A primer of special relativity by P.L. Sardesai

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By P.L. Sardesai

A complete bankruptcy during this identify is dedicated to purposes of the idea to explain lots of issues the scholars (B.Sc. Physics) come upon in sleek Physics. exact and well-selected examples are used to light up facets of the idea in addition to to teach recommendations of software. numerous Illustrative Examples permits the scholars to realize self belief to unravel any challenge in relativity usually anticipated of B.Sc. scholars. The e-book meets the full specifications of a textbook for B.Sc. normal and Honours classes in certain concept of relativity advised by means of the U.G.C. current syllabi in a few our universities were taken into consideration in making plans the publication. The constitution of the e-book allows loads of flexibility. The e-book can accordingly be used as a textual content for a couple of present classes (with diverse dispensed classes) almost immediately time-honored in lots of Indian Universities.

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1a, 1b, 1c and 5) may be re-written as because 2 = b2 = x¢ = y¢ = y z¢ = z x - vt 1 - v2 / c2 = G(x – vt) ... (6a) ... (6b) ... (6c) Lorentz Transformations and Some Consequences 19 tand t¢ = vx c2 2 v 1c2 vx = G æç t - ö÷ è c2 ø ... (6d) These equations are known as Lorentz Transformations. The inverse equations may be readily written down by interchanging primed and unprimed quantities and replacing v by –v. They are x ¢ + vt ¢ x= 1 - v2 / c2 = G(x¢ + v¢t) ... (7a) y = y¢ z = z¢ t¢ + t= ... (7b) ...

If the interval between two events is spacelike, it is possible to find a reference frame in which the two events appear to be simultaneous. An event (x, t) is specified by a point on the X-t diagram. World line is a chain of events. World lines of all particles (–c £ v £ c) lie between the light lines x = ± ct. The region between the light lines consists of (i) events lying in the absolute future and (ii) events lying in the absolute past with respect to the event O (0, 0). The region outside is referred to as conditional present.

Then x¢ = G1 (x – v1t) etc. and x¢¢ = G2(x¢ – v2t¢) etc. Show that é æ ù v1 v2 ö x¢¢ = G1G2 ê x ç1 + - ( v1 + v2 ) t ú ÷ 2 c ø ë è û v1 v2 ö é v1 + v2 æ x= G1G2 ç1 + ê ÷ v1 v2 è c2 ø ê 1+ êë c2 ù tú ú úû 34 A Primer of Special Relativity = G(x – vt) where 8. 9. 10. 11. 12. 1 G= 1/2 and v= v1 + v2 vv æ v2 ö 1+ 1 2 çè1 - 2 ÷ø c2 c Show that space contraction can be derived by assuming that an observer in frame S measures the time interval between the passing of his origin by the two ends of a metre stick in frame S¢.

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