2 c a b is an invariant under rotations corollary if

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Ask a homework question - tutors are online