Cosmological Relativity: The Special and General Theories of the Structure of the Universe

by Carmeli, Moshe

• ISBN13: 9789812700759
• ISBN10: 9812700757
• Format: Hardcover
• Copyright: 2006-10-30
• Publisher: World Scientific Pub Co Inc

Summary

The theory presented in this book is a combination of Einstein's original special and general relativity, but now the starting point is not the propagation of light but the expansion of the Universe. The traditional Hubble constant H0 (which is not constant) is called in this book the Hubble parameter. Its value at low gravity is denoted by h, and its reciprocal is denoted by t. Thus t is the Big Bang time (some authors call it the Hubble-Carmeli constant). This is actually the only constant that appears in this theory, just as c is the only constant that appears in this theory, just as c is the only constant that appears in Einstein's theory. There is no cosmological constant but there is a critical mass density. The theory presents general relativity in the space-velocity (of the receding galaxies) which is later on extended to include the time dimension. So far all experimental findings are satisfied by this theory.

Author Biography

Moshe Carmeli is Albert Einstein Emeritus Professor of Theoretical Physics at Ben Gurion University in Israel.

Table of Contents

Preface	p. V
Introduction	p. 1
Remarks on cosmological special relativity	p. 1
Cosmological Special Relativity	p. 3
The Galileo transformation and its generalization	p. 3
The Galileo transformation	p. 3
Difficulties with light	p. 5
Role of velocity in classical physics	p. 5
Nonrelativistic cosmological transformation	p. 6
Nonrelativistic transformation	p. 6
Difficulties at the Big Bang	p. 6
Extension to the Lorentz transformation	p. 8
Invariance of light propagation	p. 8
The Lorentz transformation	p. 8
Extension to the cosmological transformation	p. 9
Invariance of the Big Bang time	p. 9
The cosmological transformation	p. 9
Temperature of the Universe	p. 10
Conclusions	p. 11
Line elements in Einstein's special relativity and in cosmological special relativity	p. 11
Line element in Einstein's relativity	p. 11
Light propagation	p. 12
Line element in cosmological special relativity	p. 12
Hubble's expansion	p. 12
Inflation of the Universe	p. 15
Matter density	p. 15
Ratio of volumes	p. 16
Minimal acceleration in Nature	p. 16
Relation to Pioneer spacecrafts	p. 17
Redshift and cosmic time	p. 17
Field equations of a different kind	p. 19
Examples	p. 21
Cosmological special relativity in five dimensions	p. 22
Subtransformations	p. 23
Electrodynamics in five dimensions	p. 24
Field equations	p. 25
Generalized Maxwell's equations	p. 25
The mix-up	p. 26
Does the Cabibbo angle describe a rotation in the time-velocity plane?	p. 28
Elements of General Relativity	p. 29
Riemannian geometry	p. 29
Transformation of coordinates	p. 29
Contravariant vectors	p. 30
Invariants. Covariant vectors	p. 31
Tensors	p. 32
Metric tensor	p. 32
Christoffel symbols	p. 33
Covariant differentiation	p. 34
Riemann, Ricci and Einstein tensors	p. 36
Geodesics	p. 37
Bianchi identities	p. 38
Principle of equivalence	p. 39
Null experiments. Eotvos experiment	p. 39
Principle of general covariance	p. 41
Gravitational field equations	p. 42
Einstein's field equations	p. 43
Deduction of Einstein's equations from variational principle	p. 44
The electromagnetic energy-momentum tensor	p. 45
The Schwarzschild metric	p. 46
Experimental tests of general relativity	p. 51
Gravitational red shift	p. 51
Effects on planetary motion	p. 52
Deflection of light	p. 56
Gravitational radiation experiments	p. 59
Radar experiment	p. 59
Low-temperature experiments	p. 60
Equations of motion	p. 61
Geodesic postulate	p. 61
Equations of motion as a consequence of field equations	p. 61
Self-action terms	p. 63
Einstein-Infeld-Hoffmann method	p. 67
Newtonian equation of motion	p. 69
Einstein-Infeld-Hoffmann equation	p. 70
Decomposition of the Riemann tensor	p. 71
Cosmological General Relativity	p. 73
Introduction	p. 73
Space and velocity	p. 74
Gravitational field equations	p. 74
Universe expansion	p. 75
Energy-momentum tensor	p. 75
Independent field equations	p. 76
Solution of the field equations	p. 76
Simple solution	p. 76
Pressure	p. 77
Line element	p. 77
Physical meaning	p. 77
[Omega subscript m] > 1	p. 78
[Omega subscript m] < 1	p. 78
[Omega subscript m] = 1	p. 78
The accelerating Universe	p. 78
Tri-phase expansion	p. 79
Theory versus experiment	p. 80
Value of the Big Bang time [tau]	p. 80
Value of [Characters not reproducible]	p. 82
Comparison with general relativity	p. 84
Recent developments on dark matter	p. 84
Cosmological General Relativity in Five Dimensions	p. 87
Introduction	p. 87
Five-dimensional manifold of space, time and velocity	p. 87
Universe with gravitation	p. 88
The Bianchi identities	p. 89
The gravitational field equations	p. 89
Velocity as an independent coordinate	p. 90
Effective mass density in cosmology	p. 90
The accelerating Universe	p. 91
Preliminaries	p. 91
Expanding Universe	p. 93
Decelerating, constant and accelerating expansions	p. 95
Accelerating Universe	p. 96
The Tully-Fisher formula: Nonexistence of halo dark matter	p. 97
The Geodesic Equation	p. 98
Equations of motion	p. 99
The Tully-Fisher law	p. 102
Cosmological redshift analysis	p. 104
The redshift formula	p. 104
Particular cases	p. 105
Conclusions	p. 106
Verification of the classical general relativity tests	p. 106
Comparison with general relativity	p. 106
Gravitational redshift	p. 109
Motion in a centrally symmetric gravitational field	p. 111
Deflection of light in a gravitational field	p. 117
Gravitational waves	p. 120
Mathematical Conventions	p. 123
Components of the Ricci tensor	p. 124
Integration of the Universe Expansion Equation	p. 127
Index	p. 129
Table of Contents provided by Ingram. All Rights Reserved.