Tevian Dray

The Geometry of Special Relativity (eBook, ePUB)

• Format: ePub

Produktbeschreibung

The book treats the geometry of hyperbolas as the key to understanding special relativity. The author simplifies the formulas and emphasizes their geometric content. Prior mastery of (ordinary) trigonometry is sufficient for most of the material presented.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 196
• Erscheinungstermin: 10. Juni 2021
• Englisch
• ISBN-13: 9781351663205
• Artikelnr.: 61662311

Autorenporträt

Tevian Dray is a Professor of Mathematics at Oregon State University. His research lies at the interface between mathematics and physics, involving differential geometry and general relativity, as well as nonassociative algebra and particle physics; he also studies student understanding of "middle-division" mathematics and physics content. Educated at MIT and Berkeley, he held postdoctoral positions in both mathematics and physics in several countries prior to coming to OSU in 1988. Professor Dray is a Fellow of the American Physical Society for his work in relativity, and an award-winning teacher.

Inhaltsangabe

1. Introduction. 1.1 Newton's Relativity. 1.2. Einstein's Relativity. 2.
The Physics of Special Relativity. 2.1. Observers and Measurement. 2.2. The
Postulates of Special Relativity. 2.3. Time Dilation and Length
Contraction. 2.4. Lorentz Transformations. 2.5. Addition of Velocities.
2.6. The Interval. 3. Circle Geometry. 3.1. The Geometry of Trigonometry.
3.2. Distance. 3.3. Circle Trigonometry. 3.4. Triangle Trigonometry. 3.5.
Rotations. 3.6. Projections. 3.7. Addition Formulas. 4. Hyperbola Geometry.
4.1. Hyperbolic Trigonometry. 4.2 Distance. 4.3. Hyperbola Trigonometry.
4.4. Triangle Trigonometry. 4.5. Rotations. 4.6. Projections. 4.7. Addition
Formulas. 4.8. Combining Circle and Hyperbola Trigonometry. 5. The Geometry
of Special Relativity. 5.1. The Surveyors. 5.2. Spacetime Diagrams. 5.3.
Lorentz Transformations. 5.4. Space and Time. 5.5. The Geometry of Lorentz
Transformations. 5.6. Dot Product. 6. Applications. 6.1. Drawing Spacetime
Diagrams. 6.2. Addition of Velocities. 6.3. Length Contraction. 6.4. Time
Dilation. 6.5. Doppler Shift. 7. Problems I. 7.1. Warmup. 7.2. Practice.
7.3. The Getaway. 7.4. Angles Are Not Invariant. 7.5. Interstellar Travel.
7.6. Observation. 7.7 Cosmic Rays. 7.8. Doppler Effect. 8. Paradoxes. 8.1.
Special Relativity Paradoxes. 8.2. The Pole and Barn Paradox. 8.3. The Twin
Paradox. 8.4. Manhole Covers. 9. Relativistic Mechanics. 9.1. Proper Time.
9.2. Velocity. 9.3. Conservation Laws. 9.4. Energy. 9.5. Useful Formulas.
9.6. Higher Dimensions. 10. Problems II. 10.1. Mass Isn't Conserved. 10.2.
Identical Particles. 10.3. Pion Decay I. 10.4. Mass and Energy. 10.5. Pion
Decay II. 11. Relativistic Electromagnetism. 11.1. Magnetism from
Electricity. 11.2. Lorentz Transformations. 11.3. Vectors. 11.4. Tensors.
11.5. The Electromagnetic Field. 11.6. Maxwell's Equations. 11.7. The
Unification of Special Relativity. 12. Problems III. 12.1. Vanishing
Fields. 12.2. Parallel and Perpendicular Fields. 13. Beyond Special
Relativity. 13.1. Problems with Special Relativity. 13.2. Tidal Effects.
13.3. Differential Geometry. 13.4. General Relativity. 13.5. Uniform
Acceleration and Black Holes. 14. Three-Dimensional Spacetime Diagrams.
14.1. Introduction. 14.2. The Rising Manhole. 14.3. The Moving Spotlight.
14.4. The Lorentzian Inner Product. 14.5. Transverse Directions. 15.
Minkowski Area via Light Boxes. 15.1. Area in Special Relativity. 15.2.
Measuring with Light Boxes. 16. Hyperbolic Geometry. 16.1. Non-Euclidean
Geometry. 16.2. The Hyperboloid. 16.3. The Poincaré Disk. 16.4. The Klein
Disk. 16.5. The Pseudosphere. 17. Calculus. 17.1. Circle Trigonometry.
17.2. Hyperbolic Trigonometry. 17.3. Exponentials (and Logarithms).
Bibliography. Index.