1 
Course Overview
 Overview of Course Contents
 Practical Issues and Advice
 Related Subjects; Brief History of Physics

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2 
Symmetry and Invariance
 Background and History
 Galilean Transformation, Inertial Reference Frames
 Classical Wave Equations; Transformation to Other Frames
 MichelsonMorley Experiment; Aether

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3 
Symmetry and Invariance (cont.)
 Postulates of Special Relativity
 First Discussion of Minkowski Diagrams, World Lines

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4 
Relativistic Kinematics
 Derivation of LorentzEinstein Transformations
 Introduction of FourVectors

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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

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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

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7 
Relativistic Kinematics (cont.)
 Stellar Aberration
 Doppler Effect and Angle Transformation via Transformation of Phase of Plane Waves
 Fully Calibrated Minkowski Diagrams
 PoleVaulter Problem
 Twin Paradox with Constant Velocity Plus a Reversal
 Twin Paradox with Arbitrary Acceleration

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8 
Variational Calculus
 Short Discourse on the Calculus of Variations
 Extremization of Path Integrals
 The EulerLagrange 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

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9 
Relativistic Dynamics and Particle Physics
 Relativistic Momentum Inferred from Gedanken Experiment with Inelastic Collisions
 Relativistic Relations between Force and Acceleration
 Relativistic Version of WorkEnergy Theorem
 Kinetic Energy, Rest Energy, Equivalence of MassEnergy
 E^{2}  p^{2} Invariant
 Nuclear Binding Energies
 Atomic Mass Excesses, SemiEmpirical Binding Energy Equation
 Nuclear Reactions
 Solar pp Chain

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10 
Relativistic Dynamics and Particle Physics (cont.)

Relativistic Motion in a B Field, Lorentz Force

Further Gedanken Experiments Relating to MassEnergy Equivalence, Relativistic Momentum

Quantum Nature of Light
 Photoelectric Effect, Photons

betaDecay and the Inference of Neutrino

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11 
Quiz 1 

12 
Relativistic Dynamics and Particle Physics (cont.)
 Absorption and Emission of Light Quanta
 Atomic and Nuclear Recoil
 Mössbauer Effect
 PoundRebka Experiment
 Collisions
 Between Photons and Moving Atoms
 Elastic
 Compton
 Inverse Compton
 Between Photon and Relativistic Particle

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13 
Relativistic Dynamics and Particle Physics (cont.)
 Particle Production
 Threshold Energy
 Colliding Particle Beams
 Two Photons Producing an Electron/Positron Pair

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14 
Relativistic Dynamics and Particle Physics (cont.)
 Formal Transformation of E and P as a FourVector
 Revisit the Relativistic Doppler Effect
 Relativistic Invariant E^{2}  p^{2} for a Collection of Particles

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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

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16 
Relativity and Electromagnetism (cont.)
 General Transformation Laws for E and B
 Magnetic Force due to CurrentBearing Wire
 Force between CurrentBearing Wires

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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

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18 
General Relativity and Cosmology
 Cosmological Redshifts and the Hubble Law

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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 Omega_{m}, Omega_{Lambda} and Omega_{k}

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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 Omega_{m}, Omega_{Lambda} and Omega_{k}
 Acceleration Parameter as a Function of Scale Factor
 Current S Status of Cosmology, Unsolved Puzzles

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21 
Quiz 2 

22 
General Relativity and Cosmology (cont.)
 Handout Defining Einstein Field Equations, Einstein Tensor, StressEnergy 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 Nonzero Components are Functions of Radius Only
 The Differential Equations for G00 and G11
 Shell Radius vs. Bookkeepers Radial Coordinate

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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

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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 WeakField Limit

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25 
General Relativity and Black Holes (cont.)
 Keplers Third Law in the Schwarzschild Metric
 Relativistic Precession in the WeakField Limit
 TaylorHulse Binary Neutron Star System
 Derivation of the Last Stable Circular Orbit at 6M
 Analytic E and L for Circular Orbits

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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 WeakField Limit
 Shapiro Time Delay

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