Four-vector

A four-vector is an object with four components that transforms under Lorentz transformations. Its components mix between inertial frames while its Minkowski norm remains invariant.

Minkowski spacetime: The four-dimensional spacetime model of special relativity, equipped with an invariant metric. Its metric defines the invariant norm shared by all four-vectors.
Lorentz boost: A Lorentz transformation between inertial frames moving at constant relative velocity. A boost mixes a vector's time component with its component along the motion.
Four-momentum: The relativistic energy and three-momentum assembled into a four-vector. Its invariant norm gives the particle's mass, while its components encode energy and momentum.
Three-vector: A vector with three spatial components that transforms under rotations in three-dimensional space. A four-vector also has a time component, and boosts mix it with space.
Lorentz transformation: A linear transformation between inertial frames that preserves the spacetime interval. It specifies how four-vector components change between inertial observers.
Four-vector transformation law: The rule that transforms a four-vector's components using a Lorentz transformation matrix. This law distinguishes a four-vector from four unrelated quantities.
Four-position: The time and spatial coordinates of an event assembled into a four-vector. It represents event coordinates in a form that transforms between inertial frames.
Four-scalar: A Lorentz-invariant quantity whose value is unchanged by transformations between inertial frames. Unlike a four-vector, a scalar has no components that mix under boosts.
Spacetime interval: The invariant separation between two events in Minkowski spacetime. Four-vector norms use the same invariant spacetime geometry.
Minkowski inner product: A bilinear product defined by the Minkowski metric, invariant under Lorentz transformations. It produces frame-independent scalar quantities from four-vectors.

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