EQUATION REGISTRY

Longitudinal round-trip time in the equal-arm model

Ideal equal-arm configuration with apparatus imperfections omitted. The compared observable is the arm-to-arm difference.

Theory · DERIVEDEquation version 1.0.0

Based on the final manuscript · Chapter 1

ASD-WEB-LVE-012
t1′=Lcγ(1−β),t2′=Lcγ(1+β)T∥′=t1′+t2′=2γLc\begin{aligned}t_1^{\prime}&=\frac Lc\gamma(1-\beta),&t_2^{\prime}&=\frac Lc\gamma(1+\beta)\\T_{\parallel}^{\prime}&=t_1^{\prime}+t_2^{\prime}=\frac{2\gamma L}{c}\end{aligned}

Ideal equal-arm configuration with apparatus imperfections omitted. The compared observable is the arm-to-arm difference.
Chapter reference: Final consolidated manuscript · Chapter 1, Section 3.2, Eqs. (1.26)–(1.28) · ASD-BOOK-ddbade997b45

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Adopted source, conditions and previous versions

Final consolidated manuscript · Chapter 1, Section 3.2, Eqs. (1.26)–(1.28)

Ideal equal-arm configuration with apparatus imperfections omitted. The compared observable is the arm-to-arm difference.

Conditions retained in this adoption

  • Apparatus, direction and counting conditions remain with each entry
  • Muon inputs are illustrative approximations, not a complete survival fit

Specific unresolved source issues

  • FINAL-CH1-FIZEAU-DIMENSION
  • FINAL-CH1-MUON-OBSERVABLE
  • FINAL-CH1-CLOCK-PROTOCOL

Source locators: p0412 · p0414 · p0416

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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Previous source, retained as history

CH1-caf38018fc5a · 第一章 §3.2,式(1.26)–(1.28),PDF 第 13 页

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