Special relativity is built on two postulates: the laws of physics are the same in all inertial frames, and the speed of light in vacuum, $c$, is the same for all inertial observers. These postulates force revisions to absolute time, absolute simultaneity, and Galilean velocity addition.

Events are described by four coordinates $(ct,x,y,z)$, and the invariant spacetime interval is $$s^2 = c^2t^2 - x^2 - y^2 - z^2.$$ Quantities that preserve this interval under Lorentz transformations are fundamental to relativistic physics.

A moving clock ticks more slowly relative to a stationary observer, by a factor related to $\gamma = 1/\sqrt{1-v^2/c^2}$. Similarly, lengths parallel to the motion contract by the same Lorentz factor. These are not optical illusions; they are geometric consequences of spacetime structure.

Relativistic energy and momentum satisfy $$E^2 = p^2c^2 + m^2c^4.$$ In the limit of low speed, this reduces to familiar Newtonian expressions, while at high speed it governs particle collisions and mass-energy conversion.