By P.L. Sardesai
A complete bankruptcy during this identify is dedicated to purposes of the idea to explain numerous themes the scholars (B.Sc. Physics) stumble upon in smooth Physics. specific and well-selected examples are used to light up features of the speculation in addition to to teach ideas of software. lots of Illustrative Examples allows the scholars to realize self assurance to unravel any challenge in relativity mostly anticipated of B.Sc. scholars. The booklet meets the total necessities of a textbook for B.Sc. common and Honours classes in unique thought of relativity instructed through the U.G.C. latest syllabi in a few our universities were taken into consideration in making plans the booklet. The constitution of the ebook allows loads of flexibility. The e-book can accordingly be used as a textual content for a couple of current classes (with diverse dispensed classes) almost immediately standard in lots of Indian Universities.
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Extra resources for A primer of special relativity
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) ... (7c) vx ¢ c2 2 v 1c2 vx ¢ ö = G æç t ¢ + ÷ è c2 ø ... T. T. only when v/c is appreciable, that is only at high speeds.
6 ´ 108 m and 2 s. What is the proper time interval between these events? Solution Proper time interval between two events is the time interval measured by an observer in frame say S¢ for whom the two events are colocal. 8 ´ 108 m/s. = 2 Dt Relativity of Simultaneity, Colocality, Etc. 6 s úû 4 EXERCISES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. Explain the terms (i) event and (ii) world line. What is an event? What are (i) coincident (ii) colocal and (iii) simultaneous events? Discuss the relativity of (i) coincident (ii) colocal and (iii) simultaneous events.
The object has velocity components U x¢ , U y¢ and U z¢ in S¢. Let us find the velocity of the object as observed by an observer in frame S if S¢ is moving with a constant speed v along X-axis relative to frames S as shown in Fig. 3. Y¢ Y S S¢ vt O Z Fig. T. In particular, vx ¢ ö æ x = G(x¢ + vt¢); y = y¢; z = z¢ and t = G ç t ¢ + ÷ è c2 ø where æ v2 ö G = ç1 ÷ è c2 ø -1/2 Taking differentials, dx = G(dx¢ + vdt¢); dy = dy¢; dz = dz¢ and vdx ¢ ö æ dt = G ç dt ¢ + ÷ è c2 ø 22 A Primer of Special Relativity In frame S, the velocity components of the object are dy dx ; Uy = dt dt From above equations we get Ux = Ux = and Uz = dz dt dx ¢ + vdt ¢ dx G ( dx ¢ + vdt ¢ ) = = dt vdx ¢ v dx ¢ ö G çæ dt ¢ + 2 ÷ö dt ¢ çæ1 + 2 ÷ è è c ø c dt ¢ ø dx ¢ + v U x¢ + v dt ¢ = = ¢ 1 + v U x¢ 1 + v dx c2 c 2 dt ¢ ...
A primer of special relativity by P.L. Sardesai