By Ta-Pei Cheng
There are many graduate textbooks on common relativity, issues out Cheng (physics, U. of Missouri), and many renowned works describing in for lay readers. He deals an intermediate textbook for undergraduate scholars that may be utilized by teachers who're no longer themselves experts in relativity. scholars are anticipated to have the standard arithmetic on the calculus point, a few familiarity with matrices, and the physics of mechanics and electromagnetism together with differential equations of Maxwell's concept.
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Additional resources for Relativity, Gravitation and Cosmology: A Basic Introduction (2005)(en)(356s)
Example text
2. Under a Lorentz transformation, the electric and magnetic fields transform into each other. Give a simple physical explanation of a situation when a static electric field between two charges gives rise to magnetic field when viewed by a moving observer. 7. From the condition expressing the invariance of the metric, derive the explicit form of the Lorentz transformation for a boost v = +v xˆ . 8. In the spacetime diagram, display the timelike, spacelike, and lightlike regions. Also, draw in the worldline for some inertial observer.
For an Euclidean space, we can have the Cartesian coordinates with a set of orthonormal bases ei · ej = δij . Namely, the metric is simply given by the identity matrix, [g] = 1. 5 Consider the scalar product of two vectors i = j ei · ej V i U j = i, j Making it more explicit U j ej V i ei · V·U= gij V i U j . 36) i, j g11 g21 1 2 V · U = V ,V ,... .. g12 g22 .. 1 ... U U 2 . . . 37) The metric is needed to relate the scalar product to the vector components. For the case V = U, the above equation is an expression for the (squared) length of the vector.
When observed in another frame O , this interval also has a vanishing value s 2 = 0, because the velocity of light remains the same in the new frame O . 29) s 2 = F s2 , where F is the proportional factor, and it can in principle depend on the coordinates and the relative velocity of these two frames: F = F(x, t, v). e. 2 The new kinematics of space and time point in space and in time) implies that there cannot be any dependence of x and t. That space is isotropic means that the proportional factor cannot depend on the direction of their relative velocity v.