Download Relativity Lecture

Black Holes and
General Relativity
Stuff that warps your mind
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Goals
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Why should time be affected by motion?
Why should light be affected by gravity?
Why should time be affected by gravity?
What proof is there that they are?
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Special Relativity
2 Main Postulates:
1. The speed of light is always c.
Thou shalt not add your speed to the speed of light!
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Special Relativity
2. Moving and nonaccelerating reference
frames are
indistinguishable from
one another.
If it happens at rest, it
must happen in
(constant) motion.
At rest
Constant velocity
Are you moving, or are you at rest right now?
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Time Dilation
Tick!
Compare
distance
time 
c
Tock!
Tick!
Tock!
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Moving clocks run slow
• Since:
distance
time 
c
Compare
S
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How slow?
 v
Time Moving  Time Rest  1   
c
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Travel to Vega: Distance = 25 LY (7.5 pc)
Time = Distance / velocity
velocity = 0.999c
TimeRest = 25 years
Copyright Lynette Cook, used with permission
TimeMoving = 25 years x 0.04 = 1year!
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How slow?
 v
Time Moving  Time Rest  1   
c
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Travel to Milky Way’s supermassive black hole:
Distance = 28,000 LY (8.5 kpc)
Time = Distance / velocity
velocity = 0.999999c
TimeRest = 28 thousand years
TimeMoving = 28 thousand years x 0.0014 = 40 yrs!
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Twin Paradox
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Twins. One goes to Vega. One stays home.
What happens?
What does each see?
How can one age, and the other not?
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General Relativity
2 Main Postulates:
1. The speed of light is always c.
Thou shalt not add your speed to the speed of light!
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General Relativity
2. Accelerating reference
frames are
indistinguishable
from a gravitational
force.
The Star Tours ride at Disneyland is awesome!
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Gravity Bends Light
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Is there Proof?
Scientific Method:
1. Hypothesis: predict gravity bends light.
2. Test: The Sun has a lot of gravity and should
deflect star light.
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Solar Eclipse of 1919
• Hard to see stars near the
Sun.
• Can see stars near the Sun
during an eclipse.
• Can predict time and
position of Sun during
eclipse years in advance.
SOHO spacecraft
• Measure the positions of
stars 6 months before when
they are up at night.
Result: Theory of Relativity confirmed!
• During eclipse, measure
their positions again.
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Gravitational Lensing
• If geometry right: gravity cause multiple
images.
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Einstein Lenses
Copyright – Charles R Evans (UNC)
Einstein Ring
Copyright – L. J. King (U. Manchester)
Copyright – J. Rhoads, WIYN
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Abell 2218
Copyright – A. Fruchter (STScI)
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Space is Curved
• Einstein said to picture gravity as a warp in space.
– Sagan : A “pucker” in fabric of space.
• Kepler’s Laws
explained by
movement around
“puckers.”
• Everything moving
is affected,
regardless of mass.
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distance
time 
c
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Gravity makes time slow
F
F
S
S
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Proof?
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GPS satellites use atomic clocks.
Position determined by timing radio signals.
In orbit Fg = ¼ Fg at Earth surface.
Clock on satellite runs fast by 45 msec per day.
D=vt
D=ct
DD = cDt
DD = 3 x 105 km/s * 45 x 10-6 s/day
DD = 13.5 km/day
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