By Thomas A. Moore
A normal Relativity Workbook is a textbook meant to help a one-semester undergraduate path on common relativity. via its special workbook-based layout, it permits scholars to improve a pretty good mastery of either the physics and the aiding tensor calculus through guiding them to paintings throughout the implications. the maths is brought steadily and in a very actual context. each one bankruptcy, that's designed to correspond to 1 type consultation, comprises a brief review of the thoughts with no obscuring derivations or information, via a sequence of bins that consultant scholars in the course of the means of operating issues out. This active-learning technique permits scholars to enhance a safer mastery of the cloth than extra conventional ways. greater than 350 homework difficulties help additional studying.
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Extra resources for A general relativity workbook
5 Frame-independence of the Spacetime Interval Consider two events whose coordinate separations in an IRF S are given by ∆t, ∆x, ∆y, ∆z. 23) independent of the values of the coordinate differences or the value of b. 1 . Show this in the space below. 6 Frame-Dependence of the Time Order of Events If event A causes event B, then it follows that event A must occur before event B in all IRFs; otherwise, in some IRFs, observers would see an event preceding its cause, which is absurd. For the sake of simplicity in our argument, let us define coordinates so that both events occur on the +x axis in a certain frame S.
3 by m to see that this is true), meaning that p is also a four-vector. 14) Conservation of Four-Momentum . 9 implies that the spatial components of an object’s four-momentum reduce to the corresponding components of the object’s newtonian momentum: p x . mvx, p y . mvy, p z . 15) so an object’s four-momentum represents a reasonable relativistic generalization of the concept of newtonian momentum. In newtonian physics, we assume that an isolated system’s total newtonian momentum is conserved. But what is really conserved, its total newtonian momentum or its total four-momentum?
Let events F and B happen simultaneously in the S frame (∆t = 0) at the two ends of the object. The distance between these events in frame S is therefore defined to be the object’s length in that frame: L = ∆x. The distance ∆x´ between these same events in the object’s own frame S´ will be its rest length LR. 1 . 5). 9 The Einstein Velocity Transformation Consider two IRFs S and S´ in standard orientation. Imagine an object moves through both frames. We can use the Lorentz transformation to determine the object’s velocity components in S´ if we know its velocity components in frame S.
A general relativity workbook by Thomas A. Moore