Relativity

Readings

SES #	TOPICS	READINGS
1	Course Overview Overview of Course Contents Practical Issues and Advice Related Subjects; Brief History of Physics	Resnick: Chapter 1 and beginning of Chapter 2. French: Chapters 1 and 2. Course Study Guide Handout (PDF)
2	Symmetry and Invariance Background and History Galilean Transformation, Inertial Reference Frames Classical Wave Equations; Transformation to Other Frames Michelson-Morley Experiment; Aether	Resnick: Chapter 1 and beginning of Chapter 2. French: Chapters 1 and 2. Symmetry Handout (PDF)
3	Symmetry and Invariance (cont.) Postulates of Special Relativity First Discussion of Minkowski Diagrams, World Lines	Resnick: Chapter 1 and beginning of Chapter 2. French: Chapters 1 and 2. Symmetry Handout (PDF)
4	Relativistic Kinematics Derivation of Lorentz-Einstein Transformations  Matrix Representation Introduction of Four-Vectors	Resnick: Chapter 2. French: Chapters 3 and 4. Matrix Primer Handout (PDF) Kinematics Handout (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	Resnick: Chapter 2. French: Chapters 3 and 4. Matrix Primer handout (PDF) Kinematics Handout (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	French: Chapter 5. Kinematics Handout (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	French: Chapter 5. Kinematics Handout (PDF)
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	Resnick: Supplementary Topics A and B in pages 188-209.
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 E2 - p2 Invariant Nuclear Binding Energies  Atomic Mass Excesses, Semi-Empirical Binding Energy Equation Nuclear Reactions Solar p-p Chain	Resnick: Supplementary Topics A and B in pages 188-209. Relativistic Dynamics Handout (PDF) Particle Physics Handout (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	Relativistic Dynamics Chapters in Resnick and French. Relativistic Dynamics Handout (PDF) Particle Physics Handout (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	Relativistic Dynamics Chapters in Resnick and French. Relativistic Dynamics Handout (PDF) Particle Physics Handout (PDF)
13	Relativistic Dynamics and Particle Physics (cont.) Particle Production  Threshold Energy  Colliding Particle Beams Two Photons Producing an Electron/Positron Pair	Resnick: Chapter 3. French: Chapters 6 and 7. Relativistic Dynamics Handout (PDF) Particle Physics Handout (PDF)
14	Relativistic Dynamics and Particle Physics (cont.) Formal Transformation of E and P as a Four-Vector  Revisit the Relativistic Doppler Effect Relativistic Invariant E2 - p2 for a Collection of Particles	Resnick: Chapter 3. French: Chapters 6 and 7. Relativistic Dynamics Handout (PDF) Particle Physics Handout (PDF)
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	Resnick: Chapter 4. French: Chapter 8. Note: As stressed in lecture, please don’t get bogged down with their excessive E&M algebra. Electromagnetism Handout (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	Resnick: Chapter 4. French: Chapter 8. Electromagnetism Handout (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	Taylor and Wheeler: Until pp. 2-18, in addition to Project G. Please also read the following: Cosmology: Spacetime Overview  Tegmark, Max. “Spacetime.” Science 296 (2002): 1427-1433. Cosmology: Ned Wright’s Tutorial.
18	General Relativity and Cosmology Cosmological Redshifts and the Hubble Law	Taylor and Wheeler: Until page 2-18, also project G. Please also read the following: Cosmology: Popular Overview  Lemonick, Michael D. “The End.” Time, June 25, 2001, 48-56. Cosmology: Spacetime Overview  Tegmark, Max. “Spacetime.” Science 296 (2002): 1427-1433. Cosmology: Ned Wright’s Tutorial.
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 Omegam, OmegaLambda and Omegak	Taylor and Wheeler: Until pp. 2-18, also Project G. Please also read the following: Cosmology: Popular Overview  Lemonick, Michael D. “The End.” Time, June 25, 2001, 48-56. Cosmology: Spacetime Overview  Tegmark, Max. “Spacetime.” Science 296 (2002): 1427-1433. Cosmology: Ned Wright’s Tutorial.
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 Omegam, OmegaLambda and Omegak Acceleration Parameter as a Function of Scale Factor Current S Status of Cosmology, Unsolved Puzzles	Taylor and Wheeler: Until pp. 2-18, also Project G. Please also read the following: Cosmology: Popular Overview  Lemonick, Michael D. “The End.” Time, June 25, 2001, 48-56. Cosmology: Spacetime Overview  Tegmark, Max. “Spacetime.” Science 296 (2002): 1427-1433. Cosmology: Ned Wright’s Tutorial.
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	Taylor and Wheeler: Chapters 2, 3, 4, 5, and Project D. Note: You will be responsible only for the corresponding material that was actually covered in the lectures. Project E should also be understandable, but this topic will be mentioned only very briefly in lecture. General Relativity Handout (PDF)
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	Taylor and Wheeler: Chapters 2, 3, 4, 5, and Project D. General Relativity Handout (PDF) Einstein’s Field Equations Handout (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	Taylor and Wheeler: Chapters 2, 3, 4, 5, and Project D. General Relativity Handout (PDF) Einstein’s Field Equations Handout (PDF)
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	Taylor and Wheeler: Chapters 2, 3, 4, 5, and Project D. General Relativity Handout (PDF) Einstein’s Field Equations Handout (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	Taylor and Wheeler: Chapters 2, 3, 4, 5, and Project D. General Relativity Handout (PDF) Einstein’s Field Equations Handout (PDF)