relativity_4a - PHY2061 R. D. Field PHY2060 Review Analogy...

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PHY2061 R. D. Field Department of Physics relativity_4a.doc University of Florida Analogy with Rotations Consider two frames of reference the O-frame (label points according to x,y) and the O'- frame (label points according to x',y'). Let the origins of the two frames coincide and rotate the O'- frame about the z-axis by an angle θ . The two frames are related by the following transformation ( i.e. by a rotation). θ cos sin sin cos y x y y x x + = = cos sin sin cos y x y y x x + = + = Vector Notation: = y x y x cos sin sin cos r R r = r r = cos sin sin cos R = y x r r = y x r r Rotational Invariant: 2 2 2 2 2 2 r r r y x y x r r r = = + = + = = r r r r Lorentz Transformation: Let cosh θ = γ and sinh θ = βγ βγ then
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