Carmeli, Moshe, 1933-
Cosmological special relativity : the large scale structure of space, time and velocity / Moshe Carmeli. - 2nd ed. - River Edge, N.J. : World Scientific, c2002. - xvi, 207 p. : ill. ; 22 cm.
Includes bibliographical references and index.
Machine generated contents note: 1 Introduction -- 1.1 Historical background -- 1.2 Cosmology and special relativity -- 1.3 References -- 2 Cosmological Special Relativity -- 2.1 Introduction -- 2.2 Fundamentals of special relativity -- 2.3 Present-day cosmology -- 2.4 Postulates -- 2.5 Cosmic frames -- 2.6 Spacevelocity in cosmology -- 2.7 Pre-special-relativity -- 2.8 Relative cosmic time -- 2.9 Inadequacy of the classical transformation -- 2.10 Universe expansion versus light propagation -- 2.11 The cosmological transformation -- 2.12 Interpretation of the cosmological transformation -- 2.13 Another derivation of the -- cosmological transformation -- 2.14 The galaxy cone -- 2.15 Consequences of the cosmological transformation -- 2.15.1 Classical limit -- 2.15.2 Length contraction -- 2.15.3 Velocity contraction -- 2.15.4 Law of addition of cosmic times -- 2.15.5 Inflation of the Universe -- 2.15.6 Minimal acceleration in nature -- 2.15.7 Cosmological redshift -- 2.16 Concluding remarks -- 2.17 References -- 3 Extension of the Lorentz Group to Cosmology -- 3.1 Preliminaries -- 3.2 The line element -- 3.3 The transformations explicitly -- 3.4 The generalized transformation -- 3.5 Concluding remarks -- 3.6 References -- 4 Fundamentals of Einstein's Special Relativity -- 4.1 Postulates of special relativity -- 4.1.1 The principle of relativity. Constancy of -- the speed of light -- 4.1.2 Coordinates -- 4.1.3 Inertial coordinate system -- 4.1.4 Simultaneity -- 4.2 The Galilean transformation -- 4.2.1 The Galilean group -- 4.3 The Lorentz transformation -- 4.3.1 Measuring rods and clocks -- 4.3.2 Spatial coordinates and time -- 4.3.3 Einstein's paradox -- 4.3.4 Apparent incompatibility of the special rel- -- ativity postulates -- 4.3.5 Remark on action-at-a-distance -- 4.3.6 Derivation of the Lorentz -- transformation -- 4.3.7 The Lorentz group -- 4.3.8 Problems -- 4.4 Consequences of the Lorentz transformation -- 4.4.1 Nonrelativistic limit -- 4.4.2 The Lorentz contraction of lengths -- 4.4.3 The dilation of time -- 4.4.4 The addition of velocities law -- 4.4.5 Problems -- 4.5 References -- 5 Structure of Spacetime -- 5.1 Special relativity as a -- valuable guide -- 5.2 Four dimensions in -- classical mechanics -- 5.3 The Minkowskian spacetime -- 5.4 Proper time -- 5.5 Velocity and acceleration four-vectors -- 5.6 Problems -- 5.7 References -- 6 The Light Cone -- 6.1 The light cone -- 6.2 Events and coordinate systems -- 6.3 Problems -- 6.4 Future and past -- 6.5 References -- 7 Mass, Energy and Momentum -- 7.1 Preliminaries -- 7.2 Mass, energy and momentum -- 7.3 Angular-momentum representation -- 7.4 Energy-momentum four-vector -- 7.5 Problems -- 7.6 References -- 8 Velocity, Acceleration and Cosmic Distances -- 8.1 Preliminaries -- 8.2 Velocity and acceleration four-vectors -- 8.3 Acceleration and distances -- 8.4 Energy in ESR versus cosmic -- distance in CSR -- 8.5 Distance-velocity four-vector -- 8.6 Conclusions -- 8.7 References -- 9 First Days of the Universe -- 9.1 Preliminaries -- 9.2 Lengths of days -- 9.3 Comparison with Einstein's special relativity -- 9.4 References -- A Cosmological General Relativity -- A.1 Preliminaries -- A.2 Cosmology in spacevelocity -- A.3 Gravitational field equations -- A.4 Solution of the field equations -- A.5 Classification of universes -- A.6 Physical meaning -- A.7 The accelerating universe -- A.8 Theory versus experiment -- A.9 Concluding remarks -- A.10 References -- B Five-Dimensional Brane World Theory -- B.1 Introduction -- B.1.1 Cosmic coordinate systems: The -- Hubble transformation -- B.1.2 Lorentz-like cosmological -- transformation -- B.1.3 Five-dimensional manifold of space, -- time and velocity -- B.2 Universe with gravitation -- B.2.1 The Bianchi identities -- B.2.2 The gravitational field equations -- B.2.3 Velocity as an independent coordinate -- B.2.4 Effective mass density in cosmology -- B.3 The accelerating Universe -- B.3.1 Preliminaries -- B.3.2 Expanding Universe -- B.3.3 Decelerating, constant and -- accelerating expansions -- B.3.4 Accelerating Universe -- B.4 The Tully-Fisher formula: Halo dark matter -- B.4.1 The geodesic equation -- B.4.2 Equations of motion -- B.4.3 The Tully-Fisher law -- B.5 The cosmological constant -- B.5.1 The cosmological term -- B.5.2 The supernovae experiments value for the -- cosmological constant -- B.5.3 The Behar-Carmeli predicted value for the -- cosmological constant -- B.5.4 Comparison with experiment -- B.6 Cosmological redshift analysis -- B.6.1 The redshift formula -- B.6.2 Particular cases -- B.6.3 Conclusions -- B.7 Concluding remarks -- B.8 Mathematical conventions and Christoffel symbols -- B.9 Components of the Ricci tensor -- B.10 Integration of the Universe expansion equation -- B.11 References -- C Cosmic Temperature Decline -- C.1 Introduction. -- C.2 Temperature formula without -- gravity -- C.3 Comparison -- C.4 References.
9810249365 (alk. paper)
Cosmology.
Special relativity (Physics)
Gravitational fields.
Space and time.
523.1
Cosmological special relativity : the large scale structure of space, time and velocity / Moshe Carmeli. - 2nd ed. - River Edge, N.J. : World Scientific, c2002. - xvi, 207 p. : ill. ; 22 cm.
Includes bibliographical references and index.
Machine generated contents note: 1 Introduction -- 1.1 Historical background -- 1.2 Cosmology and special relativity -- 1.3 References -- 2 Cosmological Special Relativity -- 2.1 Introduction -- 2.2 Fundamentals of special relativity -- 2.3 Present-day cosmology -- 2.4 Postulates -- 2.5 Cosmic frames -- 2.6 Spacevelocity in cosmology -- 2.7 Pre-special-relativity -- 2.8 Relative cosmic time -- 2.9 Inadequacy of the classical transformation -- 2.10 Universe expansion versus light propagation -- 2.11 The cosmological transformation -- 2.12 Interpretation of the cosmological transformation -- 2.13 Another derivation of the -- cosmological transformation -- 2.14 The galaxy cone -- 2.15 Consequences of the cosmological transformation -- 2.15.1 Classical limit -- 2.15.2 Length contraction -- 2.15.3 Velocity contraction -- 2.15.4 Law of addition of cosmic times -- 2.15.5 Inflation of the Universe -- 2.15.6 Minimal acceleration in nature -- 2.15.7 Cosmological redshift -- 2.16 Concluding remarks -- 2.17 References -- 3 Extension of the Lorentz Group to Cosmology -- 3.1 Preliminaries -- 3.2 The line element -- 3.3 The transformations explicitly -- 3.4 The generalized transformation -- 3.5 Concluding remarks -- 3.6 References -- 4 Fundamentals of Einstein's Special Relativity -- 4.1 Postulates of special relativity -- 4.1.1 The principle of relativity. Constancy of -- the speed of light -- 4.1.2 Coordinates -- 4.1.3 Inertial coordinate system -- 4.1.4 Simultaneity -- 4.2 The Galilean transformation -- 4.2.1 The Galilean group -- 4.3 The Lorentz transformation -- 4.3.1 Measuring rods and clocks -- 4.3.2 Spatial coordinates and time -- 4.3.3 Einstein's paradox -- 4.3.4 Apparent incompatibility of the special rel- -- ativity postulates -- 4.3.5 Remark on action-at-a-distance -- 4.3.6 Derivation of the Lorentz -- transformation -- 4.3.7 The Lorentz group -- 4.3.8 Problems -- 4.4 Consequences of the Lorentz transformation -- 4.4.1 Nonrelativistic limit -- 4.4.2 The Lorentz contraction of lengths -- 4.4.3 The dilation of time -- 4.4.4 The addition of velocities law -- 4.4.5 Problems -- 4.5 References -- 5 Structure of Spacetime -- 5.1 Special relativity as a -- valuable guide -- 5.2 Four dimensions in -- classical mechanics -- 5.3 The Minkowskian spacetime -- 5.4 Proper time -- 5.5 Velocity and acceleration four-vectors -- 5.6 Problems -- 5.7 References -- 6 The Light Cone -- 6.1 The light cone -- 6.2 Events and coordinate systems -- 6.3 Problems -- 6.4 Future and past -- 6.5 References -- 7 Mass, Energy and Momentum -- 7.1 Preliminaries -- 7.2 Mass, energy and momentum -- 7.3 Angular-momentum representation -- 7.4 Energy-momentum four-vector -- 7.5 Problems -- 7.6 References -- 8 Velocity, Acceleration and Cosmic Distances -- 8.1 Preliminaries -- 8.2 Velocity and acceleration four-vectors -- 8.3 Acceleration and distances -- 8.4 Energy in ESR versus cosmic -- distance in CSR -- 8.5 Distance-velocity four-vector -- 8.6 Conclusions -- 8.7 References -- 9 First Days of the Universe -- 9.1 Preliminaries -- 9.2 Lengths of days -- 9.3 Comparison with Einstein's special relativity -- 9.4 References -- A Cosmological General Relativity -- A.1 Preliminaries -- A.2 Cosmology in spacevelocity -- A.3 Gravitational field equations -- A.4 Solution of the field equations -- A.5 Classification of universes -- A.6 Physical meaning -- A.7 The accelerating universe -- A.8 Theory versus experiment -- A.9 Concluding remarks -- A.10 References -- B Five-Dimensional Brane World Theory -- B.1 Introduction -- B.1.1 Cosmic coordinate systems: The -- Hubble transformation -- B.1.2 Lorentz-like cosmological -- transformation -- B.1.3 Five-dimensional manifold of space, -- time and velocity -- B.2 Universe with gravitation -- B.2.1 The Bianchi identities -- B.2.2 The gravitational field equations -- B.2.3 Velocity as an independent coordinate -- B.2.4 Effective mass density in cosmology -- B.3 The accelerating Universe -- B.3.1 Preliminaries -- B.3.2 Expanding Universe -- B.3.3 Decelerating, constant and -- accelerating expansions -- B.3.4 Accelerating Universe -- B.4 The Tully-Fisher formula: Halo dark matter -- B.4.1 The geodesic equation -- B.4.2 Equations of motion -- B.4.3 The Tully-Fisher law -- B.5 The cosmological constant -- B.5.1 The cosmological term -- B.5.2 The supernovae experiments value for the -- cosmological constant -- B.5.3 The Behar-Carmeli predicted value for the -- cosmological constant -- B.5.4 Comparison with experiment -- B.6 Cosmological redshift analysis -- B.6.1 The redshift formula -- B.6.2 Particular cases -- B.6.3 Conclusions -- B.7 Concluding remarks -- B.8 Mathematical conventions and Christoffel symbols -- B.9 Components of the Ricci tensor -- B.10 Integration of the Universe expansion equation -- B.11 References -- C Cosmic Temperature Decline -- C.1 Introduction. -- C.2 Temperature formula without -- gravity -- C.3 Comparison -- C.4 References.
9810249365 (alk. paper)
Cosmology.
Special relativity (Physics)
Gravitational fields.
Space and time.
523.1