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Alice, an inertial observer, see Bob undergoing hyperbolic motion given by the parametric equations xº (7) = sinh , x(T) = cosh in her frame. a) Using an appropriate Lorentz transform with Bob's coordinates taken as primed coordinates, show by taking the differentials of the parametric equations, that AT At', that is, that is Bob's proper time, and that his rapidity is .. b) Transform the differentials Axº and Ax you calculated in part a) to primed coordinates to reinforce the correctness of part a) calculation. c) Taylor expand to second order in Ar the results for Axº and Ax to provide the physical interpretation of the parameter g.

Alice, an inertial observer, see Bob undergoing hyperbolic motion given by the parametric equations xº (7) = sinh , x(T) = cosh in her frame. a) Using an appropriate Lorentz transform with Bob's coordinates taken as primed coordinates, show by taking the differentials of the parametric equations, that AT At', that is, that is Bob's proper time, and that his rapidity is .. b) Transform the differentials Axº and Ax you calculated in part a) to primed coordinates to reinforce the correctness of part a) calculation. c) Taylor expand to second order in Ar the results for Axº and Ax to provide the physical interpretation of the parameter g.

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Alice, an inertial observer, see Bob undergoing hyperbolic motion given by the parametric equations z (r) = sinh * x(T) = cosh in her frame. 9 с 9 a) Using an appropriate Lorentz transform with Bob's coordinates taken as primed coordinates, show by taking the differentials of the parametric equations, that AT = At', that is, that 7 is Bob's proper time, and that his rapidity gt " is b) Transform the differentials Axº and Ax you calculated in part a) to primed coordinates to reinforce the correctness of part a) calculation. c) Taylor expand to second order in AT the results for Axº and Ax to provide the physical interpretation of the parameter g.
Transcribed Image Text:Alice, an inertial observer, see Bob undergoing hyperbolic motion given by the parametric equations z (r) = sinh * x(T) = cosh in her frame. 9 с 9 a) Using an appropriate Lorentz transform with Bob's coordinates taken as primed coordinates, show by taking the differentials of the parametric equations, that AT = At', that is, that 7 is Bob's proper time, and that his rapidity gt " is b) Transform the differentials Axº and Ax you calculated in part a) to primed coordinates to reinforce the correctness of part a) calculation. c) Taylor expand to second order in AT the results for Axº and Ax to provide the physical interpretation of the parameter g.
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