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January 17, 20260 citationsOpen Access

Finite Relaxation Geometry of Spacetime: Microscopic Scales and Emergent Effective Quantumness

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PZP. A. Zabrodin

Key Points

  • This research aims to explore how finite relaxation time in spacetime affects its geometric properties and leads to emergent quantum behavior.
  • Developed a geometric framework describing spacetime with finite relaxation time.
  • Analyzed the response of spacetime geometry to matter-energy distributions at microscopic scales.
  • Examined the implications of delayed geometric responses on stochastic metric fluctuations.
  • Showed that finite relaxation time induces measurable temporal delays in spacetime response.
  • Demonstrated that these delays generate stochastic metric fluctuations reflecting effective quantum behavior.
  • Provided a coherent interpretation of quantum phenomena as emergent effects rather than requiring fundamental quantization.

Abstract

We propose a geometric framework in which spacetime is characterized by a finite relaxation time. While at macroscopic scales geometric relaxation occurs effectively instantaneously, at microscopic scales finite relaxation induces measurable temporal delays in the response of spacetime geometry to matter-energy distributions. We argue that this delayed geometric response naturally generates stochastic metric fluctuations, which manifest as effective quantum behavior without requiring fundamental quantization of spacetime itself. This approach provides a coherent interpretation of quantum-like phenomena as emergent effects of finite geometric relaxation, offering a non-competitive and complementary perspective to existing approaches in quantum gravity. Pavlo ZabrodinIndependent researcherdaleomel.dante@gmail.com

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Cite This Study

P. A. Zabrodin (2026) studied this question.

synapsesocial.com/papers/696b2616d2a12237a93494echttps://doi.org/10.5281/zenodo.18261123
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  1. 1Finite Relaxation Geometry: Spacetime Relaxation as the Origin of Dark-Sector Phenomena2026
  2. 2Finite-Relaxation Geometry (FRG) 3.1: Scale Dependence of Geometric Relaxation and the Hierarchy of Gravitational Regimes2026
  3. 3Finite-Relaxation Geometry 3.0: A Macroscopic Effective Cosmological Framework2026
  4. 4Gravitation as Geometric Response2026
  5. 5Emergent Spacetime and Gravity from Timeless Renormalization Consistency: A Quantum Gravity Framework2026