Lesson 7: Special Relativity: Postulates & Time Dilation
Demonstrating understanding of quantum phenomena, atomic structures, nuclear reactions, and special relativity.
🎯 Ngā Whāinga Akoranga | Learning Intentions
Einstein's two postulates of Special Relativity (laws of physics same in all inertial frames; speed of light c is invariant), proper time t_0, relativistic time dilation t = γ t_0, Lorentz factor γ = 1 / sqrt(1 - v^2/c^2).
Calculate Lorentz factor γ, solve time dilation problems for high-speed cosmic muons and spacecraft, and explain proper time.
🎥 Media Anchor & Pedagogical Scaffold
Einstein's Special Relativity & Time Dilation
Video Clip: Time dilation — Einstein's special relativity postulates and the time dilation formula | Khan Academy Physics (Runtime: 9m 14s).
🧠 1. Before Viewing (Activate & Predict)
Why does a clock moving at 99% the speed of light tick noticeably slower than a synchronized clock remaining stationary?
👁️ 2. During Viewing (Watch With a Job)
- Two postulates: state Einstein's two postulates of special relativity in your own words. Why is the second postulate so counterintuitive?
- Time dilation formula: write the time dilation formula (t' = γt) and explain what each symbol represents. Under what condition is t' > t?
- Muon thought experiment: the video uses muons (or similar examples) to illustrate time dilation. Describe the example and explain how it provides evidence for time dilation.
🗣️ 3. After Viewing & Kaiako Move (Process & Apply)
Kaiako Move: Use light-clock spacetime diagrams to demonstrate how constancy of c forces space and time to warp.
Immediate Task: Complete Section 7 of your Physics Portfolio: Relativistic Time Dilation & Cosmic Muon Proof Calculations.
⚡ Whakaoho | Do Now: Modern Physics Recall (10 mins)
Muons should not reach the ground. They are created high in the atmosphere and decay in about 2.2 microseconds. Even at nearly light speed, that is not enough time to fall to sea level. Detectors at sea level find them anyway.
Two minutes: something in the naive calculation is wrong, and it is not the muon's speed or its decay rate as measured in a lab. Say what you think it is. This is real evidence, not a thought experiment.
📖 Activity 1: Physics Concept Exploration & Problem Solving (25 mins)
Time dilation calculations (15 min). Calculate the Lorentz factor γ for v = 0.6c, 0.9c and 0.99c. Then compute how long a 2.2 μs muon lifetime becomes in the ground observer's frame at 0.99c, and whether that is now long enough to reach sea level.
Whose clock? (10 min). Identify the proper time in three scenarios. State the rule in your own words: proper time is measured by the clock present at both events. Getting this wrong inverts every relativity answer, so test yourself on the trickiest case.
📝 Activity 2: Level 3 Physics Portfolio Task & Merit/Excellence Scaffolding (20 mins)
Portfolio — Section 7. Submit: (1) γ calculated at three speeds with working; (2) the muon calculation resolving the paradox with numbers; (3) three proper-time identifications with justification, and a statement of both postulates in your own words.
🏫 Kaiako Planning & Pedagogy Notes
NCEA Level 3 Alignment: Direct preparation for Level 3 Physics (Demonstrate understanding of application of modern physics). Emphasise clear physical explanations and multi-step mathematical working for Merit/Excellence grades.