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Non-Local Retrocausal Information Extraction via Center-Shifted Toroidal Geodesics and Interaction-Free Berry Phase Shifts

Ali Unsal

Published Jul 26, 2026• 0 citations
Publisher

Abstract

This paper introduces a self-consistent, non-paradoxical mathematical framework for non-local information extraction from future spacetime boundaries using Center-Shifted Toroidal Spacetime Cavities and Interaction-Free Measurement (IFM) protocols. By establishing the rotational axis (bearing center) of the temporal geodesic loop at a future coordinate $t_{\text{center}} = r$, the lower boundary of the loop tangentially intersects the present at $t = 0$, strictly confining the temporal coordinate to non-negative values ($t \ge 0$) and eliminating any reliance on historical metric generators or closed timelike curve (CTC) grandfather paradoxes. Furthermore, photons interacting with future boundary conditions at $t = 2r$ via an IFM exclusion protocol encode the spatial configuration of the future state directly into a topologically protected Berry Phase Shift ($\Delta \Phi_{\text{Berry}} \approx 0.142 \text{ rad}$) without quantum state collapse. Utilizing an effective optical metric (analog gravity via nonlinear Kerr media), this model offers a novel, verifiable pathway for retrocausal quantum optics experiments.

DOI
10.5281/zenodo.21609280

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This paper introduces a self-consistent, non-paradoxical mathematical framework for non-local information extraction from future spacetime boundaries using Center-Shifted Toroidal Spacetime Cavities and Interaction-Free Measurement (IFM) protocols. By establishing the rotational axis (bearing center) of the temporal geodesic loop at a future coordinate tcenter=rt_{\text{center}} = rtcenter​=r, the lower boundary of the loop tangentially intersects the present at t=0t = 0t=0, strictly confining the temporal coordinate to non-negative values (t≥0t \ge 0t≥0) and eliminating any reliance on historical metric generators or closed timelike curve (CTC) grandfather paradoxes. Furthermore, photons interacting with future boundary conditions at t=2rt = 2rt=2r via an IFM exclusion protocol encode the spatial configuration of the future state directly into a topologically protected Berry Phase Shift (ΔΦBerry≈0.142 rad\Delta \Phi_{\text{Berry}} \approx 0.142 \text{ rad}ΔΦBerry​≈0.142 rad) without quantum state collapse. Utilizing an effective optical metric (analog gravity via nonlinear Kerr media), this model offers a novel, verifiable pathway for retrocausal quantum optics experiments.
We propose that quantum entanglement, Einstein–Rosen bridges, and post-selected closed timelike curves are interconnected manifestations of a unified causal-consistency mechanism in quantum gravity. In this framework—Paradox-Constraining Time-Causal Structures (PCTCS)—entanglement supplies retrocausal boundary constraints, ER bridges provide geometric connectivity, and P-CTCs eliminate paradoxical histories via post-selection. This model preserves causality without requiring faster-than-light signaling and offers testable predictions in entangled photon experiments and quantum-computer simulations.
Starting from the discrete spacetime structure predicted by loop quantum gravity (LQG), this paper constructs a universal model of quantum-dot information storage and systematically explores its logical correlation with time travel. We first formulate the discreteness of spacetime at the Planck scale and argue that the discrete spectra of geometric operators (area and volume) provide a natural quantized substrate for information storage. Crucially, we do not assert a direct physical isomorphism between Planck-scale spacetime quanta and mesoscopic quantum-dot spin states—a gap of roughly 26 orders of magnitude. Instead, using renormalization-group (RG) ideas and scale invariance, we reframe the link as a topological isomorphism of information structure and, operationally, as a quantum simulation: a quantum-dot array is a laboratory simulator of the discrete-spacetime information network rather than a physical counterpart of Planck-scale atoms. To address the causal paradoxes of closed timelike curves (CTCs), we propose a quantum-information self-consistency principle and connect it to Deutsch’s D-CTC model (1991; density-matrix fixed point) and the Lloyd et al. P-CTC model (2011; post-selected CTCs). We argue that spacetime discreteness supplies a natural ultraviolet cutoff which, together with non-local (entanglement-based) storage in the dot network, dissolves the grandfather paradox at the level of information. The metaphysical “isomorphism claim” is sharpened into a falsifiable “same-universality-class” hypothesis, accompanied by concrete criteria (entanglement-entropy scaling, power-law exponents, topological entanglement entropy). The proposed quantum-dot loop experiment is clarified as a quantum simulation of the information-propagation logic of CTCs, in the same paradigm as the Sycamore traversable-wormhole experiment (Jafferis et al., 2022), and is not a realization of macroscopic time travel. Building on the above, this paper advances two core theoretical constructs, each developed in a dedicated chapter. The first is the quantum-dot information-extension model (Chapter 8): the existence of a piece of spacetime information is identified with the existence of a timelike information world-tube—when information is created at an event, the quantum point carrying it extends along a timelike direction into a world-tube that persists until the information is erased. From this picture we derive a conservation law for the active quantum-point number density, a holographic–persistence capacity bound for the world-tube cross-section, and the thermodynamic costs of information creation, persistence, and annihilation. The second is the information dynamics of time travel (Chapter 9): within the world-tube language, two self-consistent routes for returning to the past are proposed—jumping to a parallel branch universe that already possesses a time machine (memory fully retained), or rewinding along one's own world-tube so that the extended quantum point recedes and annihilates at its initial event (entailing invalidation of downstream information, merging of the future and past operators' information, and the impossibility of retaining future memory). The two routes correspond respectively to cross-branch and same-branch fixed points of the causal-consistency functional. We emphasize that the pictures of Chapters 8 and 9 are theoretical hypotheses and conjectures proposed herein, intended to provide a mathematically self-consistent and in-principle falsifiable analytical framework rather than a claim about the physical realizability of time machines.
This preprint proposes a novel fundamental paradigm in physics based on the concept of an autonomous, three-dimensional pseudo-Euclidean time continuum, referred to as the "Event Space" (3D-T). The model introduces the physical equivalent of "Observer Mass" M(obs), defined as the informational-entropic density of interaction. We postulate that this information density is the primary source of local curvature within the temporal metric. The paper provides a strict geometric derivation of fundamental quantum phenomena, treating them as non-linear effects of this local temporal gravity: Macroscopic Decoherence: The collapse of the wave function is explained as the mandatory fixation of an object at the bottom of a deep Temporal Well (Event Attractor), generated by the colossal M(obs) of the surrounding macroscopic environment. This process definitively eliminates anthropocentrism from physics. Quantum Paradoxes: Geometric interpretations are offered for Wave-Particle Duality, Quantum Tunneling (as a temporal detour), Quantum Entanglement (as a topological resonance bridge across a null temporal interval), and Quantum Teleportation. Furthermore, the work presents specific, falsifiable experimental predictions to verify the model at the Large Hadron Collider (CERN) and in high-precision optical Bell tests. This 3D-time model constructs a rigorous geometric bridge between General Relativity and Quantum Mechanics, forming a reliable topological basis for a future theory of quantum gravity.
We demonstrate that when absolute unitary evolution of the wavefunction is enforced alongside the requirement of a single, self-consistent world, the standard quantum measurement problem dissolves. The resulting framework, Relational Retrocausal Quantum Mechanics (RRQM), requires that the state of any system is strictly relational, and that measurement retroactively rewrites the entire history of the wavefunction. By extending RRQM to incorporate Quantum Reference Frames (QRFs) and mapping them onto a doubly non-commutative phase-space matrix algebra, we derive exact continuous causality. We prove that the spatial ([Xµ,Xν] = iθµν) and momentum ([Pµ,Pν] = iBµν) non-commutativities dynamically deform the phase-space integration measure. This rigidity generates localized geometric stress upon measurement, mathematically inducing the non-linear curvature of the Einstein-Hilbert action. Furthermore, we provide a complete, gapless algebraic derivation proving that gravitational binding energy—the classical mass defect—emerges purely from the relational interaction between non-commutative momentum operators, establishing macroscopic gravity as a thermodynamic shadow of retrocausal constraints.
This paper establishes a geometric bridge between two operational results concerning gravity-mediated entanglement and phase-based field structure. First, prior work showed that entanglement in minimal gravity-mediated interferometric models arises if and only if the interaction phases contain a non-factorable plaquette invariant. This invariant represents an oriented loop phase that cannot be decomposed into local contributions and therefore serves as a necessary and sufficient condition for entanglement generation. Second, the Harmonic Code framework describes persistent physical effects as loop-structured phase geometry, in which closed phase loops encode enduring information about curvature and field structure. The present work unifies these viewpoints by demonstrating that the plaquette phase emerges naturally as a curvature-induced loop holonomy. An effective phase-gradient field is introduced, and the oriented loop phase is defined as Π = ∮ k · dℓ = ∬ (∇ × k) · dA, showing that the non-factorable phase invariant is directly generated by the curl of the phase-gradient field. A minimal rotational field model is used to derive the relation Π = 2εA, where A is the enclosed area and ε is the curl parameter. Numerical simulations verify the key geometric properties expected of a true holonomy: Linear scaling with enclosed area Shape independence at fixed area Sign reversal under orientation flip Convergence under discretization refinement The loop phase Π is then mapped to standard two-qubit entanglement measures. For the separable input state |++⟩, the concurrence and negativity are shown to depend only on Π: C(Π) = |sin(Π/2)| N(Π) = C/2 These results demonstrate that the non-factorable phase structure required for gravity-mediated entanglement has a direct geometric origin as a curvature-induced loop holonomy. The paper therefore provides a unified operational statement: Curvature generates loop phases, and those loop phases are exactly the structures responsible for gravity-mediated entanglement. This establishes a concrete geometric mechanism linking spacetime curvature, phase holonomy, and quantum entanglement, and offers a clear, experimentally testable framework for probing quantum aspects of gravity.
What if the mystery of quantum entanglement—Einstein’s famous "spooky action at a distance"—could be understood through shared temporal structures rather than superluminal signals? This paper explores the quantum foundations sector of Temporal Texture Gravity, introducing a candidate mechanism called the "Non-Separable Temporal Bubble". It investigates how entangled particles might share a single, spatially extended temporal configuration that coordinates their measurement outcomes while remaining strictly non-signaling at the observable level. The paper frames this mechanism with complete transparency, outlining both its mathematical predictions and its current boundaries: A Shared Temporal Substrate: Proposes that entangled particles are connected through an extended temporal bubble. Under standard quantum probability rules, this shared substrate exactly reproduces quantum correlation laws and the famous Tsirelson bound for quantum measurement limits. Strict No-Signaling Discipline: Addresses the fundamental requirement that quantum correlations must never allow faster-than-light communication. The paper documents an internal refutation of an earlier model version that leaked information, establishing the exact mathematical conditions required to keep hidden non-local states completely unreadable to outside observers. Gravitational Test Signatures: Examines how quantum bubbles interact with gravitational curvature (such as around black holes or massive bodies). The paper derives three distinct structural signatures—a "magic angle" where tidal distortions cancel out, an isotropy null where symmetric bubbles decouple, and a clear separation between phase shifts and visibility loss. Presented as an exploratory candidate extension rather than a derived result of the core action, this paper establishes a rigorous roadmap for bridging temporal geometry with quantum non-locality.