By Robert Resnick
This e-book provides an exceptional creation to the idea of particular relativity. Professor Resnick offers a primary and unified improvement of the topic with surprisingly transparent discussions of the features that typically hassle rookies. He comprises, for instance, a bit at the good judgment of relativity. His presentation is full of life and interspersed with old, philosophical and exact subject matters (such because the dual paradox) that would arouse and carry the reader's curiosity. you will find many special beneficial properties that assist you clutch the fabric, equivalent to worked-out examples,summary tables,thought questions and a wealth of fine difficulties. The emphasis during the e-book is actual. The experimental history, experimental affirmation of predictions, and the actual interpretation of rules are under pressure. The booklet treats relativistic kinematics, relativistic dynamics, and relativity and electromagnetism and comprises exact appendices at the geometric illustration of space-time and on basic relativity. Its association allows an teacher to change the size and intensity of his therapy and to take advantage of the booklet both with or following classical physics. those gains make it a terrific significant other for introductory classes.
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Extra resources for An introduction to the special theory of relativity
Let X(u1, u2) be a surface and let gij and Γrij be as deﬁned in Sections 4 and 5. Then Γijk = Xij · Xk Γijk = and 1 ∂gik ∂gjk ∂gij + − k 2 ∂uj ∂ui ∂u ∂gik ∂gjk ∂gij 1 Γrij = g kr + − k . 2 ∂uj ∂ui ∂u Proof. Since Xij = Γrij Xr + Lij U (by deﬁnition, see page 43) then Xij · Xk = Γrij Xr · Xk + (Lij U ) · Xk = Γrij grk + 0 = Γijk establishing the ﬁrst identity (recall grk = Xr · Xk ). Next, ∂gik ∂ = j [Xi · Xk ] = Xij · Xk + Xkj · Xi = Γijk + Γkji . j ∂u ∂u Permuting the indices: ∂gji ∂gkj = Γ + Γ and = Γkij + Γjik .
E. when we deal with two dimensions). In dimensions 3 and greater (in particular, in the 4 dimensional spacetime of Chapter III) we have a third case which we state now, and address in detail later: Theorem. In dimensions 3 and greater, if coordinates are mutually orthogonal, then for i, j, r all distinct, Γrij = 0. ) Note. In the case of orthogonal coordinates, if we return to Gauss’ notation: g11 = E, g12 = g21 = F = 0, g22 = G we have the First Fundamental Form (or metric form) ds2 = Edu2 + Gdv 2 on surface X(u, v).
3 (d), page 38, U = (− cos u cos v, − cos u sin v, − sin u). So ∂U = (sin u cos v, sin u sin v, − cos u) ∂u ∂U = = (cos u sin v, − cos u cos v, 0). ∂v U1 = U2 Therefore U1 × U2 = (− cos2 u cos v, − cos2 u sin v, − sin u cos u cos2 v − sin u cos u sin2 v) = (− cos2 u cos v, − cos2 u sin v, − sin u cos u) and U · U1 × U2 = cos3 u cos2 v + cos3 u sin2 v + sin2 u cos u = cos3 u + sin2 u cos u. So the total curvature is π π −π −π (cos3 u + sin2 u cos u) du dv. Now cos3 u + sin2 u cos u is an even function, so the integral is 0 and the total curvature is 0.
An introduction to the special theory of relativity by Robert Resnick