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

By Ta-Pei Cheng

This complex undergraduate textual content introduces Einstein's normal conception of relativity. the subjects lined comprise geometric formula of precise relativity, the primary of equivalence, Einstein's box equation and its spherical-symmetric answer, in addition to cosmology. An emphasis is put on actual examples and straightforward functions with no the total tensor equipment. It starts via studying the physics of the equivalence precept and appears at the way it encouraged Einstein's notion of curved spacetime because the gravitational box. At a extra mathematically available point, it presents a metric description of a warped house, permitting the reader to check many attention-grabbing phenomena equivalent to gravitational time dilation, GPS operation, mild deflection, precession of Mercury's perihelion, and black holes. a number of smooth 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 prior ebook, 'Relativity, Gravitation and Cosmology: A simple Introduction', this article has been adapted to the complex scholar. 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 obtainable creation of basic relativity and cosmology for these readers who are looking to learn the topic on their lonesome. the correct tensor formula of Einstein's box equation is gifted in an appendix bankruptcy for these wishing to glimpse additional on the mathematical details.

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Extra resources for A College Course on Relativity and Cosmology

Sample text

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 ). Show that in the low-velocity limit it reduces to the Galilean transformation. Write the inverse transformation (t , x , y , z ) –→ (t, x, y, z), as well as the transformation of the space and time derivatives (∂t , ∂x , ∂y , ∂z ) –→ (∂t , ∂x , ∂y , ∂z ).

Letting the number of years Al has aged be A and the number of years Bill has aged be B, we have A = 30, B = 50 (Bill’s viewpoint). 42) Of course, this SR prediction of asymmetric aging of the twins, while counterintuitive according to our low-velocity experience, is not paradoxical. It is just an example of time dilation, which is counterintuitive but real. However, there appears to be a reciprocity puzzle. If relativity is truly relative, we could just as well consider this separation and reunion from the viewpoint of Al, who sees Bill moving.

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 ). Show that in the low-velocity limit it reduces to the Galilean transformation. Write the inverse transformation (t , x , y , z ) –→ (t, x, y, z), as well as the transformation of the space and time derivatives (∂t , ∂x , ∂y , ∂z ) –→ (∂t , ∂x , ∂y , ∂z ).

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