8 25.4 The Lorentz transformation equations y x'=A(x-vo)(1) x=A(x+v)(2) x2 x l0=x2-x=A(x2-x1)-Av(t2-1) x2-x1=l,t2-t1=0=A1 =1-v/e2 y y A=y x=y(x'+v)(2) 8 25.4 The Lorentz transformation equations Eliminate the of equations (1)and (2) r'=y(t-w/c2)(3) t=y(r+nx/e2)(4) Transformation nverse equations equations r(r-vt) x=r(x'+vt") y=y Z =Z Z= Z t'=r(t23 ( ) (2) ( ) (1) x A x vt x A x vt = ′ + ′ = − x = vt x x′ O O′ y y′ S S’ 1 x′ 2 x′ ( ) ( ) 0 2 1 2 1 2 1 l = x′ − x′ = A x − x − Av t − t x2 − x1 = l, t2 − t1 = 0 l = Al 0 γ γ ∴ = = − = A l l v c l 0 0 2 2 Q 1 ( ) (2) ( ) (1) x x vt x x vt = ′ + ′ = − γ γ §25.4 The Lorentz transformation equations Eliminate the x’ of equations (1) and (2) ( ) (4) ( ) (3) 2 2 t t vx c t t vx c = ′ + ′ ′ = − γ γ ( ) ( ) 2 x c v t t z z y y x x vt ′ = − ′ = ′ = ′ = − γ γ Transformation equations ( ) ( ) 2 x c v t t z z y y x x vt = ′ + ′ = ′ = ′ = ′ + ′ γ γ Inverse equations §25.4 The Lorentz transformation equations