The Spacetime World: The Minkowski World (UMAP)

With this unit, the student will be able to: 1) recognize the speed of light as the limiting speed of ordinary particles, and the light cone as a corresponding barrier in spacetime; 2) relate the Minkowski spacetime diagram to the required invariance of the speed of light and invariance of spacetime interval; 3) relate the classical Doppler effect to fundamental concepts of wave motion; 4) accomodate modification of the Doppler effect equation to include the effect of time dilation; 5) apply the Minkowski diagram to resolution of the twin paradox (clock paradox); and 6) describe the crucial role of acceleration in the twin paradox.

Table of Contents:

INTRODUCTION

1. DIAGRAMMING SPACETIME

2. THE LIGHT CONE

3. THE MINKOWSKI DIAGRAM

4. CALIBRATION OF THE AXES OF THE MINKOWSKI DIAGRAM

5. TIME DILATION AND THE DOPPLER EFFECT

6. THE TWIN PARADOX

7. LENGTH CONTRACTION

8. SUMMARY

9. GLOSSARY

10. ANSWERS TO THE EXERCISES

11. MODEL EXAMINATION

12. ANSWERS TO THE MODEL EXAMINATION