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By Bernard Schutz

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 of relativity that fascinate astrophysical researchers and scholars alike are covered.

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3}. (b) Since s¯2 = 0 in Eq. 3) for any { xi }, replace xi by − xi in Eq. 3) and subtract the resulting equation from Eq. 3) to establish that M0i = 0 for i = 1, 2, 3. t 30 Special relativity 9 10 11 12 (c) Use Eq. 3) with s¯2 = 0 to establish Eq. 4b). ) Explain why the line PQ in Fig. 7 is drawn in the manner described in the text. For the pairs of events whose coordinates (t, x, y, z) in some frame are given below, classify their separations as timelike, spacelike, or null. (a) (0, 0, 0, 0) and (−1,1, 0, 0), (b) (1, 1, −1, 0) and (−1, 1, 0, 2), (c) (6, 0, 1, 0) and (5, 0, 1, 0), (d) (−1, 1, −1, 1) and (4, 1, −1, 6).

Then, at rest in frame O, ¯ we have x¯ = y¯ = z¯ = 0, so since the clock is at rest in O, s2 = − ¯t2 = − τ 2 . 9) The proper time is just the square root of the negative of the interval. By expressing the interval in terms of O’s coordinates we get τ = [( t)2 − ( x)2 − ( y)2 − ( z)2 ]1/2 √ = t (1 − v 2 ). This is the time dilation all over again. 13 The proper length of AC is the length of the rod in its rest frame, while that of AB is its length in O. Lore ntz contraction ¯ Its length in O¯ is the square In Fig.

15)) relative to O. this point. We can rewrite the last expression as ν eβ¯ = β¯ (−v)eν . ¯ This doesn’t change anything: it is still the same four Here we have just changed μ¯ to β. ¯ In this form we can put it into the expression for eα , equations, one for each value of β. Eq. 14): eα = β¯ β¯ = α (v)eβ¯ ν α (v) β¯ (−v)eν . 16) In this equation only the basis of O appears. It must therefore be an identity for all v. On the right there are two sums, one on β¯ and one on ν. If we imagine performing the β¯ sum first, then the right is a sum over the basis {eν } in which each basis vector eν has coefficient β¯ α (v) ν β¯ β¯ (−v).

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