A world where velocities just add
Walk forward at 5 km/h inside a train that is gliding at 100 km/h, and a friend on the platform sees you moving at 105 km/h. This is common sense: to change frames you just add the relative velocity. For three centuries this was the bedrock of physics, and it works beautifully for trains, planets and thrown balls.
Behind it sits a deep and correct idea. Sit in a windowless cabin moving smoothly at constant velocity — an inertial frame — and no experiment you do inside can tell you how fast you are going, or even whether you are moving at all. Only changes in velocity can be felt. Galileo saw this first, and we call it the principle of relativity.
Galilean velocity addition: an object moving at u in the ground frame moves at u' in a frame that itself moves at v. Intuitive — and, for light, wrong.
The trouble with light
In the 1860s Maxwell's equations unified electricity and magnetism and predicted a self-sustaining electromagnetic wave that travels at a definite speed, c \approx 3.00\times10^{8} m/s. But a speed relative to what? Every other wave — sound, ripples, waves on a string — moves at a fixed speed relative to a medium. Physicists assumed light too had a medium, the invisible 'luminiferous ether' filling all space.
If the ether were real, Earth's motion through it should produce an 'ether wind', making light a little faster or slower depending on direction. In 1887 Michelson and Morley built an exquisitely sensitive interferometer to catch that difference. They found nothing — light's speed was the same in every direction, no matter how Earth moved. The most famous null result in physics demanded an explanation.
Einstein's two postulates
In 1905 Einstein made the boldest possible choice: take the awkward fact at face value. His special relativity rests on just two postulates. (1) The laws of physics are identical in every inertial frame — Galileo's principle, now including electromagnetism. (2) Light travels through empty space at the same speed c for every inertial observer, regardless of how the source or the observer moves.
The price: space and time must give
Speed is distance divided by time. If everyone must get the same number for the speed of light, then observers in relative motion cannot agree on distances and times. The thing Newton held absolute — a single universal clock ticking the same for all — is exactly what Einstein sacrificed. Over the next guides this cashes out as three concrete effects: moving clocks run slow (time dilation), moving objects shorten (length contraction), and observers disagree about which events happen 'at the same time'.