Chapter 26a Cosmology

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Chapter 26a Cosmology Einstein's Theory of
Relativity Special and General Olbers
Paradox Cosmological Assumptions Models 1916
Einsteins static universe and the cosmological
constant 1921-1935 FRW models 1922 Three models
by A Friedmann H. P. Robertson, A. G. Walker---
Three Models---plus Friedmann
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Einsteins Theory of Relativity
Albert Einstein (1879-1955) is pictured here in
the Swiss Patent Office where he did much of his
great work.
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Special Relativity Space
and Time
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• 1905 Postulates of Special Relativity
• 1. The speed of light is the same as measured by
  all nonacclerating (Inertial) observers.
• 2. No experiment can single out any special
  inertial reference frame ( non accelerating).

• Consequences
• Moving Lengths Contract
• Moving clocks run slow
• Moving Mass appears to increase
• EM C2

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Lorentz Contraction
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Length Contraction
As speed increases, length in the direction of
motion decreases. Lengths in the perpendicular
direction do not change.
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The meter stick is measured to be half as long
when traveling at 87 the speed of light
relative to the observer.
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time dilation
The Clock is at rest
My clock ticks are 2.3 sec apart .
The Moving Clock
V 0.9c
The clock ticks on the moving clock are 5 sec
apart
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Energy-Mass Equivalence 
 E mc2   

• When a uranium nucleus
• splits, the mass of the
• remnants is less than the
• original mass. The difference
• appears as light, heat, and
• kinetic energy.

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Energy is mass  m E /c2
Mass is energy  E mc2 
You can create a particle-antiparticle pair when
high-energy photons collide. In this process,
called pair production, the photons disappear,
and their energy is replaced by the mass of the
particle-antiparticle pair.
In the process of annihilation, a colliding
particle-antiparticle pair disappears and high
energy photons appear
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General Theory of Relativity1915
It took Einstein 10 years from the publication of
special relativity to the publication of GR
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What is Gravity?
Einstein's Picture
Newtons Picture
Isaac Newton (1642-1726)
the gravitational field.
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The key idea of General Relativity, called the
Equivalence Principle, is that gravity is
equivalent to an acceleration.
Principle of Equivalence It is impossible to
tell, from within a closed system, whether one is
in a gravitational field, or accelerating
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General Relativity and Gravity
In Einsteins General Theory of Relativity,
gravity arises from the curvature of spacetime
continuum.
The curvature of the spacetime continuum is
produced by the presence of mass. Massive
object distorts spacetime continuum more.
Spacetime is stretched near objects with large
mass, like our Earth.
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Mass and Curvature

• Einstein no longer thought of gravity as a force
  but a curvature of space-time.
• Space is "curved" by massive objects causing
  objects to fall toward them.

Orbits of Planets
43 arcsec/100years
The extra amount of precession of planet
Mercurys orbit is explained by GTR.
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Eddingtons Eclipse Expedition Experience, 1919
Consequences of GR Bending of Light

• Went to Principe Island in the Gulf of Guinea.
  After months of drought, it was pouring rain on
  the day of the eclipse Clouds parted just in
  time, they took photographic plates showing the
  location of stars around the limb of the sun
• Deflection in agreement with the GR prediction

Einstein urged astronomers to measure the effect
of gravity on starlight, as in this 1913 letter
to the American G.E. Hale. They could not respond
until the First World War ended.
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GRAVITATIONAL LENSE
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Clocks and Curvature(Gravity)
fast
slow
Harvard 1959 Atomic clock in basement - slower
by about 2.50x10-15
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Fast
slow
The stronger a gravitational field, the slower a
clock runs. A clock at the surface of the Earth
runs slower than a clock farther away.
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More mass more spacetime curvature
Flat space
Neutron star
Black hole
The sun
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More curvature means stronger attraction
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Clocks in stronger gravity fields appear to
slow down to an external observer.
Time Slows
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Gravitational
Red Shift Light emitted from compact object(
strong gravity) is red shifted The photon is
giving up energy as it escapes from the pull of
the gravitational field
The more massive and/or more compact an object,
the greater the redshift. 0.01 10-8 cm shift
for the Sun. 1 10-8 cm shift for a white
dwarf.
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• What is a black hole?
• A curvature so steep light cannot climb out

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The gravitational force or warping of space-time
increases at the surface of a collapsing star.
Light rays find it increasingly more difficult
to escape the surface. A black hole is a
collapsed star where light cannot escape.
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• The blackhole has such a high density that at its
  Surface the escape speed exceeds the speed of
  light so nothing can escape

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Black Hole
2GM
Rs
c2
Event Horizon Rs distance where escape speed
equals speed of light!
A black hole a big as the solar system, e.g. Rs
40 AU, has a mass M 2 Billion Mo
Singularity
Singularity Mathematical point at center,
where the point of the funnel comes to a head
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Anything that falls into a black hole disappears
form the observable universe.
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The center of the Blackhole

• Could a black hole somehow be connected to
  another part of spacetime, or even some other
  universe?
• General relativity predicts that such
  connections, called wormholes, might exist for
  black holes

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THE FUTURE? Travel
through a black hole and wormhole to Vega!
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Gravitational waves

• GR predicts that ripples in spacetime propagate
  at the speed of light gravitational waves
• Mergers of compact objects (e.g. black holes)
  produce immense amounts of gravitational
  radiation
• Note that the universe is not dim in terms of
  gravitational radiation all mass produces it
• Exceptionally difficult to detect because of the
  weak coupling to matter Fgrav/Felec10-36

Laser Interferometer Gravitational Wave
Observatory LIGO (Livingston, Louisiana)
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General Relativity and the Universe on Large
Scales-------Cosmology
Historical Time Line

• 1823 Olbers Paradox
• Cosmological Assumptions
• 1916 Einsteins static universe and the
  cosmological constant (Force)
• 1929 Hubbles Law---the universe is expanding
• 1930 Einsteins biggest mistake ---the
  cosmological constant is zero.
• 1921-1935 FRW models--- A Friedmann H. P.
  Robertson,
• and A. G. Walker

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Olberss Paradox Why is the
night sky dark?
1823 - Heinrich Olbers Paradox The sky should
be uniformly bright. Assume universe is
infinite and stars are randomly scattered. Then
in every direction you will eventually come to a
star and the sky will be glowing!
Resolution Stars are moving away so light is
red-shift and not as bright. The universe is not
infinitely old - so some light hasn't had time to
reach us.
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Cosmological
Assumptions
1. Universality of Physical Law 2. The
Cosmological Principle (or Copernican view) The
place we occupy in the Universe is not special.
The matter in the universe is homogeneous and
isotropic when averaged over very large scales
greater than about 300 Mpc. a. Homogeneity
b. Isotropic
Consequences 1. Laws of Physics are the same
through out the universe 2. No center 3. No
edge, 4. All observers see the same
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Time Line for the beginnings of Cosmology
1916 Einsteins static universe and the
cosmological constant (Force) 1922 Three models
of the Universe by A Friedmann
1929 Hubbles Law---the universe is expanding
1930 Einsteins biggest mistake ---the
cosmological constant is zero.
1935 H. P. Robertson, A. G. Walker--- Three
Models
Geoffrey Walker
H.P. Robertson
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In 1917 Einstein constructed a static model of
the Universe. Models of the Universe were a
natural out come of Einstein's General Relativity
as applied to a homogeneous universe.
Static Universe
The idea that the universe was expanding was
thought to be absurd so Einstein invented the
Cosmological constant as a term in his General
Relativity theory that allowed for a static
universe
Repulsive force Cosmological Constant
Attractive Gravity
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1930 Hubble Expansion

• 1930 Einstein learns the Universe is Expanding
• Einstein was unhappy with the cosmological
  constant and dropped it.
• Einsteins biggest mistake
• ---the cosmological constant is zero

Hubbles Law Galaxies are receding with
velocities directly proportional to the distance
away
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1921-1935 FRW models
The Russian mathematician Friedmann realized in
1921 that Einstein equations could describe an
expanding universe.
Alexander Friedmann
The joint work of Walker and colleague H P
Robertson in the late 1930s put Friedmann's
theories of an expanding universe on a sound
mathematical foundation. This theory is called
the FRW model and still forms the basis for
models of the universe in modern cosmology.
Geoffrey Walker
H.P. Robertson
The British astronomer Fred Hoyle dismissively
called it the "Big Bang'', and the name stuck.
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This model implied that the Universe was born at
one moment, about ten billion years ago All the
matter, indeed the Universe itself, was created
at just one instant.
Time
The Space continued to expand after the
initial burst.
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The End of Chapter 26a