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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 physics, the Lorentz transformations are a six-parameter family of linear ... is the Lorentz factor. This formula represents a passive transformation, as it ...
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 same ...
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.
In physics, a particle is called ultrarelativistic when its speed is very close to the speed of light c. Notations commonly used are v ≈ c {\displaystyle v\approx c} or β ≈ 1 {\displaystyle \beta \approx 1} or γ ≫ 1 {\displaystyle \gamma \gg 1} where γ {\displaystyle \gamma } is the Lorentz factor , β = v / c {\displaystyle \beta =v/c ...
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]
Lorentz's theory of electrons. Formulas for the Lorentz force (I, ponderomotive force) and the Maxwell equations for the divergence of the electrical field E (II) and the magnetic field B (III), La théorie electromagnétique de Maxwell et son application aux corps mouvants, 1892, p. 451. V is the velocity of light.
This is the formula for the relativistic doppler shift where the difference in velocity between the emitter and observer is not on the x-axis. There are two special cases of this equation. The first is the case where the velocity between the emitter and observer is along the x-axis. In that case θ = 0, and cos θ = 1, which gives: