theorem 40.5 Energy–momentum relation
open in the book ·
parts/04-special-relativity/04-relativistic-dynamics.tex:93
· p. 1230
Rests on
-
depends_on
definition 40.4
Four-momentum
¶
-
depends_on
definition 40.2
Four-velocity
¶
-
depends_on
definition 38.12
Proper time
¶
-
depends_on
definition 38.6
Minkowski metric and interval
¶
- depends_on proposition 38.5 The invariant interval ¶
- depends_on proposition 38.5 The invariant interval ¶ ↺
-
depends_on
definition 38.6
Minkowski metric and interval
¶
-
depends_on
definition 40.1
Four-vector
¶
- depends_on definition 38.6 Minkowski metric and interval ¶ ↺
- depends_on equation 38.14 eq:lor-invariance-condition ¶
-
depends_on
definition 38.12
Proper time
¶
-
depends_on
definition 40.2
Four-velocity
¶
-
depends_on
proposition 40.3
Normalization of the four-velocity
¶
- depends_on definition 38.6 Minkowski metric and interval ¶ ↺
- depends_on equation 40.2 eq:rdyn-fourvelocity ¶
- proves proof ch:04-relativistic-dynamics@proof-1 ¶
- proves proof ch:04-relativistic-dynamics@proof-2 ¶
Supports
- 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 |
→ | Four-momentum | declared | parts/04-special-relativity/04-relativistic-dynamics.tex:98 |
depends_on |
→ | Normalization of the four-velocity | declared | parts/04-special-relativity/04-relativistic-dynamics.tex:98 |
depends_on |
← | Compton scattering | declared | parts/04-special-relativity/04-relativistic-dynamics.tex:325 |
depends_on |
← | Electron–positron pair creation | declared | parts/11-qft-standard-model/01-canonical-quantization.tex:222 |
depends_on |
← | Reparametrization invariance and the mass-shell constraint | declared | parts/03-classical-mechanics/09-constrained-hamiltonian-dynamics.tex:1071 |
depends_on |
← | Ground-state pressure of the ideal Fermi gas | declared | parts/05-general-relativity-cosmology/08-compact-stars.tex:149 |
proves |
← | ch:04-relativistic-dynamics@proof-2 | declared | parts/04-special-relativity/04-relativistic-dynamics.tex:101 |