By Bernard Schutz

ISBN-10: 0511539118

ISBN-13: 9780511539114

ISBN-10: 0511539959

ISBN-13: 9780511539954

ISBN-10: 0511650655

ISBN-13: 9780511650659

ISBN-10: 0511984189

ISBN-13: 9780511984181

ISBN-10: 0521887054

ISBN-13: 9780521887052

Readability, clarity and rigor mix within the moment version of this widely-used textbook to supply step one into common relativity for undergraduate scholars with a minimum heritage in arithmetic. issues inside relativity that fascinate astrophysical researchers and scholars alike are covered.

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If O¯ moves with velocity v with respect to O, then Eq. 12) implies x = ( x¯ + v ¯t)/(1 − v 2 )1/2 and t = ( ¯t + v x¯ )/(1 − v 2 )1/2 . Then we have x = t x¯ / = 1+v W = ( x¯ + v ( ¯t + v ¯t + v = x¯ / ¯t ¯t)/(1 − v 2 )1/2 x¯ )/(1 − v 2 )1/2 W +v . 13) This is the Einstein law of composition of velocities. The important point is that |W | never exceeds 1 if |W| and |v| are both smaller than one. To see this, set W = 1. Then Eq. 13) implies (1 − v)(1 − W) = 0, that is that either v or W must also equal 1.

3} is a collection of four arbitrary numbers. 3 i 2 (b) i=1 ( x ) . 5 (a) Use the spacetime diagram of an observer O to describe the following experiment performed by O. 5 are emitted from x = 0 at t = −2 m, one traveling in the positive x direction and the other in the negative x direction. These encounter detectors located at x = ±2 m. 75. (b) The signals arrive back at x = 0 at the same event. ) From this the experimenter concludes that the particle detectors did indeed send out their signals simultaneously, since he knows they are equal distances from x = 0.

For example, O can say that A and F are simultaneous, and he is correct in the sense that they have the same value of the coordinate t. For him this is a useful thing to know, as it helps locate the events in spacetime. 9 The Lorentz transformation Any single observer can make consistent observations using concepts that are valid for him but that may not transfer to other observers. All the so-called paradoxes of relativity involve, not the inconsistency of a single observer’s deductions, but the inconsistency of assuming that certain concepts are independent of the observer when they are in fact very observer dependent.

### A first course in general relativity by Bernard Schutz

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