proposition 40.3 Normalization of the four-velocity

open in the book · parts/04-special-relativity/04-relativistic-dynamics.tex:51 · p. 1229

Rests on

depends_on definition 38.6 Minkowski metric and interval ¶
- depends_on proposition 38.5 The invariant interval ¶
  - depends_on equation 38.1 eq:lor-beta-gamma ¶
  - depends_on theorem 38.4 Lorentz boost ¶
    - 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 ¶
  - proves proof ch:02-lorentz-transformations@proof-2 ¶
depends_on equation 40.2 eq:rdyn-fourvelocity ¶
proves proof ch:04-relativistic-dynamics@proof-1 ¶

Supports

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 phenomenon 45.12 Efficiency of accretion onto compact objects ¶
- depends_on proposition 45.8 Orbit equation ¶
  - depends_on phenomenon 53.2 Measured deflection of starlight at the solar limb ¶
    - tests experiment Dyson, Eddington and Davidson: the eclipse of 1919 ¶
      - cites (method) derived bib 571-581 A determination of the deflection of light by the sun's gravitational field, from observations made at the total eclipse of May 29, 1919 ¶
      - cites (evidence) derived bib 571-581 A determination of the deflection of light by the sun's gravitational field, from observations made at the total eclipse of May 29, 1919 ¶ ↺
      - cites (evidence) derived bib 571-581 A determination of the deflection of light by the sun's gravitational field, from observations made at the total eclipse of May 29, 1919 ¶ ↺
      - cites (history) derived bib 10 Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes ¶
      - cites (history) derived bib Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie ¶
      - cites (evidence) derived bib 2 PROGRESS IN MEASUREMENTS OF THE GRAVITATIONAL BENDING OF RADIO WAVES USING THE VLBA ¶
      - cites (evidence) derived bib Gravitational deflection of light: a re-examination of the observations of the solar eclipse of 1919 ¶
      - cites (evidence) derived bib 8 Measurement of the Solar Gravitational Deflection of Radio Waves Using Very-Long-Baseline Interferometry ¶
      - cites (evidence) derived bib 0957 + 561 A, B: twin quasistellar objects or gravitational lens? ¶
      - cites (context) derived bib 1 The Confrontation between General Relativity and Experiment ¶
      - cites (context) derived bib 1 The Confrontation between General Relativity and Experiment ¶ ↺
  - depends_on phenomenon 53.1 Measured anomalous advance of Mercury's perihelion ¶
    - tests experiment Le Verrier and the perihelion of Mercury ¶
      - cites (evidence) derived bib Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole ¶
      - cites (evidence) derived bib Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole ¶ ↺
      - cites (history) derived bib Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie ¶ ↺
      - cites (history) derived bib Erklärung der Perihelbewegung des Merkur aus der allgemeinen Relativitätstheorie ¶ ↺
      - cites (data) derived bib Lettre de M. Le Verrier à M. Faye sur la théorie de Mercure et sur le mouvement du périhélie de cette planète ¶
      - cites (evidence) derived bib Lettre de M. Le Verrier à M. Faye sur la théorie de Mercure et sur le mouvement du périhélie de cette planète ¶ ↺
      - cites (evidence) derived bib The Elements of the Four Inner Planets and the Fundamental Constants of Astronomy ¶
      - cites (data) derived bib 1 The Confrontation between General Relativity and Experiment ¶ ↺
  - depends_on phenomenon 45.9 Relativistic advance of the periastron ¶
- depends_on proposition 45.21 Radial plunge: the cycloid ¶
  - depends_on proposition 45.22 The view from outside: exponential freezing ¶
    - depends_on phenomenon 45.24 Compact objects exist above every cold-support limit ¶
  - depends_on theorem 45.23 Oppenheimer–Snyder collapse ¶
    - depends_on phenomenon 45.24 Compact objects exist above every cold-support limit ¶ ↺
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 phenomenon 49.6 A maximum mass for a cold degenerate star ¶
  - depends_on phenomenon 49.8 The white-dwarf luminosity function has an edge ¶
  - depends_on phenomenon 49.1 Matter at a billion kilograms per cubic metre ¶
  - depends_on theorem 49.7 The Chandrasekhar mass ¶
    - depends_on phenomenon 49.6 A maximum mass for a cold degenerate star ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

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

Edges

type	direction	node	provenance	where
`depends_on`	→	Minkowski metric and interval	declared	parts/04-special-relativity/04-relativistic-dynamics.tex:54
`depends_on`	→	eq:rdyn-fourvelocity	declared	parts/04-special-relativity/04-relativistic-dynamics.tex:54
`depends_on`	←	The vacuum is thermal in a wedge	declared	parts/11-qft-standard-model/11-axiomatic-qft.tex:2333
`depends_on`	←	Radial equation and effective potential	declared	parts/05-general-relativity-cosmology/04-schwarzschild-black-holes.tex:296
`depends_on`	←	Energy–momentum relation	declared	parts/04-special-relativity/04-relativistic-dynamics.tex:98
`proves`	←	ch:04-relativistic-dynamics@proof-1	declared	parts/04-special-relativity/04-relativistic-dynamics.tex:57