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Illustrated Special Relativity through Its Paradoxes: A Fusion of Linear Algebra, Graphics, and Reality
 
Illustrated Special Relativity through Its Paradoxes
MAA Press: An Imprint of the American Mathematical Society
eBook ISBN:  978-1-61444-517-3
Product Code:  SPEC/78.E
List Price: $40.00
MAA Member Price: $30.00
AMS Member Price: $30.00
Illustrated Special Relativity through Its Paradoxes
Click above image for expanded view
Illustrated Special Relativity through Its Paradoxes: A Fusion of Linear Algebra, Graphics, and Reality
MAA Press: An Imprint of the American Mathematical Society
eBook ISBN:  978-1-61444-517-3
Product Code:  SPEC/78.E
List Price: $40.00
MAA Member Price: $30.00
AMS Member Price: $30.00
  • Book Details
     
     
    Spectrum
    Volume: 782013; 464 pp

    Illustrated Special Relativity shows that linear algebra is a natural language for special relativity. It illustrates and resolves several apparent paradoxes of special relativity, including the twin paradox and train-and-tunnel paradox. Assuming a minimum of technical prerequisites, the authors introduce inertial frames and use them to explain a variety of phenomena: the nature of simultaneity, the proper way to add velocities, and why faster-than-light travel is impossible. Most of these explanations are contained in the resolution of apparent paradoxes, including some lesser-known ones: the pea-shooter paradox, the bug-and-rivet paradox, and the accommodating universe paradox. The explanation of time and length contraction is especially clear and illuminating.

    At the outset of his seminal paper on special relativity, Einstein acknowledges the work of James Clerk Maxwell, whose four equations unified the theories of electricity, optics, and magnetism. For this reason, the authors develop Maxwell's equations which lead to a simple calculation for the frame-independent speed of electromagnetic waves in a vacuum. (Maxwell did not realize that light was a special case of electromagnetic waves.) Several chapters are devoted to experiments of Roemer, Fizeau, and de Sitter to measure the speed of light and the Michelson-Morley experiment abolishing the aether.

    Throughout the exposition is thorough, but not overly technical, and often illustrated by cartoons. The volume might be suitable for a one-semester, general-education introduction to special relativity. It is especially well suited for self-study by interested laypersons or use as a supplement to a more traditional text.

  • Table of Contents
     
     
    • A First Pass
    • Preface
    • 1. Introduction to the Paradoxes
    • 2. Clocks and Rods in Motion
    • 3. The Algebra of Frames
    • 4. The Graphing of Frames
    • Galilean Transformations of Frames
    • 5. Galilean Transformations
    • The Speed of Light Is Constant
    • 6. Constant $c$ in Spacetime
    • Lorentz Transformations of Frames
    • 7. Lorentz Transformations
    • 8. The Hyperbola of Time-Stamped Origins
    • Graphic Resolution of the Paradoxes
    • 9. The Accommodating Universe Paradox
    • 10. The Length-Time Comparison Paradoxes
    • 11. The Twin Paradox
    • 12. The Train-Tunnel Paradox
    • 13. The Pea-Shooter Paradox
    • 14. The Bug-Rivet Paradox
    • Energy and Mass
    • 15. $E=mc^2$
    • The Mathematics of Waves and Light
    • 16. The Nature of Waves
    • 17. Measuring the Speed of Light
    • Maxwell’s Equations
    • 18. Maxwell’s Mathematical Toolkit
    • 19. Electric and Magnetic Fields
    • 20. Electricity and Magnetism: Gauss’ Laws
    • 21. Towards Maxwell’s Equations
    • 22. Electromagnetism: A Qualitative View
    • 23. Electromagnetism: A Quantitative View
    • Final Thoughts
    • 24. Epilogue: Final Thoughts
    • Appendices
    • A. Linear Algebra Overview
    • B. Hyperbolic Functions
    • C. Deconstructing a Moving Train
    • Supplemental Material
    • D. Dimensional Analysis
    • E. Rings of Functions and Square Matrices
    • F. The Scientific Method
    • G. Logic of the Scientific Method
  • Reviews
     
     
    • This book delivered exactly what I was looking for. Presupposing only a modest background in physics, it takes the reader on a tour of special relativity, concentrating on half a dozen of the paradoxes of the subject. ... The discussion throughout the book is clear and accessible but does not flee from mathematics. ...

      Mark Hunacek, MAA Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 782013; 464 pp

Illustrated Special Relativity shows that linear algebra is a natural language for special relativity. It illustrates and resolves several apparent paradoxes of special relativity, including the twin paradox and train-and-tunnel paradox. Assuming a minimum of technical prerequisites, the authors introduce inertial frames and use them to explain a variety of phenomena: the nature of simultaneity, the proper way to add velocities, and why faster-than-light travel is impossible. Most of these explanations are contained in the resolution of apparent paradoxes, including some lesser-known ones: the pea-shooter paradox, the bug-and-rivet paradox, and the accommodating universe paradox. The explanation of time and length contraction is especially clear and illuminating.

At the outset of his seminal paper on special relativity, Einstein acknowledges the work of James Clerk Maxwell, whose four equations unified the theories of electricity, optics, and magnetism. For this reason, the authors develop Maxwell's equations which lead to a simple calculation for the frame-independent speed of electromagnetic waves in a vacuum. (Maxwell did not realize that light was a special case of electromagnetic waves.) Several chapters are devoted to experiments of Roemer, Fizeau, and de Sitter to measure the speed of light and the Michelson-Morley experiment abolishing the aether.

Throughout the exposition is thorough, but not overly technical, and often illustrated by cartoons. The volume might be suitable for a one-semester, general-education introduction to special relativity. It is especially well suited for self-study by interested laypersons or use as a supplement to a more traditional text.

  • A First Pass
  • Preface
  • 1. Introduction to the Paradoxes
  • 2. Clocks and Rods in Motion
  • 3. The Algebra of Frames
  • 4. The Graphing of Frames
  • Galilean Transformations of Frames
  • 5. Galilean Transformations
  • The Speed of Light Is Constant
  • 6. Constant $c$ in Spacetime
  • Lorentz Transformations of Frames
  • 7. Lorentz Transformations
  • 8. The Hyperbola of Time-Stamped Origins
  • Graphic Resolution of the Paradoxes
  • 9. The Accommodating Universe Paradox
  • 10. The Length-Time Comparison Paradoxes
  • 11. The Twin Paradox
  • 12. The Train-Tunnel Paradox
  • 13. The Pea-Shooter Paradox
  • 14. The Bug-Rivet Paradox
  • Energy and Mass
  • 15. $E=mc^2$
  • The Mathematics of Waves and Light
  • 16. The Nature of Waves
  • 17. Measuring the Speed of Light
  • Maxwell’s Equations
  • 18. Maxwell’s Mathematical Toolkit
  • 19. Electric and Magnetic Fields
  • 20. Electricity and Magnetism: Gauss’ Laws
  • 21. Towards Maxwell’s Equations
  • 22. Electromagnetism: A Qualitative View
  • 23. Electromagnetism: A Quantitative View
  • Final Thoughts
  • 24. Epilogue: Final Thoughts
  • Appendices
  • A. Linear Algebra Overview
  • B. Hyperbolic Functions
  • C. Deconstructing a Moving Train
  • Supplemental Material
  • D. Dimensional Analysis
  • E. Rings of Functions and Square Matrices
  • F. The Scientific Method
  • G. Logic of the Scientific Method
  • This book delivered exactly what I was looking for. Presupposing only a modest background in physics, it takes the reader on a tour of special relativity, concentrating on half a dozen of the paradoxes of the subject. ... The discussion throughout the book is clear and accessible but does not flee from mathematics. ...

    Mark Hunacek, MAA Reviews
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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