definition 40.1 Four-vector

open in the book · parts/04-special-relativity/04-relativistic-dynamics.tex:18 · p. 1229

ground object -- no derivation owed

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 38.14 eq:lor-invariance-condition ¶

Supports

depends_on definition 40.2 Four-velocity ¶
- depends_on definition 44.15 Dust ¶
  - depends_on definition 44.16 Perfect fluid ¶
    - depends_on proposition 44.37 Energy conditions for the perfect fluid ¶
    - depends_on proposition 44.20 Perfect-fluid equations of motion ¶
      - depends_on corollary 44.21 Dust flows on geodesics ¶
    - depends_on theorem 49.9 Tolman–Oppenheimer–Volkoff equations ¶
      - depends_on example 49.11 The uniform-density star ¶
      - depends_on phenomenon 49.19 Neutron stars reach two solar masses ¶
  - depends_on theorem 44.27 Newtonian correspondence of the field equations ¶
    - depends_on corollary 44.35 The field equations are essentially unique ¶
    - depends_on phenomenon 49.6 A maximum mass for a cold degenerate star ¶
    - depends_on phenomenon 49.16 Pulsars: clocks at nuclear density ¶
    - depends_on phenomenon 49.14 A neutron star is observed being born ¶
    - depends_on proposition 44.29 Linearized field equations ¶
- depends_on definition 40.4 Four-momentum ¶
  - depends_on definition 40.9 Four-force ¶
  - depends_on definition 40.12 Invariant mass ¶
    - depends_on example 40.13 Threshold energy for pair production ¶
  - depends_on phenomenon 99.3 Electron–positron pair creation ¶
  - depends_on postulate 40.11 Conservation of four-momentum ¶
    - depends_on example 40.14 Compton scattering ¶
    - depends_on example 40.13 Threshold energy for pair production ¶ ↺
  - 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 definition 40.12 Invariant mass ¶ ↺
depends_on theorem 115.31 Second-order Fermi acceleration ¶
- depends_on theorem 115.33 The spectrum from a strong shock ¶

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:27
`depends_on`	→	eq:lor-invariance-condition	declared	parts/04-special-relativity/04-relativistic-dynamics.tex:27
`depends_on`	←	Four-velocity	declared	parts/04-special-relativity/04-relativistic-dynamics.tex:43
`depends_on`	←	Invariant mass	declared	parts/04-special-relativity/04-relativistic-dynamics.tex:266
`depends_on`	←	Second-order Fermi acceleration	declared	parts/11-qft-standard-model/17-cosmic-rays-astroparticle.tex:2151