Advanced Topics in Physics: Special Relativity Course Syllabus
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1 Advanced Topics in Physics: Special Relativity Course Syllabus Day Period What How 1. Introduction 2. Course Information 3. Math Pre-Assessment Day 1. Morning 1. Physics Pre-Assessment 2. Coordinate Systems 3. Mechanics (kinematics) 1. Galilean Relativity 2. Aether Theory 1. Scientific Theories and the Aether Theory 2. Light as a Wave 3. Mechanics (dynamics) 4. Reference frames 5. Space and Special Relativity 1. Icebreaker: Bingo 2. Honor Code/Computer Use Agreement/Lab Safety Contract 3. Math Pre-Assessment Quiz 1. Physics Pre-Assessment Quiz 2. Coordinates: a. Introduce unit vectors via mechanics problems b. Properties of good coordinate systems c. Coordinate conversions 3. Practice problems with mechanics (kinematics) 1. Galilean relativity: a. Practice working through physical situations b. Reference frame transformations c. Practice problems 2. Maxwell s equations and propagation of light waves 1. Theories: a. Brainstorm qualities of a good theory b. Apply to the aether theory 2. Light: a. Speed of light b. Propagation and medium c. Wavelengths & frequencies of light waves (EM spectrum) 3. Practice mechanics problems (dynamics) 4. Practice reference frame problem 5. Space: a. What is space? b. Newtonian space and absolute reference frames c. Relative reference frames in special relativity
2 Day 2. Morning 1. Aether Hypothesis 1. Aether: a. What is aether? list b. Law of superposition and angle of aberration c. Dragged versus stationary aether d. Fizeau s experiment e. Michelson-Morley experiment 1. Theories and Experiments 2. Speed of Sound in Air 3. Speed of Light 4. Journaling/Lab Reports 1. Einstein s Cow Dream 2. The Postulates of Special Relativity Day 3. Morning 1. The Postulates of Special Relativity (continued) 2. Time Dilation 1. Length Contraction 2. Time Dilation & Length Contraction Practice 3. Space-Time Diagrams 1. Theories & experiments: a. What makes a good theory? list (brainstorm & discuss) b. What makes a good experiment? list (brainstorm & discuss) c. Discuss relationships between theories and experiments 2. Sound: a. Experiment outside on quad (clappers) b. Air columns & tuning forks 3. Speed of light microwave experiment 4. Write journal entries about experiments 1. Role-play & discussion 2. Postulates: a. Light Postulate b. Principle of Relativity 1. Discuss which is more revolutionary and why 2. Time dilation: a. Derive from photon clock on a train example b. Muon decay video c Naval test 1. Derive using muon decay example 2. Time dilation/length contraction worksheet 3. S-T diagrams: a. Explanation of construction/plotting b. Activity: plot personal activities on S-T diagram and have classmates guess the activity 2
3 1. Review 2. Quiz 3. Synchronicity 3 1. Problem sheet (mechanics, time dilation, length contraction, space-time diagrams) 2. Quiz on mechanics, time dilation, length contraction, space-time diagrams 3. Synchronicity: a. Introduction & discussion b. Activity: How can students synchronize themselves? 1. Practice problem 2. Barn-Pole paradox: a. Introduction of the potential paradox b. The Barn-Pole activity Day 3 (cont) Day 4. Morning 1. Calculations involving time dilation & length contraction 2. The Barn-Pole Paradox 3. Simultaneity 3. Reference frames and the red/green lights example 1. Review 1. Review quiz from evening of day 3 2. Lorentz Transformations 2. Derive, explain, and discuss 1. Lorentz Transformations (continued) 1. Practice with Lorentz transforms individually and do group exercise Day 5. Morning 1. Using Lorentz Transformations 1. Solve Barn-Pole paradox 2. Mr. Tomkins in Wonderland 2. Read Third Dream 3. Causality and Light Cones 3. Introduce, discuss, activity 1. Quiz on Lorentz Transformations 2. Plan for skits for joint session with Cognitive Psychology class 3. Computer Lab 4. Introduce Presentation Projects 1. Relativistic Doppler Shift 1. Derivation & discussion Day 6. Morning 1. Review of Doppler Shift 2. Review of Lorentz Transformations 3. Twins Paradox 1. Vectors and Matrices 2. Coordinate System Transformation 1. Quiz 2. Skit planning: a. Einstein s Cows b. Railroad Car 3. Velocity Raptor in the Lair of Relativity game 4. Topics related to applications, tests, or predictions of special and/or general relativity 1. Newtonian versus relativistic 2. Calculate coordinates in S (Cylon base) and S (Battlestar) 3. Twins paradox: a. Introduce and explain b. Activity (outdoor) c. Draw space-time diagrams for the three reference frames 1. Introduce, explain, and discuss 2. Activity
4 Races 1. Presentation Project Research 2. Review of Energy and Momentum Conservation in Newtonian Mechanics 3. Review of Space-Time Invariance Day 7. Morning 1. Quiz on Lorentz Transformations and Relativistic Doppler Shift 2. Velocity Addition in Special Relativity 3. Derivation of Lorentz Velocity Equations 1. Reversal of Velocity Transformations 2. Velocity of Light in Water 3. Velocity Transformations in Three Dimensions 4. Relativistic Beaming 1. In computer lab 2. Review with sample exercises 3. Review with sample exercises 1. Quiz 2. Introduce using baseball thrown at w on a train moving with v 3. Small group activity 1. Consider velocity of ball thrown by stationary observer as recorded by observer on moving train 2. Reconsider Fizeau experiment 3. Group exercise: for ball thrown inside train at 45-degree angle, what angle does a stationary observer measure for the initial velocity of the ball? 4. Brightness of the sun for observers at various points if sun is moving at v in x 1. Presentation Project Research 2. Relativistic Momentum Day 8. Morning 1. Warm-up Problem 2. Acceleration in Special Relativity 3. The Twins Paradox, version two 4. Special Relativity Jeopardy 1. Warm-up Problem 2. Relativistic Momentum versus Newtonian Momentum 3. Relativistic Energy 4. Mass as a function of velocity 1. Presentation Project Research 2. Energy and Momentum Conservation in Special Relativity 1. In computer lab 2. Introduce, derive, and explain 1. Practice problem 2. Introduce, explain, and why F = ma is beyond the scope of the course 3. Resolve using rates of signal emission and reception 4. Write Jeopardy questions 1. Practice problem: Newtonian collisions (energy & momentum conservation) 2. Explain why they are not the same, introduction of rest mass 3. Introduce and explain 4. For v << c, what is m(v)? 1. In computer lab 2. Example problems, including photon absorption by a hydrogen atom 4
5 3. Derivation and testing of E 2 = E p 2 c 2 3. Derive, explain, test using m 0 = m hydrogen and v = 0.97c) 1. Energy and momentum conservation: a. Practice problem: energy and momentum conservation across a spontaneous photon emission from a hydrogen atom b. Explain and derive c. Practice problem d. Explain Day 9. Morning 1. Energy and Momentum Conservation (continued) a. Review b. Difference in Rest Mass of an Atom Before and After Spontaneous Emission c. Scattering d. Rutherford Gold Foil Experiment 1. Rutherford Scattering Lab Activity 2. Nuclear Power 3. Special Relativity Jeopardy 1. Scattering activity using marbles 2. Read and discuss 3. Answer questions written by students previously, categories: Aether, Lorentz Transformations, Postulates, Rotations, Miscellaneous, Time Dilation/Length Contraction, etc. 1. Make poster for presentation 2. For joint session with Cognitive Psychology 1. Work on Presentations 2. Work on Skits Day 10. Morning 1. Presentations 1. Present research on topics related to Special and/or General Relativity 1. Prepare Skits 2. Joint Session with cognitive Psychology: Special Relativity and Einstein s Brain 1. For joint session with Cognitive Psychology 2. Joint Session: a. Skits b. Cognitive Psychology Presentation c. Discussion d. Guest Speaker: Einstein s Reasoning in the Discovery of Special Relativity e. Conclusions 1. Relativistic Kinematics Review 1. Kinematics: a. Relativistic billiards b. Relativistic motion c. Review sample problems d. Practice problems 5
6 Day 11. Morning 1. Relativistic Kinematics Review 2. Set Up for Game 1. Work through problems, review 2. Prepare for Relativistic Billiards Game 1. Relativistic Billiards Explanation and First Shots 2. Thought Experiments 3. Photon Rocket 1. Group Activity/Game 2. Thought Experiments: a. The Potted Plant Paradox b. The Bullet Over Water Paradox (Groups rotate through figuring shots in Relativistic Billiards Game and working on thought experiments) 1. Special Relativity and Introduction to General Relativity 2. Relativistic Electricity and Magnetism 3. Rocket Fuel Problem 6 3. Introduce and work through problem 1. Read Gardner pp Introduce and explain 3. Solve problem Day 12. Morning 1. Space Travel 1. Readings & short presentations: a. Rockets and the space shuttle program b. Prospective propulsion systems: ion propulsion, solar sails, etc. c. Extra-solar planets d. Life in space 1. Challenges of Space Travel 2. Paradox: Car Falling into a Gap 3. Explanation of Potted Plant and Bullet Thought Experiments 1. Two Rockets Acceleration Problem 2. Write Jeopardy Questions 3. Einstein s 1905 Paper 1. PowerPoint and discussion 2. Explore simultaneity and gravity in this paradox 3. Explain solutions 1. Solve problem 2. Prepare for Jeopardy Review Session 3. Read and Write in Journal Day 13. Morning 1. Introduction to General Relativity 1. General Relativity: a. Intro to math topics (e.g., Minkowski metric, etc.) b. Escape velocities for Sun, Earth, a white dwarf, a neutron star, etc. c. Black holes and Hawking radiation 1. Geodesics, Black Holes, and the Like 1. Introduction, explanation, and discussion 1. General Relativity: a. Gravity and Spacetime b. Tests of General Relativity 1. Read Gardner pp , , and Prepare for Jeopardy review Session
7 c. Models of the Universe d. Beginning and End (of the universe) 2. Write Jeopardy Questions Day 14. Morning 1. General Relativity (continued) 2. Write Jeopardy Questions 3. Review Using Questions from Instructor /La te 1. Jeopardy Review Session 2. Post-Assessment 3. Clean-Up Day 15. Morning 1. Watch Real Genius with physics class 1. Movie 1. Complete readings if necessary 2. Prepare for Jeopardy Review Session 3. Review topics to prepare for post-assessment 1. Use Jeopardy Questions to review for post-assessment 2. Complete post-assessment 3. Wrap-up 7
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