The big idea: A reference frame is just the point of view of an observer — their own ruler and clock for measuring where and when things happen. An inertial frame is one that moves 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.
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'
Worked example — a torch on a fast spaceship
A spaceship flies past a planet at 0.50c and shines a torch forward. The pilot on the ship measures the torch light moving away at speed c. What speed does an observer on the planet measure for that same light?
Solution
- Classically you might add the speeds: 0.50c (ship) + c (light) = 1.50c.
- But postulate 2 says the speed of light is the same for every inertial observer, whatever the source does.
- So the planet observer measures the light at exactly c, not 1.50c. The two observers agree on the light's speed even though they disagree about the ship's speed.
Final answer
The planet observer measures the light at c = 3.00×10⁸ m s⁻¹ (not 1.50c). The speed of light is invariant.
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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Where it shows up: The postulates are HL only (A.5):
- Paper 1A — a one-line MCQ: which statement is a postulate? or what is the same for all observers? - Paper 2 — state the two postulates (2 marks), then a short explain why... argument using them, before the calculation parts that use 1.5.3.
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'.
IB-style question — adding two large speeds
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.
Solution
- Postulate 1: the laws of physics are the same in all inertial reference frames.
- Postulate 2: the speed of light in a vacuum is the same for all inertial observers, regardless of the motion of the source or observer.
- Simply adding the speeds gives 0.90c + 0.90c = 1.80c, which is faster than light.
- Postulate 2 makes c the speed limit for any object, so the real relative speed must stay below c. Velocities do not add the everyday way — the relativistic velocity-addition formula (1.5.3) gives a value just under c.
Final answer
The two postulates are as stated. Because c is the universal speed limit, the relative speed cannot be 1.80c; it must be less than c (a value below 3.00×10⁸ m s⁻¹).