| Lec # | Topics | Key Dates |
|---|---|---|
| 1 | I. Introduction and Relativity Pre-Einstein I.1 Introduction: Intuition and Familiarity in Physical Law I.2 Relativity before Einstein Inertial Frames Non-inertial Frames Galilean Relativity Form Invariance of Newton's Laws The Galilean Transformation I.3 Light and Electromagnetism Particle and Wave Interpretations of Light Measurement of the Speed of Light | |
| 2 | I.3 Light and Electromagnetism (cont.) Maxwell's Theory of Electromagnetism, Light as an Electromagnetic Phenomenon, and the Triumph of the Wave Theory of Light Aether as the Medium in which Light Waves Propagate I.4 Search for the Aether Properties of the Aether Michelson-Morley Experiment | |
| 3 | I.4 Search for the Aether (cont.) Aether Drag, Stellar Aberration, and the Collapse of the Aether Theory II. Einstein's Principle of Relativity and a new Concept of Spacetime II.1 The Principles of Relativity Einstein's Postulates The Resolution of the Michelson-Morley Experiment The Need for a Transformation of Time (beginning) II.2 Inertial Frames, Clocks and Meter Sticks reconsidered Setting up Measurements in Inertial Frames Synchronizing Clocks Infinite Families of Inertial Frames II.3 The Lorentz Transformation The Need for a Transformation between Inertial Frames The Derivation of the Lorentz Transformation | |
| 4 | II.3 The Lorentz Transformation (cont.) Space Time Diagrams I II.4 Some Immediate Consequences Relativity of Simultaneity Spacetime, World Lines, Events | |
| 5 | II.4 Some Immediate Consequences (cont.) Lorentz Transformations of Events II.5 The Algebra of Lorentz Transformations Beta, Gamma, and the Rapidity Analogy to Rotations Inverse Lorentz Transformations | |
| 6 | III. The Great Kinematic Consequences of Relativity III.1 Length Contraction and Time Dilation Simple Derivations Reciprocity Examples -- Duality between Length Contraction and Time Dilation Careful Comparisons and the "Reality" of Length Contraction III.2 Intervals, Causality, etc. Invariance of the Interval under Lorentz Transformation Spacelike, Timelike, and Lightlike Intervals Causality: the Future, the Past, and Elsewhere Coordinates for Minkowski Space | Problem set 1 due |
| 7 | III.2 Intervals, Causality, etc. (cont.) Causality: the Future, the Past, and Elsewhere Coordinates for Minkowski Space IV. Velocity Addition and other Differential Transformations IV.1 The differential form of the Lorentz Transformation IV.2 Addition of Velocities Parallel and Perpendicular The Speed of Light is the Limit IV.3 Transformation of Angles Static Angles: Transforming Geometry Dynamical Angles: Transforming Rectilinear Motion | |
| 8 | IV.3 Transformation of Angles (cont.) Stellar Aberration a la Special Relativity IV.4 The Relativistic Doppler Effect Frequencies Longitudinal and Transverse Doppler Effects Comparison with the Non-relativistic Doppler Effect Doppler Effect at Arbitrary Angles Examples of Doppler Effects IV.5 The Visual Appearance of Rapidly Moving Objects V. Kinematics and "Paradoxes" V.1 The Polevaulter Paradox and the Failure of Rigidity Naive Analysis | |
| 9 | V.1 The Polevaulter Paradox and the Failure of Rigidity (cont.) Resolution: Careful Tracking of "Events" Special Relativity and Rigidity V.2 The Seaplane and the Hole in the Ice The View from the Ice The View from the Plane V.3 Acceleration in Special Relativity Lorentz Transformation of Acceleration | |
| 10 | V.3 Acceleration in Special Relativity (cont.) The Proper Acceleration Hyperbolic Motion Space Travel V.4 The Iceboat Paradox The View from the Ice The View from the Boat: Lorentz Transformation of Force | Problem set 2 due |
| 11 | V.5 The Twin Paradox The Simple Form Experimental Confirmation Confusion and Resolution VI. Relativistic Momentum and Energy I: Basics VI.1 Constructing Relativistic Energy and Momentum Derivation from a Physical Construction | Midterm exam |
| 12 | VI.1 Constructing Relativistic Energy and Momentum (cont.) Derivation from a Physical Construction Rest Mass Reality of the Rest Energy The Relativistic Relation between Energy, Momentum, and Mass Examples of Mass ⇔ Energy | |
| 13 | VI.1 Constructing Relativistic Energy and Momentum (cont.) Massless Particles The Pressure of Light VI.2 Relativistic Decays and Collisions A → 2B in the A Rest Frame | |
| 14 | VI.2 Relativistic Decays and Collisions (cont.) Photon Emission and Absorption Doppler Shift and the Mössbauer Effect Compton Effect and Quantum Mechanics Review of Midterm Exam | Problem set 3 due |
| 15 | VII. Relativistic Momentum and Energy II: Four Vectors and Transformation Properties VII.1 Transformation Properties under Lorentz Transformations Invariants and Things that Change The Instantaneous Rest Frame Proper Time as a Lorentz Invariant Four-vectors Definitions via Transformation Properties The Four-vector in Minkowski Space VII.2 The Four Velocity -- another Four-vector VII.3 The Lorentz Transformation of Energy and Momentum The Energy-momentum Four-vector Examples of Lorentz Transformation of Energy and Momentum | |
| 16 | VII.4 The Invariant Scalar Product The Invariant Interval as an Operation on Four-vectors The Invariant Product of Four-momenta Simplifying Kinematics for Decays and Collisions More Decays and Collisions Compton Scattering again | |
| 17 | Review of Special Relativity for Final Exam Einstein Notation and Relativity in Metric Space | Problem set 4 due |
| 18 | VIII. General Relativity: Einstein's Theory of Gravity VIII.1 The Incompleteness of Special Relativity Non-inertial Frames A General Principle of Relativity VIII.2 The Equivalence of Inertial and Gravitational Mass Newton's Law of Gravity Gravitational "Charge" and Inertial Mass The Gravitational Field Gravity as another Manifestation of Inertia VIII.3 The Principle of Equivalence Einstein's Elevator and other Inertial Frames Gravity and Acceleration | |
| 19 | VIII.4 Consequences of the Equivalence Principle The Gravitational Redshift The Pound-Rebka Experiment and Sirius B The Bending of Light in a Gravitational Field VIII.5 Considerations on a Spinning Disk Gravitational Dilation When Time Stops: the Schwartzschild Radius and Black Holes Curvature and non-Euclidean Geometry Course Evaluations | Final exam |