QCE Physics — Unit 4
Special Relativity — QCE Physics — Unit 4 Flashcards & Quiz
Special relativity (1905) rests on two postulates: the laws of physics are the same in all inertial frames, and the speed of light in vacuum is constant. QCE Physics Unit 4 asks you to apply the Lorentz factor to time dilation, length contraction and relativistic momentum and energy. Muon decay is the canonical experimental evidence — know it.
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
- Mixing up proper time (Δt₀) with dilated time (Δt) — proper time is shorter.
- Claiming only moving objects experience time dilation — each observer sees the OTHER's clock running slow.
- Applying γ = 1/√(1 + v²/c²) — the sign is MINUS inside the square root.
- Forgetting that E = mc² is only rest energy — total energy is γmc².
- 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.
Sample Flashcards
Q1: What is special relativity?
Einstein's theory (1905) describing physics for observers moving at constant velocity relative to each other. 'Special' means restricted to inertial (non-accelerating) reference frames. Revolutionized understanding of space, time, mass, and energy.
Q2: Why can't velocities simply add in special relativity?
Galilean velocity addition (v_total = v₁ + v₂) violates constancy of light speed. Relativistic velocity addition prevents exceeding c. Formula: v = (v₁+v₂)/(1+v₁v₂/c²). At low speeds approaches classical result, at high speeds prevents v>c.
Q3: What experimental evidence supports special relativity?
Particle accelerators (velocity limit, mass increase), cosmic ray muons (time dilation), atomic clocks on aircraft (verified), GPS (requires corrections), particle decay rates (velocity dependent), Michelson-Morley experiment (constant c).
Q4: Why does special relativity seem counterintuitive?
Everyday speeds v<<c make relativistic effects negligible. γ≈1 for normal velocities. Brain evolved for Newtonian physics. Never experienced near-light speeds. Effects become significant only when v/c substantial.
Q5: What does 'special' mean in special relativity?
Special = restricted to special case of inertial (non-accelerating) reference frames. Excludes gravity and acceleration. Flat spacetime. Contrasts with general relativity which handles all frames including acceleration and gravity.
Sample Quiz Questions
Q1: A clock moving at a high velocity relative to a stationary observer will appear to:
Answer: Run slower than a stationary clock.
According to the principle of time dilation in special relativity, moving clocks are observed to run slower than stationary clocks. This effect becomes significant at speeds approaching the speed of light.
Q2: Einstein's famous equation E=mc^2 relates energy (E) and mass (m). What fundamental concept does this equation represent?
Answer: The equivalence and interconversion of mass and energy.
E=mc^2 demonstrates that mass and energy are interchangeable. Mass can be converted into energy, and energy can be converted into mass. It signifies their fundamental equivalence.
Q3: According to special relativity, what is the universal speed limit for any object or information?
Answer: The speed of light in a vacuum (c).
Special relativity postulates that the speed of light in a vacuum (c) is the ultimate speed limit in the universe. Nothing with mass can reach c, and information cannot travel faster than c.
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.
Related Concepts
Last updated: 3 September 2026 · 20 sample flashcards · 20 sample quiz questions