Lorentz transformation

A linear transformation between inertial coordinate systems that preserves the spacetime interval. It describes how space and time measurements change between observers in special relativity.

Lorentz boost: A Lorentz transformation between inertial frames moving at constant relative velocity along a chosen direction. The boost gives the transformation for observers whose relative motion is along one axis.
Inertial frame: A reference frame in which free bodies move at constant velocity and Newton's first law holds. Lorentz transformations relate the coordinates assigned by inertial observers.
Hendrik Lorentz: A Dutch physicist whose work on electrodynamics and moving bodies helped establish the Lorentz transformation. His 1904 formulation supplied a key mathematical precursor to the modern interpretation.
Time dilation: The difference between elapsed times measured by observers in relative motion or different gravitational potentials. It follows when two observers compare time coordinates using a Lorentz transformation.
Galilean transformation: The classical coordinate transformation between inertial frames that assumes absolute time and unrestricted velocity addition. Unlike a Lorentz transformation, it leaves time unchanged and does not preserve the spacetime interval.
Lorentz factor: The factor γ = 1/√(1 − v²/c²) that appears in special-relativistic transformations. It sets the magnitude of time dilation, length contraction, and the boost coefficients.
Spacetime interval: A quantity combining spatial separation and time separation between two events, invariant under Lorentz transformations. Its invariance is the defining constraint on the transformation.
Henri Poincaré: A French mathematician and physicist who clarified the transformation's group structure and physical significance. He recognized that the transformations form a group and connected them to relativity.
Length contraction: The shortening of an object's measured length along its direction of motion relative to an observer. It arises when endpoints are compared at the same time in the observer's frame.
Poincaré transformation: A spacetime transformation combining a Lorentz transformation with a translation. It extends the linear transformation by allowing origins in space and time to shift.

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