Lecture 05: General Relativity - Physics & Astronomy - Northeastern ...

NortheasternIllinoisUniversityLorentz Transformations for E & BSpecialRelativityPostulatesLorentz FactorLorentzTransformationsLT for E & BLT for E & pGeneralRelativityCosmologyFor two inertial reference frames where the second framemoves at v = vê ‖ with respect to the first.t ′ = γ(t − vx ‖ /c 2 ) t = γ(t ′ + vx ′ ‖ /c2 )x ′ ‖= γ(x ‖ − vt) x ‖ = γ(x ′ ‖ + vt′ )x ′ ⊥ = x ⊥ x ⊥ = x ′ ⊥E‖ ′ = E ‖ E ‖ = E‖′E ′ ⊥ = γ(E ⊥ + v × B ⊥ ) E ⊥ = γ(E ′ ⊥ − v × B′ ⊥ )B‖ ′ = B ‖ B ‖ = B‖′B ′ ⊥ = γ(B ⊥ − v × E ⊥ /c 2 ) B ⊥ = γ(B ′ ⊥ + v × E′ ⊥ /c2 )Maxwell’s equations are preserved by the LorentzTransformations.c○2004, 2007 G. Anderson Physics III – slide 7 / 37