Key Idea: Relativity is about how the same events look to observers moving differently. At everyday speeds, Galilean relativity (just add/subtract velocities) works fine. But near the speed of light, Einstein's special relativity takes over: moving clocks run slow, moving lengths contract, and nothing can reach c. It is HL only (A.5).
💡 Einstein's two postulates
1. The laws of physics are the same in all inertial frames (no experiment finds an absolute rest frame). 2. The speed of light in a vacuum is the same, c, for every inertial observer — no matter how the source or observer moves. Postulate 2 is the strange one: it forces time and space themselves to stretch and shrink so everyone still measures light at c.
📐 The formulas you're given
- Lorentz factor (always ≥ 1)
- proper time — measured by one clock at both events (the shortest)
- proper length — measured in the object's rest frame (the longest)
- relativistic velocity addition (always stays below c)
- the invariant space-time interval — the same for all observers
✏️ IB-style worked examples (one per micro)
Two trains travel toward each other along a straight track at 25 m s⁻¹ and 30 m s⁻¹ relative to the ground. Determine the speed of one as measured from the other.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
A spaceship moving at 0.50c shines a torch forward. State the speed of the light measured by (a) an astronaut on the ship and (b) an observer on a nearby planet.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
A clock on a spaceship moving at 0.80c records a proper time of 2.0 s for an event. Determine the time an Earth observer measures.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Two events are separated by Δt = 5.0 μs and Δx = 900 m. Determine the space-time interval Δs. (c = 3.00×10⁸ m s⁻¹.)
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Important: 1. Proper time is the SHORTEST (one clock at both events) and proper length is the LONGEST (rest frame). Identify which is which before substituting. 2. Time dilation multiplies by γ (Δt = γΔt₀); length contraction divides by γ (L = L₀/γ). Don't swap them. 3. γ is always ≥ 1. If you get γ < 1, you've made a sign error under the root. 4. Never use simple Galilean addition near c — use the relativistic formula; the answer always stays below c.
Tap each card to reveal the answer.
What stays the same for every observer? The speed of light, c (postulate 2) — and the space-time interval Δs.
Which clock reads the proper time? The single clock present at both events — it reads the shortest (proper) time.
Lorentz factor at v = 0.866c? γ = 2.0 — the classic 'γ = 2' speed worth memorising.
A 100 m rocket flies past at 0.80c (γ = 1.67). Its measured length? 60 m — L = L₀/γ = 100/1.67.
Two ships approach, each at 0.50c. Their relative speed? 0.80c — u' = (0.5c+0.5c)/(1+0.25) = 0.80c, never 1.0c.
On a space-time diagram, what angle is a light ray? 45° — because ct = x for light; a stationary object is a vertical world line.
Exam Tips
- Compute γ first — everything else (time, length) hangs off it.
- Label the proper time / proper length before you substitute; it's the most common slip.
- γ = 2.0 at v = 0.866c is a handy memory check.
- Relativistic answers for speed always stay below c — if you get ≥ c, recheck.
- All inertial observers agree on the space-time interval Δs, even though they disagree on Δt and Δx.