Hendrik Lorentz in the context of "Length contraction"

In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz.

The most common form of the transformation, parametrized by the real constant ${\displaystyle v,}$ representing a velocity confined to the x-direction, is expressed as$${\displaystyle {\begin{aligned}t'&=\gamma \left(t-{\frac {vx}{c^{2}}}\right)\\x'&=\gamma \left(x-vt\right)\\y'&=y\\z'&=z\end{aligned}}}$$where (t, x, y, z) and (t′, x′, y′, z′) are the coordinates of an event in two frames with the spatial origins coinciding at t = t′ = 0, where the primed frame is seen from the unprimed frame as moving with speed v along the x-axis, where c is the speed of light, and $${\displaystyle \gamma ={\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}$$is the Lorentz factor. When speed v is much smaller than c, the Lorentz factor is negligibly different from 1, but as v approaches c, ${\displaystyle \gamma }$ grows without bound. The value of v must be smaller than c for the transformation to make sense.

In physics, Minkowski space (or Minkowski spacetime) (/mɪŋˈkɔːfski, -ˈkɒf-/) is the main mathematical description of spacetime in the absence of gravitation. It combines inertial space and time manifolds into a four-dimensional model.

The model helps show how a spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded. Mathematician Hermann Minkowski developed it from the work of Hendrik Lorentz, Henri Poincaré, and others, and said it "was grown on experimental physical grounds".

The Lorentz factor or Lorentz term (also known as the gamma factor) is a dimensionless quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves. The expression appears in several equations in special relativity, and it arises in derivations of the Lorentz transformations. The name originates from its earlier appearance in Lorentzian electrodynamics – named after the Dutch physicist Hendrik Lorentz.

It is generally denoted γ (the Greek lowercase letter gamma). Sometimes (especially in discussion of superluminal motion) the factor is written as Γ (Greek uppercase-gamma) rather than γ.

The history of special relativity consists of many theoretical results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz, Henri Poincaré and others. It culminated in the theory of special relativity proposed by Albert Einstein and subsequent work of Max Planck, Hermann Minkowski and others.

In relativistic physics, Lorentz symmetry or Lorentz invariance, named after the Dutch physicist Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame. It has also been described as "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space".

Lorentz covariance, a related concept, is a property of the underlying spacetime manifold. Lorentz covariance has two distinct, but closely related meanings: