The second postulate of special relativity, where it comes from, and what it forces upon space and time.
Last updated 27 June 2026
The postulate
Special relativity rests on two statements:
The laws of physics take the same form in every inertial frame.
Light propagates in vacuum with the same speed c in every inertial frame, independently of the motion of the source.
The second postulate is the radical one. Galilean intuition says velocities add: a photon emitted from a moving train should travel at c+v. Experiment — beginning with Michelson–Morley in 1887 — says it does not.
Where it comes from
The postulate is not an arbitrary axiom; it is forced by electromagnetism. Maxwell’s equations in vacuum yield the wave equation
∇2E−c21∂t2∂2E=0,c=μ0ε01,
with c built out of constants of nature, with no reference to any preferred frame. If the first postulate is to hold for electromagnetism, every inertial observer must measure the same c.
What it costs
Keeping c invariant means abandoning absolute simultaneity. The transformation between inertial frames can no longer be Galilean; it must preserve the quantity
Δs2=−c2Δt2+Δx2+Δy2+Δz2,
the spacetime interval. The linear maps that do so are the Lorentz transformations; for relative velocity v along x,
t′=γ(t−c2vx),x′=γ(x−vt),γ=1−v2/c21.
Time dilation and length contraction are immediate corollaries — not optical illusions but consequences of the geometry of the interval.
The light cone
Because Δs2=0 characterises light rays in every frame, the light cone through an event is an invariant structure. It partitions spacetime into timelike, null, and spacelike regions, and with it, causality itself becomes frame-independent: no observer can disagree about what may influence what.