The two postulates

Special relativity rests on two postulates Einstein proposed in 1905, and everything that follows in this course — time dilation, length contraction, E = mc² — is a logical consequence of taking them seriously. The first is a principle you already trust from ordinary mechanics: the laws of physics take the same form in every inertial (non-accelerating) reference frame. There's no experiment you can perform inside a sealed, smoothly-moving lab that reveals your speed relative to anything else — only acceleration is detectable from the inside.

The second postulate is the one that breaks with two centuries of intuition. It says the speed of light in vacuum has the same value c in every inertial frame, regardless of the motion of the source or the observer. A flashlight beam measured from a moving train and the same beam measured from the platform both clock in at exactly c — not c plus or minus the train's speed.

Classical (Galilean) mechanics says velocities simply add: if you throw a ball forward at speed u inside a train moving at speed v, a platform observer sees the ball moving at u + v. That rule works beautifully for baseballs and bullets — it's why Newtonian mechanics held up for two centuries. But apply it to light and it demands that a platform observer see the beam from an oncoming train's headlight moving faster than c, and the beam from a trailing taillight moving slower than c. Maxwell's equations allow no such thing: they predict a single, frame-independent speed for light, built from nothing but the vacuum's electric and magnetic constants. Nineteenth-century experiments designed to detect the 'ether wind' that Galilean addition would imply — most famously Michelson and Morley's — kept coming up empty.

Einstein's move was to trust postulate 2 completely rather than patch it onto Newtonian kinematics. If light really does travel at the same c for every inertial observer, then space and time themselves — not light — have to be the things that adjust between frames. That single reframing is what the rest of this unit works out in detail, starting with the strangest casualty: the idea that two events can be simultaneous.