SES # | TOPICS | LECTURE SLIDES |
---|---|---|

1 | ## Course Overview- Overview of Course Contents
- Practical Issues and Advice
- Related Subjects; Brief History of Physics
| (PDF) |

2 | ## Symmetry and Invariance- Background and History
- Galilean Transformation, Inertial Reference Frames
- Classical Wave Equations; Transformation to Other Frames
- Michelson-Morley Experiment; Aether
| (PDF) |

3 | ## Symmetry and Invariance (cont.)- Postulates of Special Relativity
- First Discussion of Minkowski Diagrams, World Lines
| (PDF) |

4 | ## Relativistic Kinematics- Derivation of Lorentz-Einstein Transformations
- Matrix Representation
- Introduction of Four-Vectors
| (PDF) |

5 | ## Relativistic Kinematics (cont.)- Time Dilation and Length Contraction
- Decay of Atmospheric Muons
- Pole Vaulter Problem
- Alternative Looks at Time Dilation and Length Contraction
- Spacetime Intervals
- First Discussion of Accelerated Clocks
| (PDF) |

6 | ## Relativistic Kinematics (cont.)- Addition of Velocities
- Angle Transformation for Trajectories
- Doppler Effect
- Classical Doppler Effect for Sound
- Relativistic Doppler Effect
- Astrophysical Examples; Relativistic and Superluminal Jets
- Doppler Effect
| (PDF) |

7 | ## Relativistic Kinematics (cont.)- Stellar Aberration
- Doppler Effect and Angle Transformation via Transformation of Phase of Plane Waves
- Fully Calibrated Minkowski Diagrams
- Pole-Vaulter Problem
- Twin Paradox with Constant Velocity Plus a Reversal
- Twin Paradox with Arbitrary Acceleration
| (PDF - 1.1 MB) |

8 | ## Variational Calculus- Short Discourse on the Calculus of Variations
- Extremization of Path Integrals
- The Euler-Lagrange Equations and Constants of the Motion
- Brachistochrone Problem
- Extremal Aging for Inertially Moving Clocks
- Extremization of Path Integrals
- Optional Problems in the Use of the Calculus of Variations as Applied to Lagragian Mechanics and Other Problems in the Extremization of Path Integrals
| (PDF) |

9 | ## Relativistic Dynamics and Particle Physics- Relativistic Momentum Inferred from Gedanken Experiment with Inelastic Collisions
- Relativistic Relations between Force and Acceleration
- Relativistic Version of Work-Energy Theorem
- Kinetic Energy, Rest Energy, Equivalence of Mass-Energy
- E
^{2}- p^{2}Invariant
- Nuclear Binding Energies
- Atomic Mass Excesses, Semi-Empirical Binding Energy Equation
- Nuclear Reactions
- Solar p-p Chain
| (PDF) |

10 | ## Relativistic Dynamics and Particle Physics (cont.)- Relativistic Motion in a B Field, Lorentz Force
- Cyclotrons, Synchrotrons
- Further Gedanken Experiments Relating to Mass-Energy Equivalence, Relativistic Momentum
- Quantum Nature of Light
- Photoelectric Effect, Photons
*beta*-Decay and the Inference of Neutrino
| (PDF) |

11 | Quiz 1 | |

12 | ## Relativistic Dynamics and Particle Physics (cont.)- Absorption and Emission of Light Quanta
- Atomic and Nuclear Recoil
- Mössbauer Effect
- Pound-Rebka Experiment
- Collisions
- Between Photons and Moving Atoms
- Elastic
- Compton
- Inverse Compton
- Between Photon and Relativistic Particle
| (PDF) |

13 | ## Relativistic Dynamics and Particle Physics (cont.)- Particle Production
- Threshold Energy
- Colliding Particle Beams
- Two Photons Producing an Electron/Positron Pair
- Threshold Energy
| (PDF - 1.2 MB) |

14 | ## Relativistic Dynamics and Particle Physics (cont.)- Formal Transformation of E and P as a Four-Vector
- Revisit the Relativistic Doppler Effect
- Relativistic Invariant E
^{2}- p^{2}for a Collection of Particles
| (PDF - 2.0 MB) |

15 | ## Relativity and Electromagnetism- Coulomb's Law
- Transformation of Coulomb's Law
- Force on a Moving Test Charge
- Magnetic Field and Relativity
- Derivation of Lorentz Force
| (PDF) |

16 | ## Relativity and Electromagnetism (cont.)- General Transformation Laws for E and B
- Magnetic Force due to Current-Bearing Wire
- Force between Current-Bearing Wires
| (PDF) |

17 | ## The Equivalence Principle and General Relativity- Strong and Weak Principles of Equivalence
- Local Equivalence of Gravity and Acceleration
- Elevator Thought Experiments
- Gravitational Redshift
- Light Bending
- Relative Acceleration of Test Particles in Falling Elevator of Finite Size
- Definition of the Metric Tensor
- Analogy between the Metric Tensor and the Ordinary Potential, and between Einstein's Field Equations and Poisson's Equation
| (PDF) |

18 | ## General Relativity and Cosmology- Cosmological Redshifts and the Hubble Law
| (PDF) |

19 | ## General Relativity and Cosmology (cont.)- Cosmology
- Dynamical Equations for the Scale Factor a - Including Ordinary Matter, Dark Matter, and Dark Energy
- Critical Closure Density; Open, Closed, Flat Universes
- Solutions for Various Combinations of Omega
_{m}, Omega_{Lambda}and Omega_{k}
| (PDF) |

20 | ## General Relativity and Cosmology (cont.)- Cosmology (cont.)
- Age of the Universe, Brief History
- Relation between Scale Factor and Z from the Doppler Shift
- Lookback Age as a Function of Z for Various Values of Omega
_{m}, Omega_{Lambda}and Omega_{k} - Acceleration Parameter as a Function of Scale Factor
- Current S Status of Cosmology, Unsolved Puzzles
| (PDF - 1.4 MB) |

21 | Quiz 2 | |

22 | ## General Relativity and Cosmology (cont.)- Handout Defining Einstein Field Equations, Einstein Tensor, Stress-Energy Tensor, Curvature Scalar, Ricci Tensor, Christoffel Symbols, Riemann Curvature Tensor
- Symmetry Arguments by Which 6 Schwarzschild Metric Tensor Components Vanish
- Symmetry Arguments for Why the Non-zero Components are Functions of Radius Only
- The Differential Equations for G00 and G11
- Shell Radius vs. Bookkeepers Radial Coordinate
| (PDF - 4.1 MB) |

23 | ## General Relativity and Black Holes- Gravitational Redshift
- Application to the GPS System
- Particle Orbits
- Use Euler Equations (for External Aging) in Connection with the Schwarzschild Metric to find Constants of the Motion E and L
- Derive the Full Expression for the Effective Potential
| (PDF) |

24 | ## General Relativity and Black Holes (cont.)- Derive Analytic Results for Radial Motion
- Compare Speeds and Energies for Bookkeeper and Shell Observers
- Equations of Motion for a General Orbit
- Explain How these can be Numerically Integrated
- Expand the Effective Potential in the Weak-Field Limit
| (PDF - 1.1 MB) |

25 | ## General Relativity and Black Holes (cont.)- Keplers Third Law in the Schwarzschild Metric
- Relativistic Precession in the Weak-Field Limit
- Taylor-Hulse Binary Neutron Star System
- Derivation of the Last Stable Circular Orbit at 6M
- Analytic E and L for Circular Orbits
| (PDF) |

26 | ## General Relativity and Black Holes (cont.)- Photon Trajectories
- Derive Differential Equation for the Trajectories
- Critical Impact Parameter
- Derive Expression for Light Bending in the Weak-Field Limit
- Shapiro Time Delay
| (PDF - 1.8 MB) |