Galilean relativity works beautifully — right up until things move really, really fast. Chase a beam of light and the simple “just add the speeds” rule falls apart, giving answers the Universe flatly refuses to allow. Einstein fixed this with two short, almost innocent-sounding statements. They look simple, but they quietly rewrite space and time themselves. These are the postulates of special relativity.
📘 What you need to know
Galilean velocity addition works only for speeds much less than the speed of light, c
Near c, adding speeds gives impossible answers — nothing can exceed c
First postulate: the laws of physics are the same in all inertial frames of reference
Second postulate: the speed of light in a vacuum is the same in all inertial frames
Every observer measures the speed of light as c, whatever their own motion
Because of this, space and time become relative — not fixed and absolute
Where Galilean relativity breaks
Newton, and Galileo before him, treated space and time as fixed and absolute: a second is a second and a metre is a metre for everyone, so you can just add velocities. For cars, trains and swimmers that’s spot on. The trouble starts when speeds approach the speed of light.
Suppose a rocket flies past at 0.7c and fires a probe straight ahead at 0.5c relative to itself. Galilean addition says a stationary observer sees the probe at 0.7c + 0.5c = 1.2c. But nothing — nothing at all — can travel faster than light. The rule has produced an answer the Universe simply won’t allow.
Galilean addition gives 1.2c — faster than light, which is impossible. The rule that works for trains and swimmers fails near the speed of light.
This is the clue that something deep is wrong. If simple velocity addition gives a forbidden answer, then one of our “obvious” assumptions must be false. Einstein’s genius was spotting exactly which one: the idea that time and distance are the same for everyone. Give that up, and everything clicks back into place.
The two postulates
Einstein built all of special relativity on just two statements. Learn them word for word — they’re worth marks directly, and every later equation flows from them.
First postulate
First postulate
The laws of physics are the same in all inertial frames of reference
This is Galilean relativity’s big idea, kept intact. In your own frame you are always at rest, so you can never tell whether you’re “really” moving. An experiment done on a smoothly cruising train gives the exact same results as one done on a still platform — there’s no test you could run to reveal absolute motion, because there’s no absolute frame to measure it against.
Second postulate
Second postulate
The speed of light in a vacuum is the same in all inertial frames of reference
This is the revolutionary one. Every observer measures light travelling at c (about 3.0 × 108 m s−1), no matter how fast they themselves are moving. A runner shining a torch ahead measures the beam leaving at c — and so does someone standing still watching them, who sees it as c too, notc plus the runner’s speed.
Both the moving runner and the stationary observer measure the same beam at exactly c. The light’s speed doesn’t pick up the runner’s motion — it can’t, or you’d be able to tell who was “really” moving.
Look how neatly the two postulates lock together. If light did add on the runner’s speed, you could measure the beam, compare it to c, and work out your own absolute motion — which the first postulate forbids. So light must travel at c for everyone. The two postulates aren’t independent; the second is what keeps the first honest.
1st postulate same laws, all frames
forces
2nd postulate c is the same for all
so
space & time become relative
What this costs us
Here’s the price. If everyone measures light at the same c, and speed is distance ÷ time, then something in “distance” and “time” has to give instead. That’s exactly what happens: at high speeds, lengths contract and time dilates, and observers no longer agree on when or where things happen. Newton’s absolute space and time quietly dissolve.
This only shows up when speeds are a serious fraction of c. At everyday speeds the effects are far too tiny to notice, which is why Galilean relativity felt perfectly correct for centuries. It was right — just only as an approximation.
CHECK
A spaceship travels at 0.9c and switches on its headlights. At what speed does the pilot measure the headlight beam leaving the ship? And what speed does a stationary observer watching the ship measure for the same beam?
Pilot’s measurement
by the 2nd postulate, light always travels at c
cStationary observer’s measurement
also c — NOT 0.9c + c
cThe tempting “1.9c” is the trap. Light’s speed never adds on the source’s motion — both agree on c.
💡 Top tips
Memorise both postulates. They’re worth direct marks — learn the exact wording.
Light never adds. A beam is measured at c by everyone, regardless of source speed.
“Inertial” matters. Both postulates are stated for inertial (non-accelerating) frames.
They’re linked. The invariance of c is what makes “no absolute frame” possible.
Relativity of space & time is a consequence — it follows from the two postulates, not the other way round.
Quick recap: Galilean velocity addition fails near c. Einstein’s two postulates — the laws of physics are the same in every inertial frame, and light travels at c for every observer — fix this, at the cost of making space and time relative rather than absolute.
⚠ Common mistakes
Adding a source’s speed to light: a beam is alwaysc, never c + v
Thinking the postulates apply to accelerating frames — they’re for inertial frames only
Believing space and time stay absolute — they become relative once c is invariant
Assuming Galilean addition is simply “wrong” — it’s a low-speed approximation that still works everyday
Muddling the two postulates — one is about the laws of physics, the other about the speed of light
These two little sentences are the launchpad for everything that follows. Now that adding velocities the old way is off the table, we need a proper correction for high speeds. Next comes the Lorentz transformations — the upgraded version of the Galilean equations, complete with the famous gamma factor that stretches time and shrinks space. That’s where the strange, wonderful predictions really begin.
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