University of Delaware


Quarks, Gluons, and the Big Bang

Maurice Barnhill

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Last revised 1999/04/26

Class Notes X: General Relativity

This section is largely a translation out of mathematics of Essential Relativity by Wolfgang Rindler.


  1. Equivalence Principle
    1. Weak: Gravitational mass = inertial mass
      1. FC = k Q q / R2 = mI a
      2. FG = G M mG / R2 = mI a
    2. Strong
      1. Local inertial frames
        1. In free fall
        2. Not rotating
        3. May cover only a small region (local)
      2. Implications
        1. Space is curved
          1. Light moving across a local inertial frame must travel in straight line, by EP
          2. Local frame is accelerating compared to nearby bodies.
          3. Light-path is therefore curved as seen from other bodies.
          4. Curvature is independent of material properties.
          5. Therefore simplest to attribute curvature to space.
          6. Gravity theories that do not attribute the curvature to space eventually work their way to empirically incorrect conclusions.
          7. Experiments agree with these results to 1% accuracy.
        2. Gravitational red shift
          1. Light moving against gravitation comes up through bottom of local inertial frame.
          2. By EP this light is never Doppler shifted in inertial frame.
          3. So for a "stationary" observer, who sees the inertial observer moving, the light must be red-shifted.
          4. Light near large masses is therefore detectably red-shifted.
          5. Clocks based on atomic vibrations therefore run dectably more slowly near large masses.
          6. From E = h f , light loses energy moving against a gravitational force.
          7. Experiments agree to 1% accuracy.
  2. Curved Space
    1. Rough visualizations -- spheres
    2. Distance measures
      1. Coordinate distance
      2. Angular spread measure
      3. Brightness measure
        1. Effect of angular spread
        2. Doppler effect: detector is moving away from photons
      4. Red shift measure
  3. Cosmological constant, a kind of negative pressure

  4. Strings
    1. Problems with point particles
      1. Mass renormalization
      2. Infinities
      3. Gravity and infinities
    2. Way strings cure problems
    3. General makeup of strings
      1. Strings and general relativity
      2. Extra dimensions
        1. Higher dimensions picked out
        2. Compactification
        3. Most-likely version has
          1. "Left-moving bosons" in 26 space-time dimensions
          2. Compactify 10 space dimensions
          3. Right-moving "supersymmetric" objects added
          4. Compactify 6 more space dimensions, leaving 4-dim space-time
      3. Quarks and leptons
      4. Supersymmetry breaking
      5. Graviton
  5. Cosmology

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