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PreprintCC BY 4.0Zenodo

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

  • Risto Vanhanen1
  1. 1Independent Researcher
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Abstract

Relativistic kinematics and quantum phase evolution involve two kinds of angle: the hyperbolic rapidity of a Lorentz boost and the circular angle of a unitary phase. Special-relativistic quantum field theory combines them consistently, yet gravity remains unreconciled with quantum mechanics. Building on a dual-domain ontology in which spacetime emerges from a timeless quantum domain (QD) of pure entanglement, this paper introduces the entanglement-strain angle θ as the geometric variable that bridges the two domains.

For uniform motion and static, spherically symmetric gravity, time dilation, length contraction, energy increase, and gravitational redshift are expressed as elementary functions of θ. The Lorentz factor and the Schwarzschild metric become direct functions of θ, while the Gudermannian map relates the hyperbolic angle of a boost to θ. The speed of light is reinterpreted as the maximum rate at which the internal quantum phase synchronizes with θ, its value remaining underived. The Planck mass is identified with the standard Compton–Schwarzschild crossover and read as the scale where quantum coherence and gravitational strain become inseparable. A speculative extension relates local gravity and late-time expansion to the same entanglement structure; the associated gradient stress has equation of state w=-1/3 and does not itself accelerate the expansion.

The formalism modifies no empirical prediction of general relativity or quantum mechanics. It reinterprets both as consequences of entanglement strain, offering a unified geometric language in which motion and gravity are two regimes of one parameter and pointing toward an ontology in which entanglement is fundamental.

Keywords: entanglement‑strain angle; quantum entanglement; general relativity; quantum mechanics; quantum gravity; dark energy

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Cite

BibTeXRIS
BibTeX
@misc{vanhanen2026entanglementstrain,
  title = {{Entanglement‑Strain Angle: Geometric Unification of Relativistic Kinematics, Gravitation, and Quantum Phase}},
  author = {Risto Vanhanen},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23563694},
  url = {https://zenodo.org/records/23563694},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Entanglement‑Strain Angle: Geometric Unification of Relativistic Kinematics, Gravitation, and Quantum Phase
AU  - Risto Vanhanen
PY  - 2026
DA  - 2026/10/22
PB  - Zenodo
DO  - 10.5281/zenodo.23563694
UR  - https://zenodo.org/records/23563694
AB  - Relativistic kinematics and quantum phase evolution involve two kinds of angle: the hyperbolic rapidity of a Lorentz boost and the circular angle of a unitary phase. Special-relativistic quantum field theory combines them consistently, yet gravity remains unreconciled with quantum mechanics. Building on a dual-domain ontology in which spacetime emerges from a timeless quantum domain (QD) of pure entanglement, this paper introduces the entanglement-strain angle θ as the geometric variable that bridges the two domains.  For uniform motion and static, spherically symmetric gravity, time dilation, length contraction, energy increase, and gravitational redshift are expressed as elementary functions of θ. The Lorentz factor and the Schwarzschild metric become direct functions of θ, while the Gudermannian map relates the hyperbolic angle of a boost to θ. The speed of light is reinterpreted as the maximum rate at which the internal quantum phase synchronizes with θ, its value remaining underived. The Planck mass is identified with the standard Compton–Schwarzschild crossover and read as the scale where quantum coherence and gravitational strain become inseparable. A speculative extension relates local gravity and late-time expansion to the same entanglement structure; the associated gradient stress has equation of state w=-1/3 and does not itself accelerate the expansion.  The formalism modifies no empirical prediction of general relativity or quantum mechanics. It reinterprets both as consequences of entanglement strain, offering a unified geometric language in which motion and gravity are two regimes of one parameter and pointing toward an ontology in which entanglement is fundamental.  Keywords: entanglement‑strain angle; quantum entanglement; general relativity; quantum mechanics; quantum gravity; dark energy
ER  -