= Four-vector
{title2=$U^\mu$}
{wiki}
= Lorentz four-vector
{c}
{synonym}
A <four-vector> is a <vector> whose four <vector components> transform under a <Lorentz transformation> as $U'^\mu=\Lambda^\mu{}_\nu U^\nu$. Its individual <vector components> generally change between <inertial frames>; the <Minkowski metric> combines them into invariant scalar products. Listing four quantities is not enough to make a <four-vector>: their transformation law matters.
The most direct example is the displacement between two <spacetime events>, written $(c\Delta t,\Delta x,\Delta y,\Delta z)$. Multiplying the time difference by the <speed of light> gives all four <vector components> the same length units. A <position four-vector> describes an event relative to a chosen origin, while a displacement does not depend on a common translation of the origin. <Four-momentum> and <four-velocity> use the same transformation rule for different physical quantities.
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