Time and Space Weight and Inertia - 1st Edition - ISBN: 9781483212739, 9781483226163

Time and Space Weight and Inertia

1st Edition

A Chronogeometrical Introduction to Einstein's Theory

Authors: A. D. Fokker
Editors: D. ter Haar
eBook ISBN: 9781483226163
Imprint: Pergamon
Published Date: 1st January 1965
Page Count: 206
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Time and Space Weight and Inertia covers the relationship between time, space weight, and inertia using the principles of theory of relativity and chronogeometry.
This book is composed of 12 chapters, and begins with a brief overview of the fundamental aspects of space and time within events. The subsequent chapters deal with the chronogeometry of time and space, and the concept of the Lorentz transformations and pseudo-revolutions. These topics are followed by discussions on the dynamical relationships of metric and other tensors and a presentation of the equations of the theory of electrons. The remaining chapters describe the unique value of the acceleration in free fall, geodesic coordinates carried along in free fall, and the field equations, as well as the so-called curving of light rays. This book will prove useful to physicists and mathematicians.

Table of Contents

Preface to the English Edition


I. Foundations

1. Reality, Viewed as a Stream of Events. Space and Time within Events

2 . Pictures and Diagrams

3 . Coordinates. Point-Instants

4. Rotations and Translations

5. The Fundamental Velocity

6. Einstein's Fundamental Thesis of the Constant Velocity of Light. The Transformation Formulae for Translations

7. Intervals. Durations, Distances and Telethigmata

8. Newton and Einstein

II. One-Plus-One-Dimensional Chronogeometry

1. The Enduring Path

2. Rhombuses of Conjugate Intervals and Rectangles of Here-Now Rays

3 . Triangles

4. Metre Stick and Clock

5. The Slowing Down of Translating Clocks and the Contraction of Translating Measuring Rods

6. Chronogeometrically Uniform Acceleration

7. The Accelerated Rigid Measuring Rod

8. The Accelerated Ideal Metre Clock

III. The Chromogeometry of TIme and Space

1. The Intervals with (1 + 3 ) Components

2 . Conjugate Intervals

3. Tetrads of Conjugate Vectors

4. The Various Manifolds and their Mutual Relationships

5. The Separation Interval of Non-intersecting Time Tracks and Straight Lines

6. Durationless Planes and Straight Lines. Here-Now Rays

7. The Algebraic Determination of Magnitudes

8. Tensors and Dual Vectors

IV. The Lorentz Transformations

1. The Tetrads of Unit Vectors

2 . Accelerationless Rotations

3 . Rotationless Accelerations (Pseudo-Revolutions)

4. Kinematic Precession

V. Rotations and Accelerations in Terms of Pseudo-Revolutions

1. The Compound Reorientation of Normalized Tetrads of Unit Vectors

2 . The Conjugate Axes of an Infinitesimal Transformation

3 . The Motion of a Rigid Body

4. A Special Case of the Motion of a Rigid Body

5. Michelson's Experiment and the Ideal Spherical Light Wave Clock

6. Accelerating Coordinates and the Equivalence Hypothesis

VI. Metric and Other Tensors

1. The Gauge Figure

2 . Contravariant, Covariant, and Mixed Tensors of Different Ranks

3 . The Metric Tensor

4. Special Tensors

5. Differentiating Tensors

VII. Dynamical Relationships

1. Mass

2 . Dynamical Variables of Two Particles

3 . Internal Angular Momentum

4. The Internal Angular Momentum of a Collection of Particles

5. External Rotation, Centre of Inertia and Polarized Inertia

6. Interaction in Terms of Telehapses

7. Creation and Annihilation of Matter

8. Action

VIII. The Dynamical Tensor

1. Density of Presence and Density of Passage

2 . The Dynamical Tensor

3 . The Principal Axes of the Dynamical Tensor

4. Conservation of Energy and Momentum

IX. The Equations of the Theory of Electrons

1. The Density of the Electric Current and Charge

2 . Polarization and Magnetization

3 . The Charge-Free Electromagnetic Field and Its Potentials

4. The Electromagnetic Field and the Charges. The Energy-Momentum Tensor

X . Accelerating and Curving Events

1. The Unique Value of the Acceleration in Free Fall

2 . The Parallel Displacement of a Vector. Geodesic Lines

3 . The Geodesic Derivatives

4. Curvature

5. The Cycle of a Chronogeometric Compass

6. The Formal Properties of the Riemann Tensor

XI. Geodesic Adaptations

1. Geodesic Lines

2 . The Free Fall

3 . Radially Adapted (Geodesic) Coordinates

4. Geodesic Coordinates Carried Along in Free Fall

5. Tidal Effects

XII. The Field Equations and the Spherical Gravitational Field

1. The Field Equations

2. The Static Field with Spherical Symmetry

3 . Free Fall of Planets Towards a Centre with Spherical Symmetry

4. The So-Called Curving of Light Rays

5. The Red-Shift of Spectral Lines

6. The Geodesic Precession

Appendix: Effect of Gravity on Nuclear Resonance Interaction




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© Pergamon 1965
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About the Author

A. D. Fokker

About the Editor

D. ter Haar

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