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

LECTURE 5

SPACE-TIME DIAGRAMS

PHYS 420-SPRING 2006

Dennis Papadopoulos

)/(

])/([

cvxcttc

ctcvxx

tconsc

cv

cv

tan

)),/(()1,0(

))/(,()0,1(

How old is traveling observer when

stationary is one?

Draw plane of simultaneity

2222

2222

/1)/(1)(

var

cvcTs

iantinxtcs

o

(0,1)

(1,0)

ct’

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 70TH BIRTHDAY IS SLIGHTLY SMALLER AND HER PHYSICAL AGE SLIGHTLY SHORTER (BY MAY BE A MICROSECOND)

tB=tA/

OUTWARD JOURNEY

222 )21()2

1()21( BAA tctVtc

xA

EXACTLY THE SAME FOR RETURN JOURNEY

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