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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 ...
Relation between the speed and the Lorentz factor γ (and hence the time dilation of moving clocks). Time dilation as predicted by special relativity is often verified by means of particle lifetime experiments. According to special relativity, the rate of a clock C traveling between two synchronized laboratory clocks A and B, as seen by a ...
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 } .
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]
However, there are indirect confirmations; for example, the behavior of colliding heavy ions can be explained if their increased density due to Lorentz contraction is considered. Contraction also leads to an increase of the intensity of the Coulomb field perpendicular to the direction of motion, whose effects already have been observed.
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.
Thus in calculating the relative proper speed, Lorentz factors multiply when coordinate speeds add. Hence each of two electrons (A and C) in a head-on collision at 45 GeV in the lab frame (B) would see the other coming toward them at v AC ~ c and w AC = 88,000 2 (1 + 1) ~ 1.55×10 10 lightseconds per traveler second.
The Doppler effect (with arbitrary direction) also modifies the perceived source intensity: this can be expressed concisely by the fact that source strength divided by the cube of the frequency is a Lorentz invariant [p 6] [note 2] This implies that the total radiant intensity (summing over all frequencies) is multiplied by the fourth power of ...