EQ-LORENTZ-FACTOR · Special Relativity
Lorentz Factor (Special Relativity)
gamma**2*(1 - v**2/c**2) - 1 = 0
Variables
variable
c
speed of light in vacuum (299 792 458 m/s)
- Object
- photon
- Property
- SpeedOfLight
- Context
- lorentz_frame
variable
gamma
Lorentz factor, γ = 1 / √(1 − v²/c²)
- Object
- lorentz_observer
- Property
- LorentzFactor
- Context
- lorentz_frame
variable
v
relative speed of the moving frame
- Object
- lorentz_observer
- Property
- Speed
- Context
- lorentz_frame
Axioms
algebraic constant_coefficients deterministic lorentz_invariant nonlinear
Assumptions
- |v| < c (subluminal relative motion)
- Both frames are inertial
- Spacetime is Minkowski (no gravitational field)
- v and c are measured in a consistent frame-invariant scheme
Derivation
- Einstein, Ann. der Physik 17 (1905), 891 (on the electrodynamics of moving bodies)
- Derived from the invariance of the spacetime interval ds² = c²dt² − dx² − dy² − dz²
- Reduces to γ → 1 in the non-relativistic limit v/c → 0, recovering Newtonian mechanics
References
- Einstein, Zur Elektrodynamik bewegter Körper, Ann. Phys. 17 (1905), 891
- Misner, Thorne & Wheeler, Gravitation (1973), §2.3
- Rindler, Introduction to Special Relativity, 2nd ed., §1-5