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Quantum Entanglement dan Kemunculan Waktu Relasional dalam Geometri Chrana

Ahmad Syifa Aqmal

Published Jan 1, 2026• 0 citations
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Abstract

This study proposes a conceptual framework called Chrana Geometry, in which time and geometry emerge from relational quantum information structures. Using a two-qubit entangled system, the research analyzes the evolution of entanglement entropy, mutual information, relational curvature, and decoherence through numerical simulation. The results suggest that temporal ordering and relational geometry may arise dynamically from quantum entanglement and gradually collapse under decoherence effects.

DOI
10.17605/osf.io/5z4ru

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This study proposes a conceptual framework called Chrana Geometry, in which time and geometry emerge from relational quantum information structures. Using a two-qubit entangled system, the research analyzes the evolution of entanglement entropy, mutual information, relational curvature, and decoherence through numerical simulation. The results suggest that temporal ordering and relational geometry may arise dynamically from quantum entanglement and gradually collapse under decoherence effects.
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I propose that quantum entanglement may reflect relational connectivity at a level where ordinary spatial distance is not fundamental. In the geometric framework considered here, particle pairs arise from an underlying field, retain a shared quantum structure, and participate in a network from which three-dimensional space emerges. Spatial separation in the emergent description need not imply complete independence at the underlying level. I formulate this idea as a conceptual hypothesis and distinguish it from established quantum mechanics, from classical common-cause explanations, and from specific proposals relating entanglement to spacetime geometry. Standard entanglement, Bell correlations, and the no-signalling condition provide consistency requirements; they are not derived from the proposed framework. No graviton-mediated mechanism, dynamical law, or experimentally distinguishable prediction is established in this paper. The hypothesis motivates a research programme requiring a defined state space, a rule for emergent geometry, a treatment of measurement and decoherence, and a quantitative comparison with quantum theory.
This paper presents a novel theoretical framework wherein spatial geometry and topological structures emerge naturally from quantum information exchange within the Relational Quantum Dynamics (RQD) paradigm. Extending prior work on geometry extraction from quantum entanglement, we introduce an awareness-weighted entanglement metric, combining quantum mutual information and integrated information—a measure reflecting the internal coherence and holism of subsystems—to quantify relational proximity among quantum systems. This new metric, termed the "awareness metric," characterizes how strongly two subsystems are mutually aware based not only on their entanglement but also on their capacity for internal information integration. Using this metric, we construct an emergent relational distance that fulfills standard metric axioms, enabling the definition of a well-formed relational geometry. We demonstrate how this awareness-based distance naturally generates topological structures: disconnected sets of subsystems correspond to informationally isolated components, and contextual quantum correlations yield nontrivial loops and topological cycles in the emergent relational space. Integrated information identifies strongly integrated clusters within this structure, suggesting the existence of higher-level composite subsystems that function as unified wholes, thus enabling a multi-scale hierarchical relational description. We further formalize this relational geometry within an enriched categorical setting, showing that it constitutes a Lawvere metric space where distances between objects correspond directly to their mutual informational relationships. By employing the Yoneda lemma, we establish that each subsystem's identity emerges solely through its informational relations to others, aligning closely with RQD’s philosophical stance that systems possess no intrinsic, observer-independent existence. Additionally, we explore the relationship between quantum contextuality and topology, demonstrating how the impossibility of a globally consistent joint informational description manifests as topological obstructions—"holes"—in the relational geometry.