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AIP conference proceedings

Unveiling the "mystery" of quantum nonlocality by conformal geometrodynamics

F. De Martini, Enrico Santamato

Published Jan 1, 2012• 2 citations
Publisher

Abstract

The problem of quantum entanglement of two spin-1/2 particles is faced in a conformally invariant geometric framework. The configuration space of the two particles is extended by adding orientational degrees of freedom and quantum effects, including entanglement, are derived from the conformal curvature of this space. A mechanism is proposed where the space curvature and the particle motion are in mutual interaction and it is proved that this feedback between geometry and dynamics reproduces all quantum features of the two-particle system. Entanglement, in particular, originates from the residual nonlocal interaction among the orientational degrees of freedom of the two spinning particles.

DOI
10.1063/1.4773128

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The problem of quantum entanglement of two spin-1/2 particles is faced in a conformally invariant geometric framework. The configuration space of the two particles is extended by adding orientational degrees of freedom and quantum effects, including entanglement, are derived from the conformal curvature of this space. A mechanism is proposed where the space curvature and the particle motion are in mutual interaction and it is proved that this feedback between geometry and dynamics reproduces all quantum features of the two-particle system. Entanglement, in particular, originates from the residual nonlocal interaction among the orientational degrees of freedom of the two spinning particles.
The problem of quantum entanglement of two spin-1/2 particles is faced in a conformally invariant geometric framework. The configuration space of the two particles is extended by adding orientational degrees of freedom and quantum effects, including entanglement, are derived from the conformal curvature of this space. A mechanism is proposed where the space curvature and the particle motion are in mutual interaction and it is proved that this feedback between geometry and dynamics reproduces all quantum features of the two-particle system. Entanglement, in particular, originates from the residual nonlocal interaction among the orientational degrees of freedom of the two spinning particles.
Quantum entanglement is often described as a mysterious nonlocal connection between two particles. While experimentally precise, this interpretation implicitly assumes that the observed multiplicity is fundamental. This paper proposes an alternative, geometrically grounded view: that so-called twin entanglement may arise from a single physical entity embedded in higher-dimensional spacetime, intersecting a 3D+1 observational slice at multiple locations. By separating the roles of space and time—allowing spatial dimensionality to vary while time remains one-dimensional—the work explains instantaneous correlations without invoking signaling, interaction, or duplication. Opposite spin correlations are shown to emerge naturally from geometric orientation of intersection, rather than from coordinated particle behavior. Within a block-universe and retrocausal framework, entanglement is reinterpreted as global consistency rather than dynamical influence. Two experimentally testable directions are outlined, including asymmetric local manipulation tests, while acknowledging the intrinsic limitations imposed by lower-dimensional observation. The paper concludes that many conceptual difficulties surrounding entanglement may stem not from nature itself, but from the language and intuition of observers confined to a limited dimensional slice. The problem was never the elephant — it was the blindness.
Quantum entanglement, a phenomenon where two or more particles become linked regardless of distance, has captivated physicists and philosophers alike. This research explores the potential of utilizing geometric principles to understand and manipulate entanglement, proposing a novel model to represent quantum entanglement as a geometric structure. We aim to investigate how the inherent geometry of entangled states can be leveraged to optimize quantum computation and communication protocols. The core claim is that establishing a geometric model of quantum entanglement will unlock new avenues for enhancing the performance of these technologies. This paper delves into the foundational concepts and proposes a mechanism for translating entanglement into a geometric framework, ultimately seeking to reveal hidden properties and potential optimizations within the space of entangled quantum states.
A rigorous ab initio derivation of the quantum mechanics of a single particle with spin is presented starting by conformally Weyl-gauge-invariant principle. The particle is described as a relativistic top with six Euler's angles and quantum effects are introduced by assuming that the Weyl's curvature of the particle configuration space acts on it as an external scalar potential. Weyl's conformal covariance is made explicit in all steps of the theory. It is shown that metric of the configuration space accounts for non-quantum relativistic effects, while the affine connections account for quantum relativistic effects. In this way, classical and quantum features acquire well distinguished geometrical origin. A scalar wave function is also introduced to recover the connection with the standard quantum description based on Dirac's four-component spinors. Finally, the case of two entangled spins is considered in the nonrelativistic limit and it is found that the nonlocality rests on the entanglement of the spin internal orientational variables, playing the role of "hidden variables". The theory was carried out in the Minkowski space-time, but it can be easily extended to a space with nonzero Riemann curvature.
Quantum entanglement, a cornerstone of quantum mechanics, presents a fascinating and potentially transformative concept for geometric study. This paper proposes a novel approach to understanding entanglement as a geometric phenomenon, exploring its inherent properties and their impact on spatial geometry. We hypothesize that entanglement can be modeled as a non-local geometric structure, leading to unique mathematical and computational implications for quantum information theory. We introduce a quantum geometry algorithm designed to investigate the intricate relationships between entangled states and the underlying geometric structure. This research aims to push the boundaries of quantum geometry, offering a new framework for analyzing and manipulating entangled systems.
Since the 1935 proposal by Einstein, Podolsky and Rosen the riddle of nonlocality, today demonstrated by the violation of Bell's inequalities within innumerable experiments, has been a cause of concern and confusion within the debate over the foundations of quantum mechanics. The present paper tackles the problem by a nonrelativistic approach based on conformal differential geometry applied to the solution of the dynamical problem of two entangled spin 1/2 particles. It is found that the quantum nonlocality may be understood on the basis of a conformal quantum geometrodynamics acting necessarily on the full "configuration space" of the entangled particles. At the end, the violation of the Bell inequalities is demonstrated without making recourse to the common nonlocality paradigm.