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I. Introduction and Relativity PreEinstein
I.1 Introduction: Intuition and Familiarity in Physical Law
I.2 Relativity before Einstein
Inertial Frames
Noninertial 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 

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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
MichelsonMorley Experiment 

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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 MichelsonMorley 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 

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II.3 The Lorentz Transformation (cont.)
Space Time Diagrams I
II.4 Some Immediate Consequences
Relativity of Simultaneity
Spacetime, World Lines, Events 

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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 

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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 
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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 

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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 Nonrelativistic 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 

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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 

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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 
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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 
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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 

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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 

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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 
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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
Fourvectors
Definitions via Transformation Properties
The Fourvector in Minkowski Space
VII.2 The Four Velocity  another Fourvector
VII.3 The Lorentz Transformation of Energy and Momentum
The Energymomentum Fourvector
Examples of Lorentz Transformation of Energy and Momentum 

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VII.4 The Invariant Scalar Product
The Invariant Interval as an Operation on Fourvectors
The Invariant Product of Fourmomenta
Simplifying Kinematics for Decays and Collisions
More Decays and Collisions
Compton Scattering again 

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Review of Special Relativity for Final Exam
Einstein Notation and Relativity in Metric Space 
Problem set 4 due 
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VIII. General Relativity: Einstein's Theory of Gravity
VIII.1 The Incompleteness of Special Relativity
Noninertial 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 

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VIII.4 Consequences of the Equivalence Principle
The Gravitational Redshift
The PoundRebka 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 nonEuclidean Geometry
Course Evaluations 
Final exam 