Special Relativity — Flashcards & Quiz

Key Points

• Postulate 1: the laws of physics are the same in all inertial reference frames.
• Postulate 2: the speed of light in vacuum (c) is constant for all observers regardless of their motion or that of the source.
• Lorentz factor γ = 1/√(1 – v²/c²); approaches 1 at low speeds and blows up as v approaches c.
• Time dilation: Δt = γΔt₀, where Δt₀ is proper time (measured in the frame where events occur at the same place).
• Length contraction: L = L₀/γ, where L₀ is proper length (measured in the frame where the object is at rest).
• Mass-energy equivalence: E = γmc², with rest energy E₀ = mc²; at v = 0 this reduces to the famous equation.

Common Mistakes to Avoid

1. Mixing up proper time (Δt₀) with dilated time (Δt) — proper time is shorter.
2. Claiming only moving objects experience time dilation — each observer sees the OTHER's clock running slow.
3. Applying γ = 1/√(1 + v²/c²) — the sign is MINUS inside the square root.
4. Forgetting that E = mc² is only rest energy — total energy is γmc².
5. Treating c as variable — it's the same in every inertial frame, that's the whole point.

Exam Strategy

QCAA Unit 4 relativity questions typically give a scenario (spacecraft, muon, particle accelerator) and ask you to calculate dilated time, contracted length, or relativistic energy. Method: (1) identify the proper quantity from the rest frame, (2) calculate γ from v/c, (3) apply the Lorentz formulas, (4) state which observer is measuring what. Muon decay experiments are the classic evidence question — be ready to explain.

Revision Tip

Relativistic calculations need careful identification of proper vs dilated quantities — drill a Revizi deck that gives you a scenario and asks which clock measures the proper time before doing the calculation.