LECTURE 5 SPACE-TIME DIAGRAMS PHYS 420-SPRING 2006 Dennis Papadopoulos.
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LECTURE 5
SPACE-TIME DIAGRAMS
PHYS 420-SPRING 2006
Dennis Papadopoulos
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)/(
])/([
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
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SIMULTANEITY
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PLANES OF SIMULTANEITY
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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.
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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)
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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
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AGE BEFORE U-TURN
AGE AFTER U-TURN
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ACCELERATION
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