Relativity

Lecture Notes

SES #	TOPICS	LECTURE SLIDES
1	Course Overview Overview of Course Contents Practical Issues and Advice Related Subjects; Brief History of Physics	(PDF)
2	Symmetry and Invariance Background and History Galilean Transformation, Inertial Reference Frames Classical Wave Equations; Transformation to Other Frames Michelson-Morley Experiment; Aether	(PDF)
3	Symmetry and Invariance (cont.) Postulates of Special Relativity First Discussion of Minkowski Diagrams, World Lines	(PDF)
4	Relativistic Kinematics Derivation of Lorentz-Einstein Transformations  Matrix Representation Introduction of Four-Vectors	(PDF)
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	(PDF)
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	(PDF)
7	Relativistic Kinematics (cont.) Stellar Aberration Doppler Effect and Angle Transformation via Transformation of Phase of Plane Waves Fully Calibrated Minkowski Diagrams  Pole-Vaulter Problem Twin Paradox with Constant Velocity Plus a Reversal Twin Paradox with Arbitrary Acceleration	(PDF - 1.1 MB)
8	Variational Calculus Short Discourse on the Calculus of Variations  Extremization of Path Integrals  The Euler-Lagrange 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	(PDF)
9	Relativistic Dynamics and Particle Physics Relativistic Momentum Inferred from Gedanken Experiment with Inelastic Collisions Relativistic Relations between Force and Acceleration 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	(PDF)
10	Relativistic Dynamics and Particle Physics (cont.) Relativistic Motion in a B Field, Lorentz Force  Cyclotrons, Synchrotrons Further Gedanken Experiments Relating to Mass-Energy Equivalence, Relativistic Momentum Quantum Nature of Light  Photoelectric Effect, Photons beta-Decay and the Inference of Neutrino	(PDF)
11	Quiz 1
12	Relativistic Dynamics and Particle Physics (cont.) Absorption and Emission of Light Quanta  Atomic and Nuclear Recoil Mössbauer Effect Pound-Rebka Experiment Collisions  Between Photons and Moving Atoms Elastic Compton Inverse Compton Between Photon and Relativistic Particle	(PDF)
13	Relativistic Dynamics and Particle Physics (cont.) Particle Production  Threshold Energy  Colliding Particle Beams Two Photons Producing an Electron/Positron Pair	(PDF - 1.2 MB)
14	Relativistic Dynamics and Particle Physics (cont.) Formal Transformation of E and P as a Four-Vector  Revisit the Relativistic Doppler Effect Relativistic Invariant E2 - p2 for a Collection of Particles	(PDF - 2.0 MB)
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	(PDF)
16	Relativity and Electromagnetism (cont.) General Transformation Laws for E and B Magnetic Force due to Current-Bearing Wire Force between Current-Bearing Wires	(PDF)
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	(PDF)
18	General Relativity and Cosmology Cosmological Redshifts and the Hubble Law	(PDF)
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 Omegam, OmegaLambda and Omegak	(PDF)
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 Omegam, OmegaLambda and Omegak Acceleration Parameter as a Function of Scale Factor Current S Status of Cosmology, Unsolved Puzzles	(PDF - 1.4 MB)
21	Quiz 2
22	General Relativity and Cosmology (cont.) Handout Defining Einstein Field Equations, Einstein Tensor, Stress-Energy 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 Non-zero Components are Functions of Radius Only The Differential Equations for G00 and G11 Shell Radius vs. Bookkeepers Radial Coordinate	(PDF - 4.1 MB)
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	(PDF)
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 Weak-Field Limit	(PDF - 1.1 MB)
25	General Relativity and Black Holes (cont.) Keplers Third Law in the Schwarzschild Metric 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	(PDF)
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 Weak-Field Limit Shapiro Time Delay	(PDF - 1.8 MB)