LECTURE 5 SPACE-TIME DIAGRAMS PHYS 420-SPRING 2006 Dennis Papadopoulos

 How old is traveling observer when stationary is one? Draw plane of simultaneity (0,1) (1,0) ct’ x’x’ ct x

SIMULTANEITY

PLANES OF SIMULTANEITY

The time measured by a heartbeat or the wristwatch of a person equqls its wordline from a to b. Curved wordlines are shorter than straight wordlines. Thus a person arriving via a bent world line has fewer heartbeats than a person following a straight- line (i.e. moving only through space) Photons never age in free space.

TWINS A AND B FOLLOW DIFFERENT LIFES ONE STAYING HOME THE OTHER TRAVELING A LOT. EVERY TIME THEY MEET AT THE SAME SPACETIME POSITION Bs WORDLINE IS SLIGTLY SHORTER SINCE SHE HAS MOVED A LOT THROUGH SPACE, WHILE HER BROTHER MOVED ONLY THROUGH SPACE. HER WORDLINE AT THEIR 70 TH BIRTHDAY IS SLIGHTLY SMALLER AND HER PHYSICAL AGE SLIGHTLY SHORTER (BY MAY BE A MICROSECOND)

tB=tA/tB=tA/ OUTWARD JOURNEY xAxA EXACTLY THE SAME FOR RETURN JOURNEY tB=tA/tB=tA/ GAMMA 50, V=.9998c IF A IS 50 YEARS OLDER B IS ONLY ONE YEAR OLDER

AGE BEFORE U-TURN AGE AFTER U-TURN

ACCELERATION