Cosmological Special Relativity : the Large-Scale Structure of Space, Time and Velocity.

Summary

Titles

• Full Title: Cosmological Special Relativity : the Large-Scale Structure of Space, Time and Velocity.
• Other Titles: Cosmological Special Relativity - The Large-Scale Structure Of Space, Time And Velocity (2nd Edition); Cosmological special relativity - the large-scale structure of space, time and velocity

Edition Statement

• 2nd ed.

Notes

• Appendix A Cosmological General Relativity.
• 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 cone2.15 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 relativity4.1.1 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 relativity 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 transformation4.4.1 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 Momentum7.1 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.

Identifiers

• Isbns: 9810249365; 9789810249366
• Oclc Number: (OCoLC)956639215

Publication Statement

• Place: Singapore
• Publisher: World Scientific Publishing Company
• Date: 2002

Physical Description

• Extent: 1 online resource (225 pages)

Table Of Contents

• 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 cone2.15 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 relativity4.1.1 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 relativity 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 transformation4.4.1 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 Momentum7.1 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.

Summary

• This book 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. A cosmological Lorentz-like transformation, which relates events at different cosmic times, is derived and applied. A new law of addition of cosmic times is obtained, and the inflation of the space at the early universe is derived, both from the cosmological transformation. The relationship between cosmic velocity, acceleration and distances is given. In the appendices gravitation is added in the form of a cosmological g.

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