equation 38.1 eq:lor-beta-gamma

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Supports

• depends_on definition 38.21 Rapidity ¶
  • depends_on proposition 38.22 Rapidities add ¶
• depends_on proposition 38.5 The invariant interval ¶
  • depends_on definition 38.6 Minkowski metric and interval ¶
    • depends_on definition 38.8 Causal classification ¶
      • depends_on proposition 38.9 Causal order is absolute ¶
    • depends_on definition 38.12 Proper time ¶
      • assumes experiment Frisch and Smith: Mount Washington to sea level ¶
        • cites (evidence) derived bib 5 Measurement of the Relativistic Time Dilation Using $\mu$-Mesons ¶
      • assumes experiment Ives and Stilwell: the moving atomic clock ¶
        • cites (evidence) derived bib 7 An Experimental Study of the Rate of a Moving Atomic Clock ¶
      • assumes experiment Rossi and Hall: muon survival with altitude ¶
        • cites (evidence) derived bib 3 Variation of the Rate of Decay of Mesotrons with Momentum ¶
      • depends_on definition 40.9 Four-force ¶
      • depends_on definition 40.2 Four-velocity ¶
        • depends_on definition 44.15 Dust ¶
        • depends_on definition 40.4 Four-momentum ¶
      • depends_on phenomenon 38.13 Time dilation ¶
        • depends_on phenomenon 53.3 Gravitational shift of gamma rays over a tower ¶
        • depends_on phenomenon 42.9 The relativistic clock budget of satellite navigation ¶
        • depends_on phenomenon 50.3 Relativistic redshift and precession of a stellar orbit ¶
        • depends_on remark 38.14 The effect is reciprocal, and that is consistent ¶
        • tests experiment Frisch and Smith: Mount Washington to sea level ¶ ↺
        • tests experiment Hafele and Keating: caesium clocks flown around the world ¶
        • tests experiment Ives and Stilwell: the moving atomic clock ¶ ↺
        • tests experiment Rossi and Hall: muon survival with altitude ¶ ↺
      • depends_on phenomenon 40.15 Differential ageing ¶
    • depends_on definition 39.1 Lorentz group ¶
      • depends_on definition 39.4 Improper Lorentz transformations ¶
        • depends_on proposition 39.8 Component structure ¶
      • depends_on definition 39.5 Orthochronous Lorentz group ¶
        • depends_on definition 39.7 Antichronous transformations ¶
        • depends_on lemma 109.42 Total inversion is a complex Lorentz transformation ¶
        • depends_on proposition 39.8 Component structure ¶ ↺
        • depends_on proposition 39.6 $L^{\uparrow}$ and $L^{\uparrow}_{+}$ are subgroups ¶
        • depends_on theorem 105.34 $CPT$ ¶
        • depends_on theorem 38.23 Polar decomposition of a Lorentz transformation ¶
      • depends_on definition 39.10 Poincaré group ¶
        • depends_on proposition 39.11 Invariance of the interval ¶
      • depends_on definition 39.3 Proper Lorentz group ¶
      • depends_on proposition 39.9 The generators ¶
      • depends_on proposition 39.2 $L$ is a Lie group ¶
    • depends_on definition 40.1 Four-vector ¶
      • depends_on definition 40.2 Four-velocity ¶ ↺
      • depends_on definition 40.12 Invariant mass ¶
        • depends_on example 40.13 Threshold energy for pair production ¶
      • depends_on theorem 115.31 Second-order Fermi acceleration ¶
        • depends_on theorem 115.33 The spectrum from a strong shock ¶
    • depends_on phenomenon 40.15 Differential ageing ¶ ↺
    • depends_on proposition 40.3 Normalization of the four-velocity ¶
      • depends_on proposition 109.74 The vacuum is thermal in a wedge ¶
      • depends_on proposition 45.6 Radial equation and effective potential ¶
        • depends_on proposition 45.10 Circular orbits and their energy ¶
        • depends_on proposition 45.8 Orbit equation ¶
        • depends_on proposition 45.21 Radial plunge: the cycloid ¶
      • depends_on theorem 40.5 Energy–momentum relation ¶
        • depends_on example 40.14 Compton scattering ¶
        • depends_on phenomenon 99.3 Electron–positron pair creation ¶
        • depends_on proposition 26.29 Reparametrization invariance and the mass-shell constraint ¶
        • depends_on proposition 49.2 Ground-state pressure of the ideal Fermi gas ¶
  • depends_on definition 38.12 Proper time ¶ ↺