Gravity

A primer of special relativity by P.L. Sardesai

By P.L. Sardesai

A complete bankruptcy during this name is dedicated to purposes of the speculation to clarify various themes the scholars (B.Sc. Physics) come upon in smooth Physics. exact and well-selected examples are used to light up elements of the speculation in addition to to teach ideas of software. a number of Illustrative Examples permits the scholars to realize self assurance to resolve any challenge in relativity in most cases anticipated of B.Sc. scholars. The booklet meets the total necessities of a textbook for B.Sc. basic and Honours classes in unique thought of relativity advised through the U.G.C. current syllabi in a few our universities were taken into consideration in making plans the e-book. The constitution of the e-book allows loads of flexibility. The ebook can consequently be used as a textual content for a few latest classes (with assorted dispensed classes) almost immediately commonplace in lots of Indian Universities.

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It then follows immediately that our common sense concepts of space, time etc. have to be radically changed. T. can be derived on the basis of two postulates or Principles viz. (1) Laws of Physics are of the same form in all inertial frames (Principle of Relativity) and (2) The speed of light in free space has the same value c in all inertial frames (Principle of Constancy of Speed of Light). ) Consider two inertial frames S and S¢ as shown in Fig. 1. S¢ moves relative to S at a constant speed v along the X-axis.

Then x1¢ = G(x1 – vt1); x2¢ = G(x2 – vt2) x2¢ - x1¢ = G[(x2 –x1) – v(t2 – t1)] \ For events to occur at the same place in S¢, we must have x1¢ = x2¢ or  x1¢ - x2¢  = 0. 6 c along the X-axis relative to frame S, the two events occur at the same place. 25 ç 20 è ø÷ c2 In S¢, the events are (0, 0) and (0, 16 s). In S¢, the time interval between the two events is 16s. This result could have been derived from time dilation or from invariance of ds2. Example 3 In an inertial frame S event A occurs at x = 0 at t = 0 and event B occurs at x = 20 c and t = 12 s.

This may be hard to accept but it is true. In fact Eqn. (4) is the analogue of Eqn. (1). However, whereas Eqn. (1) is easy to understand, the same cannot be said of Eqn. (4). Eqns. (1) and (4) once again give a hint that space and time are more intimately related than we are accustomed to think. By the way note that Eqn. (3) is just our space contraction formula. Relativity of Simultaneity, Colocality, Etc. 39 (D) Synchronization Consider two inertial frames S and S¢ equipped with clocks located at different positions on their X-axis.

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