9789810249366

Cosmological Special Relativity : The Large Scale Structure of Space, Time and Velocity

by
  • ISBN13:

    9789810249366

  • ISBN10:

    9810249365

  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2002-06-01
  • Publisher: WORLD SCIENTIFIC PUB CO INC
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Supplemental Materials

What is included with this book?

Summary

Presents Einstein's theory of space and time in detail and describes the large-scale structure of space, time and velocity as a new cosmological special relativity.

Table of Contents

Introduction
1(7)
Historical background
1(1)
Cosmology and special relativity
2(3)
References
5(2)
Cosmological Special Relativity
7(22)
Introduction
8(1)
Fundamentals of special relativity
8(1)
Present-day cosmology
9(1)
Postulates
10(1)
Cosmic frames
10(1)
Spacevelocity in cosmology
11(1)
Pre-special-relativity
11(1)
Relative cosmic time
12(1)
Inadequacy of the classical transformation
13(1)
Universe expansion versus light propagation
13(2)
The cosmological transformation
15(2)
Interpretation of the cosmological transformation
17(1)
Another derivation of the cosmological transformation
17(1)
The galaxy cone
18(2)
Consequences of the cosmological transformation
20(6)
Classical limit
20(1)
Length contraction
20(2)
Velocity contraction
22(1)
Law of addition of cosmic times
23(1)
Inflation of the Universe
24(1)
Minimal acceleration in nature
25(1)
Cosmological redshift
26(1)
Concluding remarks
26(1)
References
27(2)
Extension of the Lorentz Group to Cosmology
29(8)
Preliminaries
29(3)
The line element
32(1)
The transformations explicitly
32(2)
The generalized transformation
34(1)
Concluding remarks
35(1)
References
36(1)
Fundamentals of Einstein's Special Relativity
37(30)
Postulates of special relativity
38(2)
The principle of relativity. Constancy of the speed of light
38(1)
Coordinates
39(1)
Inertial coordinate system
39(1)
Simultaneity
40(1)
The Galilean transformation
40(1)
The Galilean group
41(1)
The Lorentz transformation
41(18)
Measuring rods and clocks
42(1)
Spatial coordinates and time
42(1)
Einstein's paradox
42(1)
Apparent incompatibility of the special relativity postulates
43(1)
Remark on action-at-a-distance
44(1)
Derivation of the Lorentz transformation
44(8)
The Lorentz group
52(2)
Problems
54(5)
Consequences of the Lorentz transformation
59(7)
Nonrelativistic limit
59(1)
The Lorentz contraction of lengths
60(1)
The dilation of time
61(1)
The addition of velocities law
61(2)
Problems
63(3)
References
66(1)
Structure of Spacetime
67(14)
Special relativity as a valuable guide
68(1)
Four dimensions in classical mechanics
68(1)
The Minkowskian spacetime
69(3)
Proper time
72(3)
Velocity and acceleration four-vectors
75(3)
Problems
78(1)
References
78(3)
The Light Cone
81(6)
The Light cone
81(1)
Events and coordinate systems
82(2)
Problems
84(1)
Future and past
84(1)
References
85(2)
Mass, Energy and Momentum
87(12)
Preliminaries
88(1)
Mass, energy and momentum
88(4)
Angular-momentum representation
92(3)
Energy-momentum four-vector
95(1)
Problems
96(1)
References
97(2)
Velocity, Acceleration and Cosmic Distances
99(10)
Preliminaries
99(1)
Velocity and acceleration four-vectors
100(2)
Accelertion and distances
102(2)
Energy in ESR versus cosmic distance in CSR
104(1)
Distance-velocity four-vector
104(2)
Conclusions
106(1)
References
107(2)
First Days of the Universe
109(6)
Preliminaries
109(1)
Lengths of days
110(1)
Comparison with Einstein's special relativity
111(1)
References
112(3)
A Cosmological General Relativity 115(30)
Preliminaries
116(1)
Cosmology in spacevelocity
117(3)
Gravitational field equations
120(3)
Solution of the field equations
123(2)
Classification of universes
125(2)
Physical meaning
127(1)
The accelerating universe
128(8)
Theory versus experiment
136(3)
Concluding remarks
139(4)
References
143(2)
B Five-Dimensional Brane World Theory 145(40)
Introduction
146(4)
Cosmic coordinate systems: The Hubble transformation
146(2)
Lorentz-like cosmological transformation
148(1)
Five-dimensional manifold of space, time and velocity
149(1)
Universe with gravitation
150(4)
The Bianchi identities
151(1)
The gravitational field equations
151(1)
Velocity as an independent coordinate
152(1)
Effective mass density in cosmology
153(1)
The accelerating Universe
154(6)
Preliminaries
154(2)
Expanding Universe
156(2)
Decelerating, constant and accelerating expansions
158(1)
Accelerating Universe
159(1)
The Tully-Fisher formula: Halo dark matter
160(8)
The geodesic equation
161(2)
Equations of motion
163(3)
The Tully-Fisher law
166(2)
The cosmological constant
168(4)
The cosmological term
168(2)
The supernovae experiments value for the cosmological constant
170(1)
The Behar-Carmeli predicted value for the cosmological constant
170(1)
Comparison with experiment
171(1)
Cosmological redshift analysis
172(3)
The redshift formula
172(1)
Particular cases
173(2)
Conclusions
175(1)
Concluding remarks
175(1)
Mathematical conventions and Christoffel symbols
176(1)
Components of the Ricci tensor
177(1)
Integration of the Universe expansion equation
178(2)
References
180(5)
C Cosmic Temperature Decline 185(4)
Introduction
185(1)
Temperature formula without gravity
186(1)
Comparison
187(1)
References
188(1)
Index 189

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