Ta-Pei Cheng's A College Course on Relativity and Cosmology PDF

By Ta-Pei Cheng

ISBN-10: 0199693404

ISBN-13: 9780199693405

This complex undergraduate textual content introduces Einstein's basic thought of relativity. the subjects coated comprise geometric formula of distinctive relativity, the main of equivalence, Einstein's box equation and its spherical-symmetric resolution, in addition to cosmology. An emphasis is put on actual examples and straightforward functions with out the whole tensor gear. It starts by means of reading the physics of the equivalence precept and appears at the way it encouraged Einstein's proposal of curved spacetime because the gravitational box. At a extra mathematically available point, it offers a metric description of a warped area, permitting the reader to review many attention-grabbing phenomena corresponding to gravitational time dilation, GPS operation, mild deflection, precession of Mercury's perihelion, and black holes. quite a few glossy subject matters in cosmology are mentioned from primordial inflation and cosmic microwave heritage to the darkish power that propels an accelerating universe.

Building on Cheng's past e-book, 'Relativity, Gravitation and Cosmology: A simple Introduction', this article has been adapted to the complicated pupil. It concentrates at the middle components of the topic making it compatible for a one-semester path on the undergraduate point. it might additionally function an available advent of common relativity and cosmology for these readers who are looking to research the topic on their lonesome. the right kind tensor formula of Einstein's box equation is gifted in an appendix bankruptcy for these wishing to glimpse additional on the mathematical info.

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Extra resources for A College Course on Relativity and Cosmology

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Let the stay-athome Bill celebrate his birthdays by setting off fireworks displays, which Al, with a powerful telescope aboard his spaceship, can always observe. Al can count the number of fireworks flashes he sees during his 30-year journey. If he sees 18 flashes, then Al’s viewpoint is right; if 50, then Bill is right. During (out) the outward-bound journey, Al sees flashes at an interval of tA , which differs from the interval tB = 1 year at which Bill sets off fireworks. First of all, the time interval is dilated by a factor of γ .

From the runner’s viewpoint, tAF < tslam R < tAR∗ < tBF < tslam F < tBR∗ . 48) Review questions 1. What does it mean that simultaneity is relative? Besides the familiar relativity of spatial equilocality, SR teaches us to expect the relativity of temporal simultaneity. What is the general lesson we can learn from this? 2. What are the two postulates of SR? 3. Two inertial frames are moving with respect to each other with velocity v = υ x. ˆ Write out the Lorentz transformation of the coordinates (t, x, y, z) –→ (t , x , y , z ).

Use the SR postulates and a simple light clock to derive the physical result of time dilation, t = γ t . Consider a physical situation that allows you to deduce the result of length contraction, x = γ –1 x , of an object in frame O when viewed by an observer in frame O in relative motion. Do you need to use the physics of time dilation for this derivation of length contraction? Why? 6. ), one often employs light signals. Why is this so? 30 Special Relativity: The New Kinematics 7. What combination of space and time intervals is invariant under Lorentz transformation?

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A College Course on Relativity and Cosmology by Ta-Pei Cheng

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