A primer of special relativity by P.L. Sardesai

By P.L. Sardesai

A whole bankruptcy during this identify is dedicated to purposes of the idea to explain loads of issues the scholars (B.Sc. Physics) encounter in smooth Physics. certain and well-selected examples are used to light up points of the speculation in addition to to teach concepts of program. numerous Illustrative Examples allows the scholars to realize self belief to resolve any challenge in relativity commonly anticipated of B.Sc. scholars. The e-book meets the total necessities of a textbook for B.Sc. common and Honours classes in precise concept of relativity prompt via the U.G.C. current syllabi in a couple of our universities were taken into consideration in making plans the ebook. The constitution of the publication allows loads of flexibility. The publication can for this reason be used as a textual content for a few present classes (with assorted distributed classes) shortly standard in lots of Indian Universities.

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1 EVENTS An event is defined as an occurrence which takes place at some point (x, y, z) at some instant of time t. Arrival of a particle at a point (x, y, z) at time t, a bulb located at (x, y, z) flashing at time t, a gun at (x, y, z) firing at time t are examples of events. An event is thus described by the set of four numbers (x, y, z, t). An event has a meaning in an inertial frame but the numbers describing its position and time (x, y, z, t) are different in different inertial frames of reference.

4 INTERVALS BETWEEN EVENTS Consider two events described by (x, y, z, t) and (x + dx, y + dy, z + dz, t + dt) in an inertial frame S. The events are separated in space and time by dx, dy, dz and dt. e. it has the same value for all inertial observers. The (positive) square root of this quantity viz. ds is called the interval between the two events. Naturally ds is an invariant. In other words, a given pair of events is separated by the same interval no matter in which frame the events are observed.

1) becomes ... (1) ... (2) vx ¢ ö æ G(x¢ + vt¢) = cG ç t ¢ + ÷ è c2 ø v v x¢ æ1 - ö = ct¢ æ1 - ö è cø è cø Similarly Eqn. (2) becomes \ or x¢ = ct¢ ... (3) or x¢ = ct¢ + d¢ say ... (4) vx ¢ ö æ G(x¢ + vt¢) = cG ç t ¢ + ÷ + d è c2 ø or x¢ = ct¢ + d v æ G 1- ö è cø Eqns. (3) and (4) show that in S¢ the pulses travel with speed c (as they should) and the distance between them is æ v2 ö d ç1 ÷ è c2 ø d d¢ = = v æ1 - v ö G æ1 - ö è cø è cø 1/2 æ c + vö =dç è c - v ø÷ 1/2 Example 10 A rigid rod of length L makes an angle q with the X-axis of the system in which it is at rest in the X – Y plane.

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