Entanglement‑Strain Angle: Geometric Unification of Relativistic Kinematics, Gravitation, and Quantum Phase

General relativity (GR) and quantum mechanics (QM) are founded on incompatible geometries: GR on hyperbolic Lorentz boosts, QM on circular unitary phase rotations. This paper proposes that both are projections of a deeper, pre‑geometric entanglement structure. Building on a dual‑domain ontology in which spacetime emerges from a timeless Quantum Domain (QD) of pure entanglement, the entanglement‑strain angle θ is introduced here as the fundamental geometric variable that bridges the two domains. All relativistic effects—time dilation, length contraction, mass increase, and gravitational redshift—are expressed as elementary functions of θ. More broadly, θ provides a single geometric parameter linking relativistic kinematics, gravitational effects, and quantum phase evolution. The Lorentz factor and the Schwarzschild metric can be re-expressed directly in terms of θ, revealing hyperbolic geometry as a projection of circular entanglement geometry. The speed of light c is reinterpreted as the maximum rate at which the internal quantum phase Φ_P can synchronize with θ, while the Planck mass emerges naturally as the crossover where the quantum coherence length equals the gravitational strain radius. Gravity's dual role—local attraction versus global expansion—follows from scale‑dependent behavior of the same θ‑field. The formalism does not modify any empirical prediction of GR or QM, but reinterprets them as manifestations of entanglement strain. It offers a unified geometric language in which motion and gravity are two sides of the same coin, and points toward a deeper ontology where entanglement is the only fundamental reality. Keywords: General relativity; Quantum mechanics; Quantum entanglement; Dual‑domain cosmology; Quantum gravity; Entanglement‑strain angle; Quantum phase; Planck mass; Gravitational redshift; Dark energy; Philosophy of physics

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-06-25
DOI
https://doi.org/10.5281/zenodo.20844320
Primary Topic
Relativity and Gravitational Theory
Type
preprint
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preprint

Entanglement‑Strain Angle: Geometric Unification of Relativistic Kinematics, Gravitation, and Quantum Phase

Risto Vanhanen
Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
preprint

Entanglement‑Strain Angle: Geometric Unification of Relativistic Kinematics, Gravitation, and Quantum Phase

Risto Vanhanen
preprint en

Abstract

General relativity (GR) and quantum mechanics (QM) are founded on incompatible geometries: GR on hyperbolic Lorentz boosts, QM on circular unitary phase rotations. This paper proposes that both are projections of a deeper, pre‑geometric entanglement structure. Building on a dual‑domain ontology in which spacetime emerges from a timeless Quantum Domain (QD) of pure entanglement, the entanglement‑strain angle θ is introduced here as the fundamental geometric variable that bridges the two domains. All relativistic effects—time dilation, length contraction, mass increase, and gravitational redshift—are expressed as elementary functions of θ. More broadly, θ provides a single geometric parameter linking relativistic kinematics, gravitational effects, and quantum phase evolution. The Lorentz factor and the Schwarzschild metric can be re-expressed directly in terms of θ, revealing hyperbolic geometry as a projection of circular entanglement geometry. The speed of light c is reinterpreted as the maximum rate at which the internal quantum phase Φ_P can synchronize with θ, while the Planck mass emerges naturally as the crossover where the quantum coherence length equals the gravitational strain radius. Gravity's dual role—local attraction versus global expansion—follows from scale‑dependent behavior of the same θ‑field. The formalism does not modify any empirical prediction of GR or QM, but reinterprets them as manifestations of entanglement strain. It offers a unified geometric language in which motion and gravity are two sides of the same coin, and points toward a deeper ontology where entanglement is the only fundamental reality. Keywords: General relativity; Quantum mechanics; Quantum entanglement; Dual‑domain cosmology; Quantum gravity; Entanglement‑strain angle; Quantum phase; Planck mass; Gravitational redshift; Dark energy; Philosophy of physics

Zenodo (CERN European Organization for Nuclear Research)
Relativity and Gravitational Theory
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Entanglement‑Strain Angle: Geometric Unification of Relativistic Kinematics, Gravitation, and Quantum Phase — Risto Vanhanen · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS