Four-vectorIn relativity, a four-vector is a vector in a four-dimensional real vector space, whose components transform like the space and time coordinates (ct, x, y, z) under spatial rotations and boosts (a change by a constant velocity to another inertial reference frame). The set of all such rotations and boosts, called Lorentz transformations and described by 4×4 matrices, forms the Lorentz group.
Examples of four-vectors include the coordinates (ct, x, y, z) themselves, the four-current (cρ, J) formed from charge density ρ and current density J, the electromagnetic four-potential (φ, A) formed from the scalar potential φ and vector potential A, and the four-momentum (E/c, p) formed from the (relativistic) energy E and momentum p. The speed of light (c) is often used to ensure that the first coordinate (time-like, labeled by index 0) has the same units as the following three coordinates (space-like, labeled by indices 1,..,3).
The scalar product between four-vectors a and b is defined as follows:
The laws of physics are also postulated to be invariant under Lorentz transformations. An object in an inertial reference frame will perceive the universe as if the universe were Lorentz-transformed so that the perceiving object is stationary.