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The Lorentz factor or Lorentz term (also known as the gamma factor [1]) is a quantity expressing how much the measurements of time, length, and other physical properties change for an object while it moves.
The Lorentz factor γ retains its definition for a boost in any direction, since it depends only on the magnitude of the relative velocity. The definition β = v/c with magnitude 0 ≤ β < 1 is also used by some authors.
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.
Replacing the Lorentz factor in the original formula leads to the relation = / In this equation both and are measured parallel to the object's line of movement. For the observer in relative movement, the length of the object is measured by subtracting the simultaneously measured distances of both ends of the object.
Hendrik Lorentz [H 1] derived the correct (up to a certain factor ) relations for accelerations, forces and masses between a resting electrostatic systems of particles (in a stationary aether), and a system emerging from it by adding a translation, with as the Lorentz factor:
Then the Lorentz transformation specifies that these coordinates are related in the following way: ′ = (/) ′ = ′ = ′ =, where = / is the Lorentz factor and c is the speed of light in vacuum, and the velocity v of S ′, relative to S, is parallel to the x-axis.
Lorentz factor as a function of speed (in natural units where c = 1). Notice that for small speeds (as v tends to zero), γ is approximately 1. In addition to the light clock used above, the formula for time dilation can be more generally derived from the temporal part of the Lorentz transformation. [28]
The following notations are used very often in special relativity: Lorentz factor = where = and v is the relative velocity between two inertial frames.. For two frames at rest, γ = 1, and increases with relative velocity between the two inertial frames.