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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 ...
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.
SI unit of measure alpha: alpha particle: angular acceleration: radian per second squared (rad/s 2) fine-structure constant: unitless beta: velocity in terms of the speed of light c: unitless beta particle: gamma: Lorentz factor: unitless photon: gamma ray: shear strain: radian heat capacity ratio
Heaviside–Lorentz units, like the Gaussian CGS units by which they generally differ by a factor of about 3.5, are frequently of rather inconvenient sizes. The ampere (coulomb/second) is reasonable unit for measuring currents commonly encountered, but the ESU/s, as demonstrated above, is far too small.
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]
Below are few ultrarelativistic approximations when .The rapidity is denoted : Motion with constant proper acceleration: d ≈ e aτ /(2a), where d is the distance traveled, a = dφ/dτ is proper acceleration (with aτ ≫ 1), τ is proper time, and travel starts at rest and without changing direction of acceleration (see proper acceleration for more details).
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]
where = is the Lorentz factor. By applying the Lorentz transformation, the spacetime axes obtained for a boosted frame will always correspond to conjugate diameters of a pair of hyperbolas. As illustrated in Fig 2-3, the boosted and unboosted spacetime axes will in general have unequal unit lengths.