Announcements

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Announcements

• Projects are graded! Almost all were quite
  good--congratulations!
• Test next week (all about stars)
• Second project is due in three weeks

So many things I would have done, But clouds got
in my way. --Joni Mitchell
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Black Holes

• 10 November 2006

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Today

• Special relativity theory (for high-speed
  motions)
• General relativity a new theory of gravity
• Black holes
• How to detect black holes

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Special Relativity Theory

• A revision of Newtons laws of motion
• Especially important when objects move at close
  to the speed of light
• Proposed by Einstein in 1905
• Resolved apparent paradoxes in electromagnetic
  theory

Albert Einstein, 1879 - 1955
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Special Relativity Theory

• The principle of relativity (Galileo,
  Descartes) says that motion is relative Theres
  no way to tell whos really moving, so long as
  the motion is straight and uniform.
• But electromagnetic waves are predicted (and
  observed) to travel at a fixed speed 300,000
  km/s.
• Before Einstein, physicists thought this meant
  that the principle of relativity doesnt apply to
  electromagnetic waves--just measure the speed of
  light relative to you, and youll learn how fast
  youre really moving.
• Einstein proposed that the speed of light is
  fixed, regardless of the motion of the source or
  the observer!
• Implications Time itself behaves in bizarre
  ways, which become noticeable only when objects
  move fast relative to each other.

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Implications of Special Relativity

• The time interval measured between two events
  depends on exactly how it is measured.

Amy
Beth
Speed 4/5 speed of light
Alpha Cent., 4 l.y. away
Amy stays home on earth, while Beth travels to
Alpha Centauri and back at 4/5 the speed of
light. Amy measures the time between Beths
departure and return to be 10 years (5 years each
way), as we would expect. Beth measures the time
to be only 6 years! ( 10 x 1(4/5)2 )
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Implications of Special Relativity

• When you add speeds, the result is less than
  you thought!

1/2 speed of light w.r.t. Beth
Beth
1/2 speed of light w.r.t. earth
Amy
Amy measures the cannon balls speed to be only
4/5 the speed of light!
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2
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1
1
1
2
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Implications of Special Relativity

• The speed of light (300,000 km/s) is a Cosmic
  Speed Limit

Combining two speeds less than the speed of light
always results in a speed that is also
less Photons and some other signals move at the
speed of light, regardless of the motion of the
source It would take an infinite amount of
energy to accelerate a physical object up to the
speed of light If a signal could travel faster
than light with respect to Amy, then it could
travel backwards in time with respect to Beth
(whos moving w.r.t. Amy).
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Special Relativity
The mathematics of special relativity isnt
advanced--just basic algebra. There are many
good books on the subject, or you can learn more
by taking Physics 2220 (Physics for Scientists
and Engineers).
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What about Gravity?
Newton Force on the moon points toward where
earth is now.
Force
Einstein Thats inconsistent with the Cosmic
Speed Limit! If the earth suddenly moves, the
force on the moon cant change until 1.3 seconds
later. We need a new theory of gravity
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General Relativity Theory

• Einsteins theory of gravity
• Especially important for fast-moving objects and
  for very dense objects
• Proposed by Einstein in 1915

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General Relativity The Basic Idea
Position
Time
The graph appears curved because space-time
itself is curved (distorted by the earths mass).
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Why does the apple fall?
Aristotle Its seeking its natural place toward
the center of the universe. Newton The earth
exerts a force, pulling the apple
downward. Einstein Its moving along the
straightest possible path through curved
space-time.
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Why do golf balls and bowling balls fall at the
same rate?
Because the trajectory is a property of
space-time itself, not a property of the object.
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Consequences of General Relativity(Advanced
mathematics required!)

• Inverse-square force law isnt exact minor
  corrections to solar system trajectories

Mercurys elliptical orbit gradually precesses,
mostly due to the gravitational pull of other
planets. But a small part of the precession (43
arc-seconds per century) is due to relativistic
corrections to Newtonian gravity.
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Consequences of General Relativity

• Gravitational deflection of light (twice the
  amount that Newton would have predicted)

Arthur Eddington (tested prediction in 1919)
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Consequences of General Relativity

• Gravitational waves ripples in space-time
  curvature that propagate outward from
  accelerating massive objects (e.g., supernova
  explosions, close binary systems)

Binary pulsar (in Aquila)
LIGO (Hanford, WA site)
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Consequences of General Relativity

• Black holes Objects so dense that not even
  light can escape.

(2-D analogy of 3-D curvature)
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Black Holes in Brief

• A spherical horizon surrounds the region from
  which nothing can escape
• The radius of the horizon is proportional to the
  black holes mass (surface area is 4pR2)
• For a solar-mass black hole, the horizon radius
  is 3 km (only a few times smaller than a neutron
  star)
• Neutron stars, like white dwarfs, shrink with
  increasing mass maximum mass is 2-3 solar masses
• So a collapsing stellar core more massive than
  this should form a black hole!

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How to detect a black hole?

• Only through its gravitational pull on other
  objects!
• An isolated black hole would be virtually
  impossible to detect
• In a close binary system, a black hole can suck
  gas off the companion staras the gas spirals
  inward it becomes extremely hot and emits x-rays
• Most famous example Cygnus X-1. Binary system
  (8000 ly away) of a blue supergiant star and a
  compact object, both 20-30 solar masses--too
  massive for a neutron star.

Dust ring (800 ly wide) swirling into center of
galaxy NGC 4261
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More Black Hole Physics

• What happens if you fall into one? Nothing
  special when you cross the horizon (unless you
  try to turn around). But from then on, youre
  doomed. The equations say that when you reach
  the center, your time stops. (The equations
  dont take quantum effects into account.)
• Because black holes are perfect absorbers of
  radiation, they also emit thermal radiation from
  their horizons! Smaller black holes are hotter.
  But for a solar-mass black hole, T is only about
  106 kelvin, so the radiation is negligible.

Stephen Hawking