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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.
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.
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: ′ = ()
A derivation for the transformation of the Lorentz force for the particular case u = 0 is given here. [4] A more general one can be seen here. [5] The transformations in this form can be made more compact by introducing the electromagnetic tensor (defined below), which is a covariant tensor.
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.
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 ...
A proof using 4-vectors and Lorentz transformation matrices Since a relativistic transformation rotates space and time into each other much as geometric rotations in the plane rotate the x - and y -axes, it is convenient to use the same units for space and time, otherwise a unit conversion factor appears throughout relativistic formulae, being ...
Parabolic Lorentz transformations are often called null rotations. Since these are likely to be the least familiar of the four types of nonidentity Lorentz transformations (elliptic, hyperbolic, loxodromic, parabolic), it is illustrated here how to determine the effect of an example of a parabolic Lorentz transformation on Minkowski spacetime.