The Relational Origin of Force in the Referential Entropy Cycle Theory: Emergence from Multi-Reference Configurations

In the Referential Entropy Cycle Theory (RECT), force is not a fundamental entity but an emergent relational network that appears only when two or more reference objects are present. Building on the covariant action established in a preceding paper, we demonstrate that all interaction terms vanish identically in the single-reference limit and become non-trivial as soon as a second reference object exists. We derive the effective two-particle force law, which takes an inverse-square form plus short-range corrections determined by the phase-field potential. The construction extends naturally to multi-particle systems and recovers the continuum stress-energy tensor of the macroscopic regime. Force is thereby shown to be a necessary consequence of multi-reference phase dynamics under the single axiom of referential-entropy maximisation. This record contains Paper II of RECT. Paper I presents the covariant action and the recovery of the Einstein and Schrödinger equations.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-26
DOI
https://doi.org/10.5281/zenodo.22110660
Primary Topic
Statistical Mechanics and Entropy
Type
preprint
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preprint

The Relational Origin of Force in the Referential Entropy Cycle Theory: Emergence from Multi-Reference Configurations

Daniel Fang
Zenodo (CERN European Organization for Nuclear Research)
Statistical Mechanics and Entropy
preprint

The Relational Origin of Force in the Referential Entropy Cycle Theory: Emergence from Multi-Reference Configurations

Daniel Fang
preprint en

Abstract

In the Referential Entropy Cycle Theory (RECT), force is not a fundamental entity but an emergent relational network that appears only when two or more reference objects are present. Building on the covariant action established in a preceding paper, we demonstrate that all interaction terms vanish identically in the single-reference limit and become non-trivial as soon as a second reference object exists. We derive the effective two-particle force law, which takes an inverse-square form plus short-range corrections determined by the phase-field potential. The construction extends naturally to multi-particle systems and recovers the continuum stress-energy tensor of the macroscopic regime. Force is thereby shown to be a necessary consequence of multi-reference phase dynamics under the single axiom of referential-entropy maximisation. This record contains Paper II of RECT. Paper I presents the covariant action and the recovery of the Einstein and Schrödinger equations.

Zenodo (CERN European Organization for Nuclear Research)
Peace, Justice and strong institutions
Statistical Mechanics and Entropy
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The Relational Origin of Force in the Referential Entropy Cycle Theory: Emergence from Multi-Reference Configurations — Daniel Fang · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS