By P.L. Sardesai
A whole bankruptcy during this identify is dedicated to purposes of the speculation to clarify quite a few subject matters the scholars (B.Sc. Physics) stumble upon in sleek Physics. targeted and well-selected examples are used to light up features of the speculation in addition to to teach recommendations of program. quite a few Illustrative Examples permits the scholars to achieve self belief to resolve any challenge in relativity usually anticipated of B.Sc. scholars. The e-book meets the entire standards of a textbook for B.Sc. common and Honours classes in designated concept of relativity steered by way of the U.G.C. current syllabi in a couple of our universities were taken under consideration in making plans the booklet. The constitution of the e-book allows loads of flexibility. The booklet can as a result be used as a textual content for a couple of latest classes (with assorted distributed sessions) shortly usual in lots of Indian Universities.
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Extra info for A primer of special relativity
Note that beating of the heart is a kind of clock mechanism. The repetitive radio signal from the space vehicle is subject to time dilation as well as Doppler effect. We have eliminated the usual Doppler effect by choosing to calculate the pulse rate at the instant when the vehicle is travelling perpendicular (transverse) to the line connecting the vehicle and the earth observer. The time dilation still brings about a shift in the frequency. Hence time dilation brings about a transverse Doppler shift.
2b) 1/2 æ u ¢2 ö = dt¢ ç 1 ÷ è c2 ø ... (3a) 1/2 ... (3b) From Eqns. (3a, b) we see that the quantity dt has the same value in all inertial frames. It is therefore an invariant for all inertial observers. This invariant is called proper time interval. It is seen from Eqns. (3a, b) that dt = dT0 = time interval measured in the frame in which the particle is at rest, that is u = 0. Therefore proper time interval can be defined to be the time shown by a clock which is moving with the body. Eqns. (3a, b) also shows that dt > dt; dt¢ > dt.
However, v ö æ he finds that clocks in frame S¢ show a time given by t¢ = G ç t x ÷ which reduces to (when t = 0) è c2 ø v x. c2 Hence the clocks read different times depending on their location. Clocks to the left of origin (x is negative) are ahead (t¢ > 0) and those to the right are behind (t¢ < 0). Only the clock at the origin reads t¢ = 0. Hence moving clocks are not synchronized. See Fig. 1(b). From the point of observer S¢, while clocks in his frame are synchronized at t¢ = 0, clocks in frame S, show time given by v t= G x¢.
A primer of special relativity by P.L. Sardesai