» MIT OpenCourseWare » Physics » Relativity, Fall 2003

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SES #	TOPICS	KEY DATES
Overview
1	Overview of Course, Related Subjects; History of Physics to 1900
Background and History
2	Galilean Transformation, Inertial Reference Frames
3	Classical Wave Equations; Transformation to Other Frames Michelson-morley Experiment; Ether
4	Postulates of Special Relativity	PS 1 Due
5	First Discussion of Minkowski Diagrams, World Lines
Relativistic Kinematics
5 (cont.)	Derivation of Lorentz-Einstein Transformations Matrix Representation Introduction of Four-vectors
6	Time Dilation and Length Contraction Decay of Atmospheric Muons, Pole Vaulter Problem
7	Alternative Looks at Time Dilation and Length Contraction	PS 2 Due
7-8	Spacetime Intervals
8	First Discussion of Accelerated Clocks Addition of Velocities Angle Transformation for Trajectories
9	Doppler Effect Classical Doppler Effect for Sound Relativistic Doppler Effect Astrophysical Examples; Relativistic and Superluminal Jets Stellar Aberration
10	Alternate Approach to Doppler Effect and Angle Transformation via Transformation of Phase of Plane Waves
11	Short Discourse on the Calculus of Variations Extremization of Path Integrals Eulers Equations and Constants of the Motion Brachistochrone Problem	PS 3 Due
12	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. Fully Calibrated Minkowski Diagrams Pole-vaulter Problem
13	Twin Paradox with Constant Velocity Plus a Reversal Twin Paradox with Arbitrary Acceleration
Relativistic Dynamics
14	Relativistic Momentum Inferred from Gedanken Experiment with Inelastic Collisions Relativistic Relations between Force and Acceleration	PS 4 Due
15	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
16	Relativistic Motion in a B Field, Lorentz Force	Quiz 1
17	Cyclotrons, Synchrotrons Further Gedanken Experiments Relating to Mass-energy Equivalence, Relativistic Momentum
18	Quantum Nature of Light Photoelectric Effect, Photons ß Decay and the Inference of Neutrinos Absorption and Emission of Light Quanta - Atomic and Nuclear Recoil
19	Mossbauer Effect Pound-Rebka Experiment
20	Collisions Between Photons and Moving Atoms Elastic Compton Inverse Compton Between Photon and Relativistic Particle	PS 5 Due
21	Particle Production Threshold Energy Colliding Particle Beams
22	Two Photons Producing an Electron/Positron Pair Formal Transformation of E and p as a Four-vector Revisit the Relativistic Doppler Effect
23	Relativistic Invariant E² - p² for a Collection of Particles Transformation of Forces and Accelerations Example of Minkowski Metric for a "Skewed, but Flat" Space	PS 6 Due
Relativity and Electromagnetism
24	Coulomb's Law Transformation of Coulomb's Law
25	Force on a Moving Test Charge Magnetic Field and Relativity Derivation of Lorentz Force
Red Shifts and Hubble Expansion of the Universe
26	Distance Ladder in Astronomy	PS 7 Due
27	Cosmological Redshifts and the Hubble Law Newtonian Cosmology Dynamical Equations for the Scale Factor, a - Including Ordinary Matter, Dark Matter, and Dark Energy
28	Critical Closure Density; Open, Closed, Flat Universe Solutions for Various Combinations of Ω_m and Ω_λ Age of the Universe
29	Relation Between Scale Factor and z from the Doppler Shift Lookback Age as a Function of z for Given Values of Ω_m and Ω_λ Acceleration Parameter as a Function of Scale Factor	PS 8 Due
Equivalence Principle
30	Strong and Weak Principles of Equivalence Local Equivalence of Gravity and Acceleration Elevator "Thought Experiments"; Gravitational Red Shift, Light Bending Relative Acceleration of Test Particles in Falling Elevator of Finite Size
Curved Space Time
31	10-page Handout defining: Einstein Field Equations, Einstein Tensor, Stress-Energy Tensor, Curvature Scalar, Ricci Tensor, Christoffel Symbols, Riemann Curvature Tensor Definition of the Metric Tensor Analogy between the Metric Tensor and the Ordinary Potential, and between Einsteins Field Equations and Poissons Equation Symmetry Arguments by which 6 Schwarzschild Metric Tensor Components Vanish Symmetry Arguments for why the Non-zero Components are Functions of Radius only	Quiz 2
32	The Differential Equations for G₀₀ and G₁₁ Shell Radius vs. Bookkeepers Radial Coordinate Gravitational Red Shift
33	Application to the GPS System Particle Orbits Use Euler Equations (for Extremal Aging) in connection with the Schwarzschild Metric to find Constants of the Motion E and L Derive the Full Expression for the Effective Potential
34	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 Kepler's Third Law in the Schwarzschild Metric	PS 9 Due
35	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
36	Photon Trajectories Derive Differential Equation for the Trajectories Critical Impact Parameter Derive Expression for Light Bending in the Weak-field Limit Shapiro Time Delay	Optional Quiz 3 PS 10 Due

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