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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 total energy can also be approximated as = where = is the Lorentz invariant momentum. This can result from holding the mass fixed and increasing the kinetic energy to very large values or by holding the energy E fixed and shrinking the mass m to very small values which also imply a very large γ {\displaystyle \gamma } .
In this example the time measured in the frame on the vehicle, t, is known as the proper time. The proper time between two events - such as the event of light being emitted on the vehicle and the event of light being received on the vehicle - is the time between the two events in a frame where the events occur at the same location.
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]
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]
It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution f ( x ; x 0 , γ ) {\displaystyle f(x;x_{0},\gamma )} is the distribution of the x -intercept of a ray issuing from ( x 0 , γ ...
The prime examples of such four-vectors are the four-position and four-momentum of a particle, and for fields the electromagnetic tensor and stress–energy tensor. The fact that these objects transform according to the Lorentz transformation is what mathematically defines them as vectors and tensors; see tensor for a definition.
is the Lorentz factor of the velocity u (the vertical bars | u | indicate the magnitude of the vector). The velocity u can be thought of the velocity of a frame Σ′ relative to a frame Σ, and v is the velocity of an object, say a particle or another frame Σ′′ relative to Σ′. In the present context, all velocities are best thought of ...