The two postulates

Einstein's two postulates of special relativity, stated in the opening pages of On the Electrodynamics of Moving Bodies (1905), are: (1) the principle of relativity — the laws of physics take the same form in every inertial frame, with no preferred frame and no observable absolute rest; (2) the constancy of the speed of light — the speed of light in vacuum c has the same numerical value in every inertial frame, independent of the motion of the source or observer. Postulate (1) generalises Galileo's mechanical relativity to all of physics, including electrodynamics. Postulate (2) elevates the empirical fact of Michelson-Morley's null result to an axiom, and is the genuinely new content: it is incompatible with the Galilean velocity-addition rule, and forces the kinematics to be Lorentzian rather than Galilean.

From these two postulates alone, every kinematic result of special relativity follows by short algebra: the relativity of simultaneity, time dilation, length contraction, the Lorentz transformation, the velocity-addition formula, the relativistic Doppler effect, and the energy-momentum relation E² = (pc)² + (mc²)². The dynamic content of the theory — that mass and energy are equivalent, that the speed of light is the asymptotic limit of any massive particle's speed, that the spacetime interval is invariant under boosts — is similarly derivable. Einstein's reformulation made the aether unnecessary by treating its alleged effects as artefacts of a clinging-to-Galilean perspective; the moment one accepts (2) as a postulate rather than a puzzle, the entire structure becomes geometrically natural.