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Chapter1_7 - PHY3063 R D Field Lorentz...

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PHY3063 R. D. Field Department of Physics Chapter1_7.doc University of Florida Lorentz Transformation (derivation) Look for a transformation of the form z z y y Ect Dx x Bx Act t c = = + = + = where A, B, D, and E are to be determined. The inverse transformation is given by z z y y BE AD t Ec x A x BE AD x B t Dc ct = = = = ) /( ) ( ) /( ) ( Also we know that for x’ = 0 dx/dt = V and for x = 0 dx’/dt’ = -V thus c D E dt dx V = = and c A E t d x d V = = and hence D = A and E = -AV/c = -A β with β = V/c. We now require that 2 2 2 2 2 2 ) (
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