Position four-vector
= Position four-vector
{title2=$X^a=(ct,\mathbf x)$}
The spacetime coordinates of an event combine into a <four-vector> $X^a=(ct,x,y,z)$ under Lorentz transformations between inertial frames sharing an origin. For a massive particle, differentiation with respect to <proper time> gives its <four-velocity>. Under a spacetime translation, positions acquire an additive offset, while displacement four-vectors transform linearly under the Lorentz part.