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Definition of the Lorentz factor γ. 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 ...
In Minkowski's 1908 paper there were three diagrams, first to illustrate the Lorentz transformation, then the partition of the plane by the light-cone, and finally illustration of worldlines. [8] The first diagram used a branch of the unit hyperbola t 2 − x 2 = 1 {\textstyle t^{2}-x^{2}=1} to show the locus of a unit of proper time depending ...
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.
As shown in Lorenz's original paper, [28] the Lorenz system is a reduced version of a larger system studied earlier by Barry Saltzman. [29] The Lorenz equations are derived from the Oberbeck–Boussinesq approximation to the equations describing fluid circulation in a shallow layer of fluid, heated uniformly from below and cooled uniformly from ...
At any time after t = t′ = 0, xx′ is not zero, so dividing both sides of the equation by xx′ results in =, which is called the "Lorentz factor". When the transformation equations are required to satisfy the light signal equations in the form x = ct and x ′ = ct ′, by substituting the x and x'-values, the same technique produces the ...
Speed is represented in terms of the Lorentz factor. As the gas becomes hotter and k B T {\displaystyle k_{\text{B}}T} approaches or exceeds m c 2 {\displaystyle mc^{2}} , the probability distribution for γ = 1 / 1 − v 2 / c 2 {\textstyle \gamma =1/{\sqrt {1-v^{2}/c^{2}}}} in this relativistic Maxwellian gas is given by the Maxwell ...
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.
Lorentz considered local time not to be "real"; rather, it represented an ad hoc change of variable. [9]: 51, 80 Impressed by Lorentz's "most ingenious idea", Poincaré saw more in local time than a mere mathematical trick. It represented the actual time that would be shown on a moving observer's clocks.