A General Relativity Workbook by Thomas A. Moore

By Thomas A. Moore

A normal Relativity Workbook is a textbook meant to help a one-semester undergraduate path on normal relativity. via its precise workbook-based layout, it permits scholars to increase a high-quality mastery of either the physics and the helping tensor calculus by way of guiding them to paintings in the course of the implications. the math is brought steadily and in a very actual context. each one bankruptcy, that is designed to correspond to 1 category consultation, contains a brief assessment of the innovations with no obscuring derivations or information, by means of a chain of bins that consultant scholars during the means of operating issues out. This active-learning process allows scholars to improve a safer mastery of the fabric than extra conventional methods. greater than 350 homework difficulties help additional studying.

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B. If the ship is supposed to go to Alpha Centauri, decelerate to rest, do some research there, and then re- turn, what will the ship’s total initial mass M have to be if the ship’s empty mass is m0 when it reaches earth? 4. a. Show that in frame S, four-momentum is conserved by this collision as long as the mass M of the final object is not 2m but rather 2m/ 1 - v2 . b. Show that four-momentum is also conserved in S´. 5 The energy of a photon is related to its wavelength m by the expression E = h/m (in GR units) where h = 1240 eV·nm.

12. Note that in absolute terms, the spatial components of u will be at least a factor of v smaller than ut : the correction term for ut will be O (v2) , while the correction terms in the spatial components will be O (v3) . 17. 1 . 25. 4 Conservation of Momentum or Four-momentum? BEFORE m v (a) m m v AFTER M BEFORE v1lx = 0, m 2v 1 + v2 (b) A single counterexample suffices to show that conservation of newtonian momentum is inconsistent with the principle of relativity. Consider the following collision as an example.

1, means that the components of u will be 1, vx, vy, vz with an error of roughly 1% in each term. 12. Note that in absolute terms, the spatial components of u will be at least a factor of v smaller than ut : the correction term for ut will be O (v2) , while the correction terms in the spatial components will be O (v3) . 17. 1 . 25. 4 Conservation of Momentum or Four-momentum? BEFORE m v (a) m m v AFTER M BEFORE v1lx = 0, m 2v 1 + v2 (b) A single counterexample suffices to show that conservation of newtonian momentum is inconsistent with the principle of relativity.

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