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  2. Lorentz transformation - Wikipedia

    en.wikipedia.org/wiki/Lorentz_transformation

    The most general proper Lorentz transformation Λ(v, θ) includes a boost and rotation together, and is a nonsymmetric matrix. As special cases, Λ(0, θ) = R(θ) and Λ(v, 0) = B(v). An explicit form of the general Lorentz transformation is cumbersome to write down and will not be given here.

  3. Derivations of the Lorentz transformations - Wikipedia

    en.wikipedia.org/wiki/Derivations_of_the_Lorentz...

    In the fundamental branches of modern physics, namely general relativity and its widely applicable subset special relativity, as well as relativistic quantum mechanics and relativistic quantum field theory, the Lorentz transformation is the transformation rule under which all four-vectors and tensors containing physical quantities transform from one frame of reference to another.

  4. Four-vector - Wikipedia

    en.wikipedia.org/wiki/Four-vector

    Given two inertial or rotated frames of reference, a four-vector is defined as a quantity which transforms according to the Lorentz transformation matrix Λ: ′ =. In index notation, the contravariant and covariant components transform according to, respectively: ′ =, ′ = in which the matrix Λ has components Λ μ ν in row μ and column ν, and the matrix (Λ −1) T has components Λ ...

  5. Lorentz group - Wikipedia

    en.wikipedia.org/wiki/Lorentz_group

    Hendrik Antoon Lorentz (1853–1928), after whom the Lorentz group is named.. In physics and mathematics, the Lorentz group is the group of all Lorentz transformations of Minkowski spacetime, the classical and quantum setting for all (non-gravitational) physical phenomena.

  6. Representation theory of the Lorentz group - Wikipedia

    en.wikipedia.org/wiki/Representation_theory_of...

    that carry both the indices (x, α) operated on by Lorentz transformations and the indices (p, σ) operated on by Poincaré transformations. This may be called the Lorentz–Poincaré connection. [25] To exhibit the connection, subject both sides of equation to a Lorentz transformation resulting in for e.g. u,

  7. List of relativistic equations - Wikipedia

    en.wikipedia.org/wiki/List_of_relativistic_equations

    Derivation of Lorentz transformation using time dilation and length contraction Now substituting the length contraction result into the Galilean transformation (i.e. x = ℓ), we have: ′ = that is: ′ = ()

  8. Lorentz covariance - Wikipedia

    en.wikipedia.org/wiki/Lorentz_covariance

    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 ...

  9. Lorentz factor - Wikipedia

    en.wikipedia.org/wiki/Lorentz_factor

    The Lorentz factor or Lorentz term (also known as the gamma factor [1]) 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.