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 clock moving relative to an observer is measured by that observer to run slow. Formula: t = t₀/√(1 − v²/c²), where t₀ is the proper time (measured in the frame in which the clock is at rest, so both events occur at the same place) and t is the dilated time measured by the observer who sees the clock moving.
Q2: What experimental evidence confirms time dilation?
Cosmic-ray muons are produced about 10–15 km up and have a mean lifetime of 2.2 μs at rest. Even at nearly c they would travel only about 660 m in one lifetime, yet large numbers reach the ground — because, in Earth's frame, their lifetime is dilated. In the Hafele–Keating experiment (1971), caesium atomic clocks flown around the world on commercial jets disagreed with ground clocks by tens to hundreds of nanoseconds, in agreement with relativity's predictions. Particle accelerators also show fast unstable particles living longer than at rest.
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: 9 October 2026 · 2 sample flashcards · 1 sample quiz questions