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14 Physics Formulary by ir. J.C.A. Wevers W 2 = m 2 0 c 4 + p 2 c 2 . p = m r v = γ m 0 v = Wv/c 2 , and pc = W β where β = v/c . The force is deFned by ± F = d ± p/dt . 4-vectors have the property that their modulus is independent of the observer: their components can change after a coordinate transformation but not their modulus. The difference of two 4-vectors transforms also as a 4-vector. The 4-vector for the velocity is given by U α = dx α d τ . The relation with the “common” velocity u i := dx i /dt is: U α =( γ u i ,ic γ ) . For particles with nonzero restmass holds: U α U α = - c 2 , for particles with zero restmass (so with v = c ) holds: U α U α =0 . The 4-vector for energy and momentum is given by: p α = m 0 U α =( γ p i ,iW/c ) . So: p α p α = - m 2 0 c 2 = p 2 - W 2 /c 2 . 3.1.2 Red and blue shift There are three causes of red and blue shifts: 1. Motion: with ± e v · ± e r =cos( ϕ ) follows: f ± f = γ ± 1 - v cos( ϕ ) c ² . This can give both red- and blueshift, also
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This note was uploaded on 11/16/2010 for the course ENGR 201 taught by Professor Elder during the Spring '10 term at Blinn College.

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