Lecture3 - RelativisticInvariance (Lorentzinvariance)

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Relativistic Invariance orentz invariance) (Lorentz invariance) The laws of physics are invariant under a transformation between two ordinate frames moving at constant coordinate frames moving at constant velocity w.r.t. each other . he world is ot variant but the laws (The world is not invariant, but the laws of physics are!)
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Review: Special Relativity Einstein’s assumption: the speed of light is independent of the (constant ) Speed of light = C = |r –r | / (t –t ) = |r –r | / (t –t ) velocity, v, of the observer. It forms the basis for special relativity. 2 1 2 1 2 1 2 1 = |dr/dt| = |dr’/dt’|
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C 2 = | d r| 2 / dt 2 = | d r’| 2 / dt 2 h iscanberewr i t ten Both measure the same speed! This can be rewritten : d( C t) 2 -|d r | 2 =d( C t’) 2 r ’| 2 = 0 d( C t) 2 -dx 2 -dy 2 -dz 2 = d( C t’) 2 –dx 2 –dy 2 –dz 2 d( C t) 2 2 2 2 is an invariant! has the same value in all frames ( = 0 ). It has the same value in all frames ( 0 ). |d r | is the distance light moves in dt w.r.t the fixed frame.
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Lt tf t i lt iti d ti i th t f A Lorentz transformation relates position and time in the two frames.
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Lecture3 - RelativisticInvariance (Lorentzinvariance)

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