Physics-Theory of Relativity and Gravitation

Relativity Made Relatively Easy

US$5.00 US$62.00

Title (user) : Relativity Made Relatively EasyISBN : 019966286X,9780199662869,9780199662852GoogleBook ID : 75rCErZkh7ECAuthors (user...
Description

Title (user) : Relativity Made Relatively Easy

ISBN : 019966286X,9780199662869,9780199662852

GoogleBook ID : 75rCErZkh7EC

Authors (user) : Andrew M. Steane

Authors (google) : Andrew M. Steane

Publisher : Oxford University Press, USA

Language : English

Publication Date : 2012

Scanned : yes (600 DPI)

File Format : pdf

Categories : Science


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Description (user) :
Offers a thorough treatment suitable for any undergraduate course on relativity
Clear and careful explanations
Profound insights into many wonderful physical phenomena
Richly illustrated
Opens up General Relativity with precision but without the need for tensor analysis
Relativity Made Relatively Easy presents an extensive study of Special Relativity and a gentle (but exact) introduction to General Relativity for undergraduate students of physics. Assuming almost no prior knowledge, it allows the student to handle all the Relativity needed for a university course, with explanations as simple, thorough, and engaging as possible.

The aim is to make manageable what would otherwise be regarded as hard; to make derivations as simple as possible and physical ideas as transparent as possible. Lorentz invariants and four-vectors are introduced early on, but tensor notation is postponed until needed. In addition to the more basic ideas such as Doppler effect and collisions, the text introduces more advanced material such as radiation from accelerating charges, Lagrangian methods, the stress-energy tensor, and introductory General Relativity, including Gaussian curvature, the Schwarzschild solution, gravitational lensing, and black holes. A second volume will extend the treatment of General Relativity somewhat more thoroughly, and also introduce Cosmology, spinors, and some field theory.

Readership: Physics students at the undergraduate and beginning graduate level.


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Description (google) :
This book unfolds the subject of Relativity for undergraduate students of physics. It is intended to allow an undergraduate physics course to extend somewhat further and wider in this area than has traditionally been the case, while ensuring that the mainstream of students can handle the material. Introducing Lorentz invariants and four-vectors early on, but postponing tensor notation till it is needed, the aim is to make manageable what would otherwise beregarded as hard; to make derivations as simple as possible and physical ideas as transparent as possible.


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Table of contents :
Cover

S Title

Relativity Made Relatively Easy

Copyright

Andrew M. Steane 2012

ISBN 978-0-19-966285-2 (hbk)

ISBN 978-0-19-966286-9 (pbk)

Dedication

Preface

Acknowledgements

Contents


Part I The relativistic world

1 Basic ideas

1.1 Newtonian physics

1.2 Special Relativity

1.2.1 The Postulates of Special Relativity

1.2.2 Central ideas about spacetime

1.3 Matrix methods

1.4 Spacetime diagrams

exercises

2 The Lorentz transformation

2.1 Introducing the Lorentz transformation

2.1.1 Derivation of Lorentz transformation

2.2 Velocities

2.3 Lorentz invariance and 4-vectors

2.3.1 Rapidity

2.4 Lorentz-invariant quantities

2.5 Basic 4-vectors

2.5.1 Proper time

2.5.2 Velocity, acceleration

2.5.3 Momentum, energy

2.5.4 The direction change of a 4-vector under a boost

2.5.5 Force

2.5.6 Wave vector

2.6 The joy of invariants

2.7 Summary

Exercises

3 Moving light sources

3.1 The Doppler effect

3.2 Aberration and the headlight effect

3.2.1 Stellar aberration

3.3 Visual appearances

Exercises

4 Dynamics

4.1 Force

4.1.1 Transformation of force

4.2 Motion under a pure force

4.2.1 Linear motion and rapidity

4.2.2 Hyperbolic motion: the `relativistic rocket'

4.2.3 4-vector treatment of hyperbolic motion

4.2.4 Motion under a constant force

4.2.5 Circular motion

4.2.6 Motion under a central force

4.2.7 (An) harmonic motion

Exercises

5 The conservation of energy-momentum

5.1 Elastic collision, following Lewis and Tolman

5.2 Energy-momentum conservation using 4-vectors

5.2.1 Mass-energy equivalence

5.3 Collisions

5.3.1 'Isolate and square

5.4 Elastic collisions

5.4.1 Billiards

5.4.2 Compton scattering

5.4.3 More general treatment of elastic collisions

5.5 Composite systems

5.6 Energy flux, momentum density, and force

Exercises

6 Further kinematics

6.1 The Principle of Most Proper Time

6.2 Four-dimensional gradient

6.3 Current density, continuity

6.4 Wave motion

6.4.1 Wave equation

6.4.2 Particles and waves

6.4.3 Group velocity and particle velocity

6.5 Acceleration and rigidity

6.5.1 The great train disaster

6.5.2 Lorentz contraction and internal stress

6.6 General Lorentz boost

6.7 Lorentz boosts and rotations

6.7.1 Two boosts at right angles

6.7.2 The Thomas precession

6.7.3 Analysis of circular motion

6.8 Generators of boosts and rotations

6.9 The Lorentz group*

6.9.1 Further group terminology

Exercises

7 Relativity and electromagnetism

7.1 Definition of electric and magnetic fields

7.1.1 Transformation of the fields (first look)

7.2 Maxwell's equations

7.2.1 Moving capacitor plates

7.3 The fields due to a moving point charge

7.4 Covariance of Maxwell's equations

7.4.1 Transformation of the fields: 4-vector method*

7.5 Introducing the Faraday tensor

7.5.1 Tensors

7.5.2 Application to electromagnetism

Exercises

8 Electromagnetic radiation

8.1 Plane waves in vacuum

8.2 Solution of Maxwell's equations for a given charge distribution

8.2.1 The 4-vector potential of a uniformly moving point charge

8.2.2 The general solution

8.2.3 The Lienard-Wierhert potentials

8.2.4 The field of an arbitrarily moving charge

8.2.5 Two example fields

8.3 Radiated power

8.3.1 Linear and circular motion

8.3.2 Angular distribution

Exercises


Part II An Introduction to General Relativity

9 The Principle of Equivalence

9.1 Flee fall

9.1.1 Free fall or free float?

9.1.2 weak Principle of Equivalence

9.1.3 The Eotvas-Pekar-Fekete experiment

9.1.4 The Strong Equivalence Principle

9.1.5 Falling light and gravitational time dilation

9.2 The uniformly accelerating reference frame

9.2.1 Accelerated rigid motion

9.2.2 Rigid constantly accelerating frame

9.3 Newtonian gravity from the Principle of Most Proper Time

9.4 Gravitational redshift and energy conservation

9.4.1 Equation of motion

Exercises

10 Warped spacetime

10.1 Two-dimensional spatial surfaces

10.1.1 Conformal flatness

10.2 Three spatial dimensions

10.3 Time and space together

10.4 Gravity and curved spacetime

Exercises

11 Physics from the metric

11.1 Example exact solutions

11.1.1 The acceleration due to gravity

11.2 Schwarzschild metric: basic properties

11.3 Geometry of Schwarzschild solution

11.3.1 Radial motion

11.3.2 Circular orbits

11.3.4 Photon orbits

11.3.5 Shapiro time delay

11.4 Gravitational lensing

11.5 Black holes

1.5.1 Horison

11.5.2 Energy near an horizon

11.6 What next?

11.6.1 Black-hole thermodynamics

Exercises


Part III Further Special Relativity

12 Tensors and index notation

12.1 Index notation in a nutshell

12.2 Tensor analysis

12.2.1 Rules for tensor algeb

12.2.2 Contravariant and covariant

12.2.3 Useful methods and ideas

12.2.4 Parity inversion and the vector product

12.2.5 Differentiation

12.3 Antisymmetric tensors and the dual

Exercises

13 Rediscovering electromagnetism

13.1 Fundamental equations

13.2 Invariants of the electromagnetic field

13.2.1 Motion of particles in an electromagnetic field

Exercises

14 Lagrangian mechanics

14.1 Classical Lagrangian mechanics

14.2 Relativistic motion

14.2.1 From classical Euler-Lagrange

14.2.2 Manifestly covaria

14.3 Conservation

14.4 Equation of motion in General Relativity

Exercises

15 Angular momentum

15.1 Conservation of angular momentum

15.2 Spin

15.2.1 Introducing spin

15.2.2 Paull-Lubanski vector

15.2.3 Thomas precesion revisited

15.2.4 Precession of the spin of a charged particle

Exercises

16 Energy density

16.1 Introducing the stress-energy tensor

16.1.1 Transport of energy and momentum

16.1.2 Ideal fluid

16.2 Stress-energy tensor for an arbitrary system

16.2.1 Interpreting the terms

16.3 Conservation of energy and momentum for a fluid

16.4 Electromagnetic energy and momentum

16.4.1 Examples of energy density and energy flow

16.4.2 Field momentum

16.4.3 Stress-energy tensor of the electromagnetic field

16.5 Field and matter pushing on one another

16.5.1 Resolution of the `4/3 problem' and the origin of mass

Exercises

17 What is spacetime?


A Some basic arguments

A.1 Early experiments

A.2 Simultaneity and radar coordinates

A.3 Proper time and time dilation

A.4 Lorentz contraction

A.5 Doppler effect, addition of velocities


B Constants and length scales


C Derivatives and index notation


D The field of an arbitrarily moving charge

D.1 Light-cone volume element

D.2 The field tensor


Bibliography

Index

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