Weak-field clock frequency ratio

Theory · FOUNDATIONEquation version 1.0.0

Based on the final manuscript · Chapters 1–2

\frac{f(r_2)}{f(r_1)}-1=\frac{\Psi(r_2)-\Psi(r_1)}{c^2}+O\!\left(\frac{\Psi^2}{c^4}\right)

Final Chapter 2 Eq. (2.2a) is an exact ratio in the specified static constitutive model. This registry entry retains its first-order weak-field expansion, requiring |Ψ|/c²≪1 at both positions and a common reference calibration; it is not the full Eq. (2.2a).
Chapter reference: Final consolidated manuscript · First-order weak-field expansion of Chapter 2, Eq. (2.2a), and its following unnumbered discussion · ASD-BOOK-ddbade997b45

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ASD-WEB-TIME-006 is the stable website equation ID. It retains existing links and does not replace the manuscript reference. Use the copy button to obtain LaTeX.

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Adopted source, conditions and previous versions

Final consolidated manuscript · First-order weak-field expansion of Chapter 2, Eq. (2.2a), and its following unnumbered discussion

Conditions retained in this adoption

Common reference calibration; static constitutive relation Φ=Ω⁻¹
Exact ratio requires 1+2Ψ/c²>0; weak-field expansion also requires |Ψ|/c²≪1

Specific unresolved source issues

FINAL-CH1-CLOCK-PROTOCOL

Source locators: p0570 · p0571

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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Previous source, retained as history

FND-3dde8d8e081d · 第二章 §一.2，式（2.2a），PDF 第 3 页

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