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Both measurements use the same scale factor. Event pairing and inverse-mapping conditions are addressed in the consistency review. This expression is not assumed to be a Lorentz transformation.

Theory · DERIVEDEquation version 1.0.0

Based on the final manuscript · Chapter 1

ASD-WEB-LVE-005
r′=γ(r−vt)v=vxi+vyj+vzkr=γ(r′+vt′)\begin{aligned}\mathbf r^{\prime}&=\gamma(\mathbf r-\mathbf v t)\\\mathbf v&=v_x\mathbf i+v_y\mathbf j+v_z\mathbf k\\\mathbf r&=\gamma(\mathbf r^{\prime}+\mathbf v t^{\prime})\end{aligned}

Both measurements use the same scale factor. Event pairing and inverse-mapping conditions are addressed in the consistency review. This expression is not assumed to be a Lorentz transformation.
Chapter reference: Final consolidated manuscript · Chapter 1, Section II, Eqs. (1.7)–(1.9) · ASD-BOOK-ddbade997b45

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Final consolidated manuscript · Chapter 1, Section II, Eqs. (1.7)–(1.9)

Both measurements use the same scale factor. Event pairing and inverse-mapping conditions are addressed in the consistency review. This expression is not assumed to be a Lorentz transformation.

Conditions retained in this adoption

  • A1–A5; tt′≠0; 0≤v<c
  • Directed effective length is not an arbitrary Euclidean vector norm

Specific unresolved source issues

  • FINAL-CH1-PAIRING

Source locators: p0327 · p0329 · p0331

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

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Previous source, retained as history

CH1-caf38018fc5a · 第一章 §二,式(1.7)–(1.9),PDF 第 5–6 页

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