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Calendar

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