By Robert Resnick
This ebook supplies an outstanding advent to the speculation of specific relativity. Professor Resnick offers a primary and unified improvement of the topic with strangely transparent discussions of the points that sometimes hassle newbies. He contains, for instance, a bit at the good judgment of relativity. His presentation is vigorous and interspersed with historic, philosophical and distinctive issues (such because the dual paradox) that may arouse and carry the reader's curiosity. you will find many exact positive aspects that assist you grab the cloth, comparable to worked-out examples,summary tables,thought questions and a wealth of good difficulties. The emphasis through the e-book is actual. The experimental heritage, experimental affirmation of predictions, and the actual interpretation of rules are under pressure. The publication treats relativistic kinematics, relativistic dynamics, and relativity and electromagnetism and comprises distinct appendices at the geometric illustration of space-time and on basic relativity. Its association allows an teacher to alter the size and intensity of his remedy and to exploit the ebook both with or following classical physics. those positive factors make it an incredible significant other for introductory classes.
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Extra info for An introduction to the special theory of relativity
1 + b i ) P L For the case bi = b f , an elastic collision, Eq. 5) 2 2 O = f ` b i + b f (1 - b i ) j . (1 + b i ) L P For this to be true for any bi , f (b 2 ) must be a constant that is independent of b 2, a scalar property of the particle called its (invariant) mass, m. Thus, by considering an elastic collision, we have determined the relativistic expression for the momentum, an expression that must be valid in inelastic collisions. With f set equal to m, Eq. 4) becomes 2bi 2bi = . 6) This implies bi must equal b f ; the collision must be elastic!
1b. By the Galilean transformation of velocities, Eqs. 12), in this frame B is at rest and A is moving with velocity 2v in the positive x direction before the collision, whereas after the collision vlf B = vi + v f j v lf A = vi - v f j. Conservation of the x component of momentum gives f (4v 2 ) 2v = f (v 2 + v 2f ) v + f (v 2 + v 2f ) v. This implies f (4v 2 ) = f (v 2 + v 2f ), which must be true for any v and v f . Thus, f (v 2 ) is a constant m called the mass of the particle. The momentum of the particle is, as expected, p = mv.
7. 6), Lorentz transformations can be implemented by matrix multiplication, that is, by a 4 # 4 matrix acting on a 4-column vector whose components are x n. (a) What is the matrix representing a canonical Lorentz transformation with relative velocity br? (b) Space rotations are Lorentz transformations— they leave dx 2 unchanged. What is the 4 # 4 matrix that represents rotation about the x 3 axis by an angle i? (c) What is the matrix that represents the Lorentz transformation that results if one first implements a rotation (b) with i = i 0, followed with a Lorentz transformation (a) and then a rotation (b) with i =- i 0?