Lorentz covariance

Lorentz covariance is the property that physical equations retain their form under Lorentz transformations between inertial reference frames. It expresses compatibility with special relativity’s spacetime symmetries.

Lorentz transformation: A linear transformation relating spacetime coordinates measured in inertial frames moving at constant velocity relative to one another. These transformations define the frame changes under which covariant equations preserve their form.
Special relativity: The theory that describes space, time, and physical laws in inertial frames, with the speed of light invariant. Lorentz covariance is the mathematical expression of special relativity’s frame symmetry.
Maxwell's equations: The four classical equations describing how electric and magnetic fields are produced and how they change. Their Lorentz-covariant formulation unifies electric and magnetic fields across inertial frames.
General covariance: The property that equations retain their form under arbitrary smooth coordinate transformations. It allows a broader class of coordinate changes than Lorentz covariance’s inertial-frame transformations.
Lorentz group: The group of linear transformations that preserves the spacetime interval of Minkowski spacetime. Its symmetry operations provide the mathematical structure behind Lorentz covariance.
Inertial frame: A reference frame in which an isolated body moves at constant velocity and Newton’s first law holds. Lorentz covariance concerns how equations relate between these nonaccelerating frames.
Electromagnetic field tensor: An antisymmetric rank-two tensor that encodes the electric and magnetic fields in special relativity. It packages electromagnetism’s field components into a Lorentz-covariant object.
Galilean transformation: A transformation relating space and time coordinates in classical mechanics between inertial frames. It describes the classical alternative, where simultaneity is absolute and light speed is not invariant.
Four-vector: A set of four quantities that transforms under Lorentz transformations like spacetime coordinates. Four-vectors let equations express relationships that transform consistently between inertial frames.
Spacetime interval: The Lorentz-invariant separation between two events in Minkowski spacetime. Its invariance motivates the transformations that covariant equations must accommodate.

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