8 25.4 The Lorentz transformation equations Notice that x=x-wt v<<c, y→1{J Z =Z 2. Important deductions Time dilation then =t2-t1 t1=y(1+/c2) 12=(+m/c) =y(2-1)+2(x-x) t2-t1)=y 8 25.4 The Lorentz transformation equations @the relativity of simultaneity In s reference frame Event 1: Musician 1 Event 2: Musician 2 be to pla begins to play x1=0 0 0 Ax=x,x=lo,4t t1=0 2424 2. Important deductions Notice that v << c, γ → 1 1time dilation if ( ) ( ) 2 2 2 0 2 1 1 0 t t vx c t t vx c = ′ + ′ = ′ + ′ γ γ 2 1 0 2 1 2 0 0 2 1 ( ) ( ) ( ) γ γτ γ τ = ′ − ′ = = ′ − ′ + ′ − ′ = − t t x x c v t t t t then t t z z y y x x vt ′ = ′ = ′ = ′ = − §25.4 The Lorentz transformation equations Event 1: Musician 1 begins to play 0 s 0 m 1 1 = = t x Event 2: Musician 2 begins to play 0 s m 2 2 0 = = t x l 0l x y o S In S reference frame , 0 ∆x = x2 − x1 = l0 ∆t = t2 − t1 = 2the relativity of simultaneity §25.4 The Lorentz transformation equations