theorem 38.4 Lorentz boost

open in the book · parts/04-special-relativity/02-lorentz-transformations.tex:74 · p. 1206

Rests on

depends_on notation 38.3 Standard configuration ¶
depends_on postulate 38.2 Invariance of the speed of light ¶
depends_on postulate 38.1 Principle of relativity ¶
proves proof ch:02-lorentz-transformations@proof-1 ¶

Supports

depends_on phenomenon 51.4 The dipole ¶
depends_on phenomenon 38.10 Relativity of simultaneity ¶
- depends_on definition 38.15 Proper length ¶
  - depends_on phenomenon 38.16 Length contraction ¶
- depends_on remark 38.14 The effect is reciprocal, and that is consistent ¶
depends_on phenomenon 38.13 Time dilation ¶
- depends_on phenomenon 53.3 Gravitational shift of gamma rays over a tower ¶
  - tests experiment Pound, Rebka and Snider: redshift in a tower ¶
    - cites (evidence) derived bib Detection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole ¶
    - cites (evidence) derived bib Detection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole ¶ ↺
    - cites (evidence) derived bib 7897 Resolving the gravitational redshift across a millimetre-scale atomic sample ¶
    - cites (evidence) derived bib 7897 Resolving the gravitational redshift across a millimetre-scale atomic sample ¶ ↺
    - cites (evidence) derived bib 5999 Optical Clocks and Relativity ¶
    - cites (evidence) derived bib 5999 Optical Clocks and Relativity ¶ ↺
    - cites (method) derived bib Kernresonanzfluoreszenz von Gammastrahlung in Ir$^{191}$ ¶
    - cites (method) derived bib Kernresonanzfluoreszenz von Gammastrahlung in Ir$^{191}$ ¶ ↺
    - cites (method) derived bib 7 Apparent Weight of Photons ¶
    - cites (evidence) derived bib 7 Apparent Weight of Photons ¶ ↺
    - cites (method) derived bib 3B Effect of Gravity on Gamma Radiation ¶
    - cites (evidence) derived bib 3B Effect of Gravity on Gamma Radiation ¶ ↺
    - … 2 more
- 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 ¶
  - cites (evidence) derived bib 5 Measurement of the Relativistic Time Dilation Using $\mu$-Mesons ¶
- tests experiment Hafele and Keating: caesium clocks flown around the world ¶
  - cites (history) derived bib 4044 Around-the-World Atomic Clocks: Predicted Relativistic Time Gains ¶
  - cites (history) derived bib 4044 Around-the-World Atomic Clocks: Predicted Relativistic Time Gains ¶ ↺
  - cites (evidence) derived bib 4044 Around-the-World Atomic Clocks: Observed Relativistic Time Gains ¶
  - cites (evidence) derived bib 4044 Around-the-World Atomic Clocks: Observed Relativistic Time Gains ¶ ↺
- tests experiment Ives and Stilwell: the moving atomic clock ¶
  - cites (evidence) derived bib 7 An Experimental Study of the Rate of a Moving Atomic Clock ¶
- tests 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 phenomenon 38.18 Relativistic composition of velocities ¶
- tests experiment Fizeau: light dragged by moving water ¶
  - cites (context) derived bib 10 Zur Elektrodynamik bewegter Körper ¶
  - cites (evidence) derived bib 13 Sur les hypothèses relatives à l'éther lumineux, et sur une expérience qui paraît démontrer que le mouvement des corps change la vitesse avec laquelle la lumière se propage dans leur intérieur ¶
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 ¶ ↺
    - assumes experiment Ives and Stilwell: the moving atomic clock ¶ ↺
    - assumes experiment Rossi and Hall: muon survival with altitude ¶ ↺
    - 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 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 ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

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partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Standard configuration	declared	parts/04-special-relativity/02-lorentz-transformations.tex:83
`depends_on`	→	Invariance of the speed of light	declared	parts/04-special-relativity/02-lorentz-transformations.tex:83
`depends_on`	→	Principle of relativity	declared	parts/04-special-relativity/02-lorentz-transformations.tex:83
`depends_on`	←	The dipole	declared	parts/05-general-relativity-cosmology/10-exp-cmb.tex:529
`depends_on`	←	Relativity of simultaneity	declared	parts/04-special-relativity/02-lorentz-transformations.tex:453
`depends_on`	←	Time dilation	declared	parts/04-special-relativity/02-lorentz-transformations.tex:524
`depends_on`	←	Relativistic composition of velocities	declared	parts/04-special-relativity/02-lorentz-transformations.tex:648
`depends_on`	←	The invariant interval	declared	parts/04-special-relativity/02-lorentz-transformations.tex:204
`proves`	←	ch:02-lorentz-transformations@proof-1	declared	parts/04-special-relativity/02-lorentz-transformations.tex:86