1 | Course Overview - Overview of Course Contents
- Practical Issues and Advice
- Related Subjects; Brief History of Physics
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2 | Symmetry and Invariance - Background and History
- Galilean Transformation, Inertial Reference Frames
- Classical Wave Equations; Transformation to Other Frames
- Michelson-Morley Experiment; Aether
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3 | Symmetry and Invariance (cont.) - Postulates of Special Relativity
- First Discussion of Minkowski Diagrams, World Lines
| Problem set 1 due |
4 | Relativistic Kinematics - Derivation of Lorentz-Einstein Transformations
- Introduction of Four-Vectors
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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
| Problem set 2 due |
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
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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
| Problem set 3 due |
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
- Optional Problems in the Use of the Calculus of Variations as Applied to Lagragian Mechanics and Other Problems in the Extremization of Path Integrals
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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
| Problem set 4 due |
10 | Relativistic Dynamics and Particle Physics (cont.) - Relativistic Motion in a B Field, Lorentz Force
- Further Gedanken Experiments Relating to Mass-Energy Equivalence, Relativistic Momentum
- Quantum Nature of Light
- Photoelectric Effect, Photons
- beta-Decay and the Inference of Neutrino
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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
| Problem set 5 due |
13 | Relativistic Dynamics and Particle Physics (cont.) - Particle Production
- Threshold Energy
- Colliding Particle Beams
- Two Photons Producing an Electron/Positron Pair
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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
| Problem set 6 due |
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
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16 | Relativity and Electromagnetism (cont.) - General Transformation Laws for E and B
- Magnetic Force due to Current-Bearing Wire
- Force between Current-Bearing Wires
| Problem set 7 due |
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
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18 | General Relativity and Cosmology - Cosmological Redshifts and the Hubble Law
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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}
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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
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| 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
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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
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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
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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
| Problem set 9 due |
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
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