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Black Holes and General
Relativity
Stuff that warps your mind
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Goals
• 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 Relativity2 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 non-accelerating reference frames are indistinguishable from one another.
If it happens at rest, it must happen in (constant) motion.Are you moving, or are you at rest right now?
At rest Constant velocity
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Time Dilation
Tick!
Tock!
Tick!
Tock!
c
distancetime
Compare
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Moving clocks run slow
• Since:
c
distancetime
Compare
S
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How slow?
Travel to Vega: Distance = 25 LY (7.5 pc)
Time = Distance / velocityvelocity = 0.999cTimeRest = 25 years
TimeMoving = 25 years x 0.04 = 1year!
2
RestMoving c
v1TimeTime
Copyright Lynette Cook, used with permission
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How slow?
Travel to Milky Way’s supermassive black hole:Distance = 28,000 LY (8.5 kpc)
Time = Distance / velocityvelocity = 0.999999cTimeRest = 28 thousand years
TimeMoving = 28 thousand years x 0.0014 = 40 yrs!
2
RestMoving c
v1TimeTime
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Twin Paradox
• 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 Relativity2 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.
• Measure the positions of stars 6 months before when they are up at night.
• During eclipse, measure their positions again.
SOHO spacecraft
Result: Theory of Relativity confirmed!
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Gravitational Lensing
• If geometry right: gravity cause multiple images.
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Einstein Lenses
Copyright – J. Rhoads, WIYN
Copyright – Charles R Evans (UNC)
Einstein Ring
Copyright – L. J. King (U. Manchester)
8Copyright – A. Fruchter (STScI)
Abell 2218
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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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c
distancetime
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Gravity makes time slow
S
F
S
F
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Proof?
• 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 = v tD = c tDD = cDtDD = 3 x 105 km/s * 45 x 10-6 s/dayDD = 13.5 km/day