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Unformatted text preview: Standard Notation = vc =- 11 2 Lorentz Transformations = + x x' vt = + t t' vxc2 = y y' = z z' Special Cases = t = L0 L Velocity Addition and Transverse Velocities = +- / ucomb u1 u21 u1u2 c2 = [ + ] uy uy' 1 vc2ux' = [ + ] uz uz' 1 vc2ux' * Here, while = , = , y y' z z' the reason as to why the velocities are different is due to the transformation of time, which are dependent on , v x' . Force Transformations In frame S , , = , Fx Fy m3ax ay In frame S' , , = ( , ) Fx' Fy' m 3ax 2ay So, , =( , ) Fx Fy Fx' Fy' Invariant Interval The quantity =- s2 x2 ct2 is conserved in all reference frames. If > s2 0 , the separation is spacelike. If < s2 0 , the separation is timelike. If = s2 0 , the separation is lightlike. Spacelike events can be reversed due to observations, but timelike event separations cannot be reversed....
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- Spring '08