2 c a b is an invariant under rotations corollary if

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Unformatted text preview: this problem, a convenient frame is one in which is diagonal : Di = i Ei ; (10) can be written as ni Di = c2 2 (n E0 ) (12) vi - v 2 Da and Db correspond to two propagation velocities : va and vb Da Db = c4 (n Ea ) (n Eb ) 3 i=1 n2 i 2 2 2 2 (va - vi ) (vb - vi ) (13) The denominator in (13) can be written as 1 2 2 2 2 (va - vi ) (vb - vi ) n2 i 2 - v 2 ) (v 2 - v 2 ) (va i i b = 1 2 2 (va - vb ) 1 2 2 (va - vb ) 3 n2 n2 i i = - 2 + 2 (14) v 2 - vi v 2 - vi i=1 i=1 a i=1 b 2 2 where the last 2 terms on the RHS are zero due to (11). Thus va - vb Da Db = 2 2 0. If the degenerate case va = vb is excluded, Da Db must vanish, in all frames. 3 3 -1 1 2 + v2 - v2 2 va - vi i b 2 Jackson 11.1 d v/2 t (a) In all Lorentz frames the speed of light is constant and equal to c. By Pyt...
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