8 25.4 The Lorentz transformation equations Using the lorentz transformation equations x'=r(x-v) x=r(x'+vt' t'=rt-x) t=r(t+,x' We can get Le=r(Ax-vAt)4x c=y(Ax'+v∠r) At'=y(At-,4r)At=y( Ac) 8 25.4 The Lorentz transformation equations Ins’ reference frame Event I: Musician 1 Event 2: Musician 2 begins to play begins to play x1=0 Ar=x2=yo 1=0s A'=t2=-l0/c Conclusions: If two events are simultaneous in one inertial reference frame, they will not be simultaneous to any other inertial reference frame moving at non speed v with respect to the first. Only when At=0, 4x=0 then 4t=025 ( ) ( ) 2 x c v t t z z y y x x vt ′ = − ′ = ′ = ′ = − γ γ ( ) ( ) 2 x c v t t z z y y x x vt = ′ + ′ = ′ = ′ = ′ + ′ γ γ ( ) ( ) 2 x c v t t x x v t ∆ γ ∆ ∆ ∆ γ ∆ ∆ ′ = − ′ = − ( ) ( ) 2 x c v t t x x v t = ′ + ′ = ′ + ′ ∆ γ ∆ ∆ ∆ γ ∆ ∆ We can get Using the Lorentz transformation equations §25.4 The Lorentz transformation equations In S’ reference frame Event 1: Musician 1 begins to play 0 s 0 m 1 1 ′ = ′ = t x Event 2: Musician 2 begins to play 2 2 0 2 0 t t vl / c x x l ∆ γ ∆ γ ′ = ′ = − ′ = ′ = Conclusions: If two events are simultaneous in one inertial reference frame, they will not be simultaneous to any other inertial reference frame moving at non speed v with respect to the first. Only when ∆t = 0, ∆x = 0 then ∆t′ = 0 §25.4 The Lorentz transformation equations