HSC Physics — Module 7
Time Dilation — Flashcards & Quiz
Time dilation is one of the most surprising consequences of special relativity and a fixture in HSC Physics Module 7: Nature of Light. You need to identify which observer measures proper time, apply the Lorentz factor, and explain how muon decay at high altitude provides experimental evidence. Examiners reward precision: time dilation is reciprocal — each inertial observer sees the other's clock running slow — but proper time is unique to the frame in which the two events occur at the same place.
Key Points
- Special relativity postulates: (1) laws of physics are the same in all inertial frames, (2) speed of light in vacuum is constant (c = 3 × 10⁸ m s⁻¹).
- Time dilation: moving clocks run slow from a stationary observer's view — Δt = Δt₀ × γ where γ = 1/√(1 − v²/c²) and Δt₀ is the proper time.
- Proper time (Δt₀): measured in the frame where the two events occur at the same place. Dilated time (Δt): measured in any other inertial frame.
- γ ≈ 1 for everyday speeds; becomes significant as v approaches c. At v = 0.87c, γ ≈ 2 (clocks run at half speed).
- Muon decay experiment: muons created in the upper atmosphere reach Earth's surface in numbers that only make sense if their (dilated) lifetime is longer from the ground frame.
- Time dilation is reciprocal: each observer sees the other's clock running slow. This is only paradoxical if you ignore relativity of simultaneity.
Common Mistakes to Avoid
- Confusing proper time (Δt₀, measured in the frame where events are co-located) with dilated time (Δt, in any other frame).
- Saying "moving clocks slow down" — moving clocks run slow AS MEASURED FROM ANOTHER FRAME. Each observer sees the other's clock running slow.
- Using γ = 1/√(1 + v²/c²) — the sign is MINUS inside: γ = 1/√(1 − v²/c²).
- Thinking time dilation is only theoretical — muon decay experiments confirm it directly.
- Applying time dilation to accelerating frames (special relativity covers inertial frames only; general relativity handles acceleration).
Exam Strategy
HSC Module 7 time dilation questions give you a scenario (muon, spaceship, particle accelerator) and ask you to calculate dilated time or distance. Method: (1) identify the proper time (Δt₀, in the object's rest frame), (2) calculate γ from the given velocity, (3) apply Δt = γΔt₀. For paradoxes, remember time dilation is reciprocal and resolved by considering simultaneity.
Sample Flashcards
Q1: What is time dilation?
A moving clock runs slower relative to a stationary observer. Formula: t = t₀/√(1 - v²/c²) = γt₀, where t₀ is proper time (measured by the moving observer), t is dilated time, and γ = 1/√(1 - v²/c²) is the Lorentz factor.
Sample Quiz Questions
Q1: A clock moving relative to an observer appears to run faster than a stationary clock.
Answer: FALSE
A moving clock appears to run SLOWER (time dilation). t = γt₀ where γ > 1, so dilated time is always longer than proper time.
Revision Tip
Relativity calculations are formula-drilling with care over signs — use Revizi flashcards to practise extracting proper time correctly from scenario descriptions.
Related Concepts
Last updated: March 2026 · 1 flashcards · 1 quiz questions