1. EPPT M2 INTRODUCTION TO RELATIVITY K Young, Physics Department, CUHK  The Chinese University of Hong Kong

2. CHAPTER 5 SPACETIME DIAGRAMS

3. Objectives  Drawing spacetime diagrams  Three regions in spacetime  Distances and times  Relation between reference frames

4. Spacetime Diagrams

5. Spacetime diagrams  P = point  Imagine z-axis x y P 4 3  P = event  Imagine y, z axes  Angle has no meaning t x P 3 4 t x P 3 4

6. Example  P travels to a star 10 ly away  at speed 0.5c  Returns immediately at 0.5c 20 x t 10 40

7. x 20 t 1010 40 20 x t 10 40

8. Three regions in spacetime

9. t x O B' B B" A C

10. t x O time-like

11. t x O space-like

12. t x O light-like

13. Conditions Time-like Space-like Light-like t x O

14. Invariant classification Time-like t x O Space-like Light-like

15. x' t' Light cone P  Invariant concept  Link to O by light ray t xO   Light cone about a point P  Light-like separation

16. Spacelike separation t x O B' B B"  O and B cannot have any causal relations     Invariant concept  Cannot send signal from O to B

17. x' The distance measured by an observer for whom the events are simultaneous Proper distance Light cone t x Proper distance

18. Timelike separation t x O C A  Can send signal O  A, C  O    Invariant concept  Future APast C This is also invariant  Particle trajectories are time-like

19. x' y x

20. t' The time measured by a co-moving clock Light cone t x Proper time

22.  Proper time  of a timelike separation = time measured in co-moving frame S'  Proper distance  s of a spacelike separation =distance measured in frame S' where the 2 events are simultaneous

23. Distances and times

24. Distances in space y x A B  cut into segments   add   Depends on path

25. Time elapsed t x A B  cut into segments   add   Depends on path

26. Twin paradox x t

27. Relation between Reference Frames

28. y' x'  Relation between ref frames y x How should x', y' axes be drawn?

29. x' t' t x

30. Objectives  Drawing spacetime diagrams  Three regions in spacetime  Distances and times  Relation between reference frames

31. Acknowledgment  I thank Miss HY Shik and Mr HT Fung for design