New PDF release: The Special Theory of Relativity: A Mathematical Approach

By Farook Rahaman

The ebook expounds the foremost themes within the distinctive thought of relativity. It offers an in depth exam of the mathematical origin of the specified concept of relativity, relativistic mass, relativistic mechanics and relativistic electrodynamics. in addition to covariant formula of relativistic mechanics and electrodynamics, the publication discusses the relativistic impact on photons. utilizing a mathematical method, the textual content bargains graduate scholars a transparent, concise view of the detailed conception of relativity. geared up into 14 chapters and appendices, the content material is gifted in a logical order, and each subject has been handled in an easy and lucid demeanour. to assist knowing of the topic, the booklet offers a number of correct labored examples in each bankruptcy. The book’s mathematical technique is helping scholars of their autonomous learn and motivates them to investigate the subject further.

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Example text

The light signal takes t1 time to reach from Y to O as (c−v) OX and the time t2 taken by the light signal from X to O is (c+v) . [c is the velocity of light in all direction. 5 The Relativistic Concept of Space and Time 19 One can note that t1 = OX OY = = t2 , as c + v = c − v , O X = OY (c − v) (c + v) Therefore, time is not absolute. e. t1 = t2 . In other words, every reference frame has its own particular time. Therefore, concept of absolute time was ruled out by Einstein. The space coordinate is transformed due to Galilean Transformation as x 1 = x − vt.

Therefore, α t1 = 1− f 2 c2 c2 etc. t If N0 is the initial flux and N is the flux after time t, then we have N = N0 e− τ , τ being the mean lifetime. t Here, N = e−β N0 , therefore e−β N0 = N0 e− τ =⇒ t = βτ = β t 1 = √ αβ 2 . 1− f Hence, the distance traversed by the beam before the flux of mesons beam is reduced to e−β times the initial flux is d = t × f c etc. 3 At what speed should a clock be moved, so that it may appear to loose α seconds in each minute. Hint: If the clock is to loose α seconds in each minute, then the moving clock with velocity v records 60 − α s for each 60 s recorded by stationary clock.

Suppose that a light signal from a light source emits a pulse at the common origin of S and S 1 at time t = t 1 = 0 and the observers in each system measures the speed of the propagate of light wave. e. 35) in Eqs. 37) v2 c2 Thus Eqs. 37) give the required Lorentz Transformations. 3 The General Lorentz Transformations Now, we search the Lorentz Transformations for an arbitrary direction of the relative → → r of a velocity − v between S and S1 frames. Let us consider the position vector − → particle separate into two components, one parallel and another perpendicular to − v.

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