By Bernard Schutz

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

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Suppose that the velocity v of O¯ relative to O is small, |v| 1. Show that the time dilation, Lorentz contraction, and velocity-addition formulae can be approximated by, respectively: (a) t ≈ (1 + 12 v 2 ) ¯t, (b) x ≈ (1 − 12 v 2 ) x¯ , 1 as well). 1? Suppose that the velocity v of O¯ relative to O is nearly that of light, |v| = 1 − ε, 0<ε 1. Show that the same formulae of Exer. 14 become √ (a) t ≈ ¯t/ (2ε), √ (b) x ≈ x¯ / (2ε), (c) w ≈ 1 − ε(1 − w)/(1 + w). 9? Use the Lorentz transformation, Eq.

For this reason, the events inside the ‘future’ or ‘forward’ light cone are sometimes called the absolute future of the apex; those within the ‘past’ or ‘backward’ light cone are called the absolute past; and those outside are called the absolute elsewhere. 9 Common past Old and new concepts of spacetime t 14 Special relativity and future. Thus, although ‘time’ and ‘space’ can in some sense be transformed into one another in SR, it is important to realize that we can still talk about ‘future’ and ‘past’ in an invariant manner.

This is a hyperbola spacelike separated from the origin. Similarly, the events on the curve −t2 + x2 = −b2 all have timelike interval −b2 from the origin, and also lie on the curve −¯t2 + x¯ 2 = −b2 . These hyperbolae are drawn in Fig. 10. They are all asymptotic to the lines with slope ±1, which are of course the light paths through the origin. In a three-dimensional diagram (in which we add the y axis, as in Fig. 8), hyperbolae of revolution would be asymptotic to the light cone. ¯ In Fig. 11 the axes of O and O¯ are drawn, along We can now calibrate the axes of O.

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