EPPT M2 INTRODUCTION TO RELATIVITY K Young, Physics Department, CUHK The Chinese University of Hong Kong
CHAPTER 5 SPACETIME DIAGRAMS
Objectives Drawing spacetime diagrams Three regions in spacetime Distances and times Relation between reference frames
Spacetime Diagrams
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
Example P travels to a star 10 ly away at speed 0.5c Returns immediately at 0.5c 20 x t 10 40
x 20 t x t 10 40
Three regions in spacetime
t x O B' B B" A C
t x O time-like
t x O space-like
t x O light-like
Conditions Time-like Space-like Light-like t x O
Invariant classification Time-like t x O Space-like Light-like
x' t' Light cone P Invariant concept Link to O by light ray t xO Light cone about a point P Light-like separation
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
x' The distance measured by an observer for whom the events are simultaneous Proper distance Light cone t x Proper distance
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
x' y x
t' The time measured by a co-moving clock Light cone t x Proper time
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
Distances and times
Distances in space y x A B cut into segments add Depends on path
Time elapsed t x A B cut into segments add Depends on path
Twin paradox x t
Relation between Reference Frames
y' x' Relation between ref frames y x How should x', y' axes be drawn?
x' t' t x
Objectives Drawing spacetime diagrams Three regions in spacetime Distances and times Relation between reference frames
Acknowledgment I thank Miss HY Shik and Mr HT Fung for design