolution. For the first time in the history of physics, experiments can probe entanglement formation in real time. The 2024 numerical/theoretical attosecond chronoscopy study by Jiang et al. [27] demonstrated that photoionization time delays in helium, computed from the full-dimensional time-dependent Schrödinger equation, can monitor the ultrafast variations of interelectronic coherence and entanglement. Institutional summaries, notably from TU Wien [34],
The present Letter — Letter ID in the Theory of Entropicity (ToE) Living Review Letters Series — introduces and fully formalizes the Entropic Seesaw Model (ESSM) as a self-contained, mathematically complete entropic theory of quantum entanglement. ESSM is developed within the broader framework of the Theory of Entropicity, an entropy-first program that posits the entropic field as the ontological ground of physical reality. The model is constructed in two conceptually distinct but mathematically unified stages. First, a formation stage, in which two previously independent entropic sectors — each described by a local entropic field configuration on its own manifold — undergo a local, finite-time, topological merger into a single shared entropic manifold. This merger is not an instantaneous kinematic fact but a genuine dynamical process requiring finite entropic resources and finite time, governed by a formation drive equation with a well-defined threshold-crossing time. Second, a persistence stage, in which the shared manifold is maintained under arbitrary spatial separation of the subsystems without the transport of any signal — the correlations survive not because information travels but because the two subsystems remain structurally identical to one entropic object, and the entropic distance between them remains near zero even as their spatial distance grows without bound. ESSM resolves the Einstein-Podolsky-Rosen paradox at the ontological level by introducing a rigorous distinction between spatial distance and entropic distance. The core of the EPR argument is the assumption that spatial separation implies ontological separation. ESSM denies this premise.
The Theory of Entropicity (ToE) posits that entropy is not merely a statistical measure but an active field that fundamentally governs interactions, motion, and causality. Central to this theory is the Entropic Time Limit (ETL), a minimum irreducible time interval required for any physical interaction, below which no interaction, observation, or measurement is possible. This paper analyzes recent groundbreaking experimental results demonstrating that quantum entanglement forms over a finite interval of approximately 232 attoseconds, providing potential empirical validation for the ETL. The observed non-instantaneity of entanglement formation supports the ToE’s proposition that all processes are constrained by entropy-driven temporal boundaries. By comparing ToE with Quantum Field Theory (QFT) and General Relativity (GR), this work highlights how the entropic field may serve as a unifying framework for physics, offering novel insights into quantum measurement, wave-function collapse, causality, and the emergence of spacetime. The study also introduces the Vuli-Ndlela Integral, an entropy-constrained and entropy-weighted reformulation of the Feynman path integral, and outlines future directions for formalizing the entropic field as the fundamental medium of all interactions.
The Einstein-Podolsky-Rosen (EPR) paradox challenges the completeness of quantum mechanics under the assumptions of separability and locality, while Bell's theorem and its loophole-free experimental confirmations rule out local hidden variables and establish that entangled correlations are nonlocal yet no-signaling. This paper formulates, within the spacetime-quantum unified-field theory, a self-contained resolution of the paradox. Starting from the six axioms of the theory, we model the entangled pair as two local excitations of the single global spacetime-quantum field, a coherent superposition of discrete spacetime quanta (Axiom 1). We show that the EPR elements of reality are not attributes of the separated subsystems but properties of the global coherent configuration established within the common past light cone, so that EPR's tacit separability premise fails in this ontology (Axioms 1 and 5). Measurement is identified as a strictly local energy exchange (Axioms 2 and 5) whose influence propagates at most at the speed of light by the local hyperbolic master equation (Axiom 3), and we prove, by the invariance of the reduced density matrix, that no signaling is possible. The Bell correlations are reproduced as a consistency condition inherited from the standard-model sector (Axiom 4), with the Tsirelson bound 2√2 following from the no-signaling structure. Complete derivations of the correlation function, the Clauser-Horne-Shimony-Holt inequality and its violation, the no-signaling theorem, the local measurement model, and the coherence-entanglement relation are provided in the appendices.
Entropy as Inference and Entropy as a Physical Field: A Comprehensive Comparison of Ariel Caticha’s Entropic Dynamics and Obidi’s Theory of Entropicity (ToE) Introduction Putting Ariel Caticha’s work on entropic dynamics (ED) side by side with Obidi’s Theory of Entropicity (ToE) is like comparing two very different bets on what “entropy” is allowed to be in physics. Both take entropy seriously, both see it as more than a bookkeeping device, and both use information‑theoretic ideas. But they diverge at the deepest level: Caticha treats entropy as an epistemic principle guiding inference about an underlying reality, while Obidi treats entropy as the ontological field that constitutes reality itself. That difference—epistemic versus ontological—is not cosmetic. It changes what counts as a law of nature, what time is, what causality is, and what it even means for something to exist. Caticha: Entropy as a principle of inference and dynamics Ariel Caticha’s program, broadly called entropic dynamics, starts from the idea that physical laws can be derived from principles of inference, especially the method of maximum entropy. The core move is: given incomplete information about a system, the best we can do is update probability distributions in a way that is consistent with known constraints and maximizes entropy subject to those constraints. From this perspective, dynamics—how systems evolve in time—can be seen as a sequence of entropic updates. Caticha shows that, under suitable assumptions, one can recover forms of classical and quantum dynamics from entropic inference. Time, in this view, is an ordering parameter for updates; it is not fundamental but emerges as a way of indexing successive states of knowledge. The underlying ontology is relatively modest: there is some “stuff” (positions, configurations, etc.), and we have incomplete information about it. Entropy quantifies that ignorance, and the laws of motion are rules for updating probabilities. So in Caticha’s world, entropy is: a measure of uncertainty, a tool for inference, a generator of effective dynamics. It is powerful, but it is not the substance of reality. It is about how we reason about reality. Obidi: Entropy as the Fundamental Field of Reality Obidi’s Theory of Entropicity (ToE) takes a much more audacious step. It does not merely use entropy to derive dynamics; it declares entropy to be the primitive physical field from which everything else emerges. Entropy is not a measure of ignorance; it is the structure that makes knowledge, states, and even ignorance possible. In ToE, the universe does not begin with spacetime, particles, or even probability distributions. It begins with an entropic field whose configurations encode distinguishability, structure, and the capacity for events to occur. Space and time are emergent bookkeeping devices that track how this entropic field differentiates itself. Causality is not geometric but entropic: events become causally related when the entropic field has evolved enough to separate and stabilize them. Measurement is not a mysterious collapse but an entropic stabilization of previously indistinguishable alternatives. Matter is "frozen" entropy; mass is stabilized internal entropic content; [absolute/inherent] identity is what survives when entropy can no longer erase distinctions [in a given system or element]. Where Caticha uses entropy to derive dynamics on an underlying configuration space, Obidi uses entropy to generate the configuration space itself, along with its geometry, its dynamics, and its ontology. Comparison of Ariel Caticha’s Entropic Dynamics and Obidi’s Theory of Entropicity: Conceptual, Philosophical, and Structural Differences A comparison between Ariel Caticha’s entropic dynamics and Obidi’s Theory of Entropicity (ToE) reveals two fundamentally different visions of what entropy is and what role it plays in physics. Caticha’s work is rooted in the epistemic tradition: entropy is a measure of uncertainty, and physical laws emerge from principles of inference. Obidi’s work is rooted in an ontological re‑founding of physics: entropy is the fundamental physical field, and the universe emerges from its evolution. Caticha’s entropic dynamics begins with the assumption that we have incomplete information about the positions or configurations of a system. Using the method of maximum entropy, he derives rules for updating probability distributions in a way that is consistent with known constraints. Under certain assumptions, these updates reproduce forms of classical and quantum dynamics. Time, in this framework, is an ordering parameter for successive entropic inferences. The underlying ontology remains modest: there is a configuration space, there are unknown variables, and entropy quantifies our uncertainty about them. Caticha’s program is therefore a powerful epistemic reconstruction of dynamics, but it does not claim that entropy is a physical field or that it generates spacetime, causality, or matter. Obidi’s Theory of Entropicity takes a radically different approach. Entropy is not a measure of ignorance but the primitive ontological field. It is the substrate from which distinguishability, time, causality, measurement, matter, and geometry emerge. The entropic and coherent sectors are not epistemic constructs but structural phases of the entropic field. The entropic sector is the domain of irreversible becoming, where the entropic field differentiates itself and writes the arrow of time. The coherent sector is the domain of stabilized being, where structures persist and interact. This two‑sector architecture is not present in Caticha’s work and has no analogue in entropic dynamics. Furthermore, Caticha does not develop a philosophical interpretation of his framework. His papers are technical, focused on inference, probability updating, and the derivation of dynamical equations. He does not address the ontological status of entropy, the metaphysics of becoming, the nature of measurement, or the philosophical implications of entropic evolution. Obidi, by contrast, explicitly engages with the philosophical foundations of physics, drawing connections to ontology, metaphysics, epistemology, and the philosophy of time. His work situates the Theory of Entropicity (ToE) within a broader intellectual tradition, including comparisons with Paul Tillich, Schopenhauer, and the classical distinction between appearance and reality. The originality of Obidi’s contribution lies in the systematic way he reorders the explanatory hierarchy of physics. Instead of deriving dynamics from inference, he derives inference, dynamics, geometry, and matter from the entropic field alone. Instead of treating probability as epistemic, he derives it as a conserved physical quantity. Instead of treating measurement as a postulate, he explains it as entropic stabilization. Instead of treating spacetime as fundamental, he derives it from information geometry via the Obidi Action. Instead of treating coherence as a mathematical artifact, he interprets and grounds it as a structural phase of the entropic field. The broader implications of this difference are profound. Caticha’s program suggests that physics is ultimately about how rational agents should update their beliefs. Obidi’s program suggests that physics is about how the universe entropically becomes what it is [and that ultimately it is not about beliefs taken as isolated givens or provisos independent of the Entropic Field (EF)]. Caticha reconstructs known laws; Obidi reconstructs the foundations from which laws arise. Caticha’s entropy is epistemic; Obidi’s entropy is ontological. Caticha’s dynamics is inferential; Obidi’s dynamics is generative. Caticha’s framework is silent on metaphysics; Obidi’s framework is a metaphysics inseparable from physics. References (Caticha): Caticha, A. Entropic Dynamics, in Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings, 2011. Caticha, A. Entropic Inference and the Foundations of Physics, 2012. Caticha, A. From Entropic Dynamics to Quantum Theory, 2014. References (Obidi): Obidi, J. O. Theory of Entropicity (ToE) Canonical Archives, 2024–2026. Obidi, J. O. Obidi’s Philosophical Analysis of Being and Becoming, 2026. Obidi, J. O. The Obidi Action, Entropic Geometry, and the Emergence of Spacetime, 2025. Obidi, J. O. The Obidi Probability Law and the Two‑Sector Hilbert Space Decomposition, 2025. Entropic and Coherent Sectors: Caticha versus Obidi The language of “entropic” and “coherent” sectors is especially revealing. In Caticha’s framework, the entropic sector is essentially the inferential machinery: probability distributions, entropy functionals, constraints, and the maximum entropy principle. Coherence, when it appears, is largely about consistency of inference and the emergence of quantum‑like structures (e.g., complex amplitudes, Hilbert space) from entropic updating. The “coherent” behavior is a feature of how probability amplitudes evolve under entropic rules, not a separate ontological sector of reality. In Obidi’s ToE, the entropic and coherent sectors are structurally deeper. The entropic sector is the domain where the entropic field is actively differentiating, where distinguishability is being created, where time’s arrow is being written. The coherent sector is the regime where structures—once formed by entropic evolution—exhibit stability, persistence, and internal consistency. Coherence here is not just a property of wavefunctions; it is a structural phase of the entropic field itself. You can think of it this way: in ToE, the entropic sector is the “becoming” of reality, while the coherent sector is the “being” that results from that becoming. The two are not separate theories but two regimes of the same entropic substrate. The entropic sector governs how new distinctions, structures, and events come into existence; the coherent secto