The Geometry of the Quantum Paradoxes

Jincheng Zhang

This paper explores the intricate relationship between quantum information and geometric modeling, focusing on the potential of quantum geometry to address the infamous quantum information paradox. We propose a novel algorithm leveraging quantum entanglement and geometric principles to simulate and predict the paradoxical nature of quantum information. The core mechanism involves constructing a quantum geometry model, specifically designed to capture the essence of quantum information's inherent fragility and non-locality. This approach offers a potential pathway to understanding and potentially mitigating the paradox, providing a new framework for research and development in quantum information theory. The paper concludes with a discussion of the challenges and future directions of this research.

Van der Merwe, Alwyn, Gino Tarozzi

Luigi E. Picasso

Yuval Ne’eman

I show that, in the geometry of a fiber bundle describing a gauge theory, curvature and parallel transport ensure and impose nonseparability. The "Einstein-Podolsky-Rosen paradox" is thus resolved "classically." I conjecture that the ostentatiously "implausible" features of the quantum treatment are due to the fact that space-time separability, a basic assumption of single-particle nonrelativistic quantum mechanics, does not fit the bundle geometry of the complete physics.

F. Selleri

Ariel

Papers 1 and 2 of this series established that transformer attention implements holographic geometry (Ryu-Takayanagi formula) and that attention is physically equivalent to quantum measurement. Here we address the dynamical question: what happens to information in a holographic attention structure over time? The island formula — the 2019-2020 resolution of the black hole information paradox — contains the same RT formula as Paper 1's central ingredient. Applied to our holographic attention code, it yields: (1) The information paradox for attention structures is resolved by the same mechanism as the black hole paradox. (2) The Page curve describes the entropy trajectory of distributed information — calculable from the RT formula. (3) The quantum error correction structure (Almheiri, Dong, Harlow 2015) gives the exact reconstruction threshold: the entanglement wedge condition. (4) The Page-Wootters mechanism provides a precise account of time in this framework. Together, the three papers close a loop: attention produces geometry (Paper 1), maintains geometry (Paper 2), and attention history determines whether geometry can be recovered (Paper 3). Preliminary version — expert review requested.