The Constant Speed of Light
Einstein's second postulate is the genuinely strange one. Velocities are supposed to add — throw a ball forward from a moving train, and its speed relative to the ground is the train's speed plus the throw's speed. Light refuses to play by that rule, and accepting that refusal is what forces the rest of special relativity into existence.
Einstein's second postulate
Alongside the principle of relativity covered in the previous lesson, Einstein's special theory of relativity rests on a second postulate: the speed of light in a vacuum, $c$, has the same value for every observer in every inertial frame, regardless of the motion of the observer or the motion of the source emitting the light.
Unlike the first postulate, which mostly formalises an intuition already familiar from ordinary mechanics (you can't tell you're moving smoothly just by looking inside your own frame), the second postulate is genuinely radical. It says something no everyday object obeys: that a particular speed, $c = 3.00\times10^8\,\text{m}\,\text{s}^{-1}$, is measured as exactly the same value by every observer, no matter how fast that observer is moving, and no matter how fast the source producing the light is moving.
Why this breaks ordinary velocity addition
Ordinary, Newtonian intuition says velocities simply add together. A ball thrown forward at $5\,\text{m}\,\text{s}^{-1}$ from inside a train moving at $20\,\text{m}\,\text{s}^{-1}$ travels at $25\,\text{m}\,\text{s}^{-1}$ relative to the ground — the two velocities combine in the obvious way, because the ball's velocity relative to the ground is simply its velocity relative to the train plus the train's velocity relative to the ground. This rule works perfectly for balls, trains, cars, planes — every ordinary moving object physicists had ever measured, right up until light itself was tested.
Light does not behave this way. However fast the source of a light beam is moving, and however fast the observer measuring it is moving, the beam is always measured travelling at exactly $c$ — never $c$ plus the source's speed, never $c$ minus the observer's speed. A spaceship travelling at half the speed of light directly toward you, shining a torch in your direction, still produces light that reaches you measured at exactly $c$ — not $1.5c$, as simple velocity addition would predict.
This invariance is exactly the fact the Michelson-Morley experiment's null result pointed toward. If light's speed depended on the motion of its source or observer (as the ether-wind hypothesis implicitly assumed), the interferometer should have detected a fringe shift as it rotated relative to the Earth's motion. It never did, at any orientation or time of year — and the single explanation that accounts for that failure is that light's speed simply doesn't depend on anyone's motion in the first place. Where earlier physicists treated this invariance as a puzzling anomaly still needing an explanation — perhaps some undiscovered property of the ether — Einstein instead took it as a fundamental starting assumption: a fact of nature to build a theory on, rather than a mystery to be explained away.
The consequence: something has to give
Accepting the second postulate at face value — genuinely accepting that $c$ is the same for every observer, with no exceptions — creates an immediate problem for ordinary Newtonian ideas about time and space. If two observers, moving at different velocities relative to each other, both measure the same beam of light travelling at exactly $c$, then something about how they each measure distance and time must be different between them. Speed is distance divided by time; if the same beam gives the same speed to both observers despite their relative motion, their measurements of distance, or their measurements of time, or both, cannot be the simple, universal, observer-independent quantities Newtonian physics assumed them to be.
This is not a minor technical wrinkle — it is the seed from which the rest of special relativity grows. Accepting this one experimentally confirmed fact forces time and space themselves to behave differently from Newtonian expectation: moving clocks must run slow relative to a stationary observer, and moving objects must be measured as contracted along their direction of motion. Exactly how and why are the subjects of the next lessons, on time dilation and length contraction.
Key takeaways
- Einstein's second postulate: the speed of light in a vacuum, $c$, is the same for every observer in every inertial frame, regardless of the motion of the source or the observer.
- Ordinary velocities add in the way everyday intuition expects — a ball thrown at $5\,\text{m}\,\text{s}^{-1}$ from a train moving at $20\,\text{m}\,\text{s}^{-1}$ travels at $25\,\text{m}\,\text{s}^{-1}$ relative to the ground.
- Light does not obey this addition rule: however fast the source or observer moves, light in a vacuum is always measured at exactly $c$, never $c$ plus or minus anything.
- This invariance is exactly the fact the Michelson-Morley null result pointed to — no ether wind was detected because light's speed doesn't depend on relative motion at all.
- Einstein took this invariance as a fundamental starting assumption for special relativity, rather than an anomaly requiring further explanation.
- Accepting that $c$ is truly invariant for every observer forces time and space themselves to behave differently from Newtonian expectation, since speed is distance divided by time.
- This sets up the next lessons: time dilation and length contraction, the direct consequences of taking the second postulate seriously.