Relativity and Cosmology

   

Correspondence Principles: A Systematic Comparison of the Cosmological Special Theory of Relativity with Special Relativity, General Relativity, and Quantum Mechanics

Authors: Sangwha Yi

The Cosmological Special Theory of Relativity (CSTR) re-derives the Lorentz transformation, relativistic quantum mechanics, quantumfield theory, and general relativity within a cosmological inertial frame, in which a local, unexpanded spatial coordinate is related to thephysically expanded coordinate of a Robertson-Walker universe through a cosmological expansion function τ (t0) (Yi, 2020, 2025). Fivecompanion reviews have each examined a different sector of this program — special-relativistic kinematics, relativistic quantum mechanics andfield quantization, the Cosmological General Theory of Relativity’s black-hole solutions, the group-theoretic structure of the transformationitself, and the theory’s observational status — and each has found that CSTR’s predictions reduce, in a precise and recurring sense, tothose of the corresponding standard theory. This paper collects that recurring correspondence into a single, systematic set of comparisontables, juxtaposing every principal CSTR equation against its special-relativistic, quantum-mechanical, quantum-field-theoretic, or generalrelativisticcounterpart, and identifies the single limit — evaluation at a fixed cosmological epoch, equivalently τ (t0) → const — responsiblefor every instance of correspondence. We further collect, in a final comparison, the specific respects in which CSTR is not merely a relabelingof standard theory: the multi-epoch groupoid structure and the associated open questions identified in a companion review. The result isintended as a single reference synthesizing the correspondence structure of the entire CSTR program.

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[v1] 2026-08-03 20:39:38

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