General Relativity

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General Relativity

• Theory of gravity developed by Einstein
• Consider accelerating reference frames
• No observer can determine by experiment whether
  he or she is accelerating or is rather in a
  gravitational field.

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Examples
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Intertial Mass Gravitional Mass

• Inertial Mass is what appears in Fma
• Gravitional Mass appears in Newtons
  Gravitational Law and determines the
  gravitational force between two objects
• No reason for them to be the same
• Principle of equivalence is really just saying
  the two masses are the same.

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Bending Light
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Experimental Test
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Space Curvature

• We determined earlier that light follows the
  fastest path between two points
• Since the light bends, space must be curved by
  the presence of an object
• Well look at the rubber sheet analogy

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Space Curvature
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Black Holes

• Let the object be so massive that it bends space
  so much that light cannot escape the curvature
• Most galaxies appear to have one or more black
  holes at the center

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Expanding Universe

• Recall the Doppler shift
• Objects retreating have light waves that are
  shifted toward the red
• Objects approaching have light waves that are
  shifted toward the blue
• Have to use special relativity to calculate

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Expanding Universe

• Receding objects

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Hubbles Law

• Lines from galaxies are red-shifted
• Amount of shift depends on distance to galaxy
• VHD
• Doesnt work for nearby galaxies in our local
  group
• H 80 km/s/Mpc

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Hubbles Law

• Implies expansion of the university
• Must have been an explosion in the past
• We are NOT in the middle
• Expansion looks the same from anywhere

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Expansion of the Universe
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Quasars

• Quasars (quasi-stellar objects) do not conform to
  Hubbles Law
• Bright as nearby stars by have enormous redshifts
• Two choices
• Near and unusual redshift
• Far and unusual brightness
• Most likely bright galaxies with large black holes

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Cosmological Principle

• The universe looks the same to observers in
  different places at the same time
• Universe is isotropic (same in all directions)
• Universe is homogeneous (would look the same if
  we relocate to another galaxy)
• Only true on a very large scale
• Galaxies (visible matter) tends to clump in
  clusters

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Age of the Universe

• Use Hubble Constant
• Midpoint of estimated range of values is 22km/s
  per million light years.

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Cosmic Microwave Background

• If the universe is finite, then it was all in one
  spot in a tiny volume approaching a point 15
  billion years ago.
• This is not just all the mass in one spot with
  empty space around it
• The spot was the entire universe
• The size of the universe has increased like
  blowing up a balloon and observing spots on the
  surface to get farther apart

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Cosmic Microwave Background

• Penzias and Wilson built radio telescope to do
  communications research
• Had a background noise that they couldnt get rid
  of
• Measuring they found noise unchanged in
  direction, time of day or time of year
• Later measurements showed blackbody spectrum at a
  temperature of 2.7 degrees Kelvin (microwaves)

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Cosmic Microwave Background

• Gamow predicted such radiation should exist as a
  result of the big bang in the late 1940s and PW
  discovered it in the 1960s
• Strong confirmation of the theory

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Early History

• Early universe very hot and very dense
• No atoms, just photons, leptons, quarks
• Photons could not escape capture by electrons
  (collisions)
• Expansion cooled things down
• Once temperature down to 3000 Kelvin, atoms can
  form and be stable
• Radiation decouplde from matter

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Early History

• Universe expanded and radiation redshifted to
  longer wavelengths that correspond to cooler
  temperatures
• Early universe was radiation-dominated
• Later, after some expansion became
  matter-dominated

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Standard Cosmological Model
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The Future

• What is the curvature of space-time?

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The Future

• How much matter compared to critical density that
  leads to big crunch?
• Visible matter is only about 1
• Appears to be dark matter based on motion of
  galaxies that cannot be explained on the basis of
  gravity and the visible matter
• Dont know what it is

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The Future

• Any evidence expansion is slowing?
• Actually evidence from some supernovae that the
  expansion is increasing in speed!!
• Dont know what this all means
• Lots of work for physicists to do in the future
• Hooray!!!!!