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# phys documents (dragged) 11 - 14 Physics Formulary by ir...

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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 defined by F = dp/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 . This can give both red- and blueshift, also to the direction of motion.
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