eBook ISBN:  9781614445173 
Product Code:  SPEC/78.E 
List Price:  $40.00 
MAA Member Price:  $30.00 
AMS Member Price:  $30.00 
eBook ISBN:  9781614445173 
Product Code:  SPEC/78.E 
List Price:  $40.00 
MAA Member Price:  $30.00 
AMS Member Price:  $30.00 

Book DetailsSpectrumVolume: 78; 2013; 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 trainandtunnel 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 fasterthanlight travel is impossible. Most of these explanations are contained in the resolution of apparent paradoxes, including some lesserknown ones: the peashooter paradox, the bugandrivet 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 frameindependent 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 MichelsonMorley 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 onesemester, generaleducation introduction to special relativity. It is especially well suited for selfstudy 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 TimeStamped Origins

Graphic Resolution of the Paradoxes

9. The Accommodating Universe Paradox

10. The LengthTime Comparison Paradoxes

11. The Twin Paradox

12. The TrainTunnel Paradox

13. The PeaShooter Paradox

14. The BugRivet 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


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Reviews
 Requests
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 trainandtunnel 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 fasterthanlight travel is impossible. Most of these explanations are contained in the resolution of apparent paradoxes, including some lesserknown ones: the peashooter paradox, the bugandrivet 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 frameindependent 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 MichelsonMorley 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 onesemester, generaleducation introduction to special relativity. It is especially well suited for selfstudy 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 TimeStamped Origins

Graphic Resolution of the Paradoxes

9. The Accommodating Universe Paradox

10. The LengthTime Comparison Paradoxes

11. The Twin Paradox

12. The TrainTunnel Paradox

13. The PeaShooter Paradox

14. The BugRivet 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