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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.
where v is the relative velocity between frames in the x-direction, c is the speed of light, and = (lowercase gamma) is the Lorentz factor. Here, v is the parameter of the transformation, for a given boost it is a constant number, but can take a continuous range of values.
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 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.
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.
identical to Lorentz (1892). By dropping the factor γ 2 under the assumption that , Poincaré gave the result t*=t-vx*/c 2, which is the form used by Lorentz in 1895. Similar physical interpretations of local time were later given by Emil Cohn (1904) [R 28] and Max Abraham (1905). [R 29]
is called the Lorentz factor and c is the speed of light in free space. Lorentz factor (γ) is the same in both systems. The inverse transformations are the same except for the substitution v → −v. An equivalent, alternative expression is: [3]
Time dilation by the Lorentz factor was predicted by several authors at the turn of the 20th century. [3] [4] Joseph Larmor (1897) wrote that, at least for those orbiting a nucleus, individual electrons describe corresponding parts of their orbits in times shorter for the [rest] system in the ratio: . [5]