The big idea: Glide past a friend on a train and you each see the other slide steadily backwards — there is no way to say who is 'really' moving. That point of view, your own ruler and clock, is your reference frame; an inertial frame is one moving at constant velocity (no speeding up, slowing down, or turning).
Special relativity asks a simple question: if two people move steadily past each other, do they have to agree on what they measure? The answer turns out to be surprising.
Inertial = no acceleration: A train rolling smoothly at a steady speed is an inertial frame. A train braking or going round a bend is not — special relativity only deals with inertial (non-accelerating) frames.
Imagine you are on a smooth train with the blinds down. There is no experiment you can do inside that tells you whether you are moving at a steady speed or sitting still. That everyday fact is the seed of Einstein's whole theory.
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Einstein's two postulates: Special relativity is built on just two starting assumptions (postulates):
1. The principle of relativity — the laws of physics are the same in every inertial frame. No steady-speed observer is more 'correct' than any other.
2. The constancy of the speed of light — the speed of light in a vacuum is the same for every inertial observer, whatever the motion of the source or the observer.
- speed of light in a vacuum (m s⁻¹)
Why postulate 2 is so strange: In everyday life speeds add up: throw a ball at 5 m s⁻¹ from a train moving at 20 m s⁻¹ and the ground sees 25 m s⁻¹. Postulate 2 says light refuses to play this game — shine a torch from a fast train and the ground still measures the light at exactly c, not c + (train's speed).
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The easiest way to feel postulate 2 is to compare what classical (Galilean) physics predicts with what really happens. Classically, speeds simply add. In reality, light always comes out at c for everyone.
Classical (Galilean) expectation
- Speeds always add: ball + train = ground speed
- Light from a moving source should arrive faster than c
- Everyone shares one universal clock — time is absolute
- Two events that look simultaneous to one observer are simultaneous for all
Relativistic reality
- Light always measures c — it never adds on the source's speed
- Nothing with mass can reach or pass c — it is the cosmic speed limit
- Moving clocks run slow — time is not absolute
- Simultaneity is relative — observers can disagree on what happened 'at the same time'
A spaceship flies past a planet at 0.50c and shines a torch forward. The pilot measures the torch light moving away at speed c. What speed does an observer on the planet measure for that same light?
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Three big consequences: Once you accept that everyone measures the same c, three famous results follow:
- c is the cosmic speed limit — nothing carrying mass or information can reach or exceed the speed of light. - Simultaneity is relative — whether two events happen 'at the same time' depends on who is looking. - Space and time are not absolute — lengths and time intervals depend on the observer's motion.
Simultaneity is relative — picture it
- A lamp at the centre of a moving train flashes once.
- On the train, light reaches the front and back walls together — the events look simultaneous.
- On the platform, the train moves while the light travels, so the back wall rushes toward the light and is hit first.
- Both observers are right — because both measured the light at the same speed c, they must disagree on timing.
Don't say 'one of them is wrong': Neither observer is mistaken. There is no master clock in the universe to settle the argument. The disagreement is a real feature of nature, forced on us by the constancy of c.
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How this is tested — the postulates are HL only (A.5):
Paper 1A
- A one-line MCQ: 'which statement is a postulate?'
- 'What is the same for all observers?' (the speed of light).
Paper 2
- State the two postulates (2 marks).
- A short 'explain why…' argument built on them, before the 1.5.3 calculations.
The classic trap: Quote the postulates precisely — markers look for 'inertial frames' and 'regardless of the motion of the source or observer'. And never let a relative speed come out at or above c.
Easy marks: (1) Learn the two postulates as one sentence each. (2) Always say the speed of light is the same for all inertial observers, regardless of the motion of the source or observer. (3) When asked to explain, tie every conclusion back to 'because everyone measures the same c'.
State Einstein's two postulates of special relativity. Two spacecraft travel directly toward each other, each moving at 0.90c relative to a space station. Explain why their speed relative to each other is NOT 1.80c.
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See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.