Foundations

Two postulates. That’s the whole show.

Special Relativity rests on two statements. They sound innocent. They are not.

1

Principle of Relativity

The laws of physics take the same form in every inertial reference frame — any frame moving at constant velocity relative to another. There is no privileged "rest frame of the universe"; absolute rest is meaningless.

Galileo already had this for mechanics. Einstein said: it must hold for electromagnetism too, including Maxwell’s equations and the speed they predict for light.

2

Constancy of the speed of light

Light travels at the same speed in vacuum in every inertial frame, regardless of how the source or observer is moving.

A flashlight on a moving train doesn’t make its beam go faster. A spaceship racing toward a flash doesn’t see it arrive faster. Every observer measures the same .

This is the postulate that does all the damage. Hold onto it; it is fundamentally incompatible with the way velocities used to add in classical mechanics.

What it looks like geometrically

Plot space along the horizontal axis and time along the vertical (a "Minkowski" diagram). The path of any light pulse traces a 45° line — the light cone. Postulate 2 says: the light cone is the same in every inertial frame.

Drag the velocity slider below to switch to a frame moving at β. Watch what happens to the primed axes. The light cone — dashed orange — never moves.

β = 0.40 γ = 1.091
xctct′x′

Black: lab frame axes. Teal: primed-frame axes for an observer moving at β. Orange dashed: light cone — invariant under any boost.

What follows from these two

From postulates 1 and 2 alone you can derive — without further assumption — that:

  • moving clocks run slow (time dilation)
  • moving rods are shortened along their direction of motion (length contraction)
  • two events simultaneous in one frame are not simultaneous in another
  • velocities don’t simply add — they combine through a relativistic rule that keeps the upper bound

The next page shows the actual collision: classical (Galilean) addition cannot survive a constant . Watch it break, then watch what replaces it.