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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 ...
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]
is the Lorentz factor for the speed (with | | =). A dot above a variable indicates a derivative with respect to the coordinate time in a given reference frame, not the proper time τ {\displaystyle \tau } (in other terms, γ ˙ u = d γ u d t {\textstyle {\dot {\gamma }}_{u}={\frac {d\gamma _{u}}{dt}}} ).
Notations commonly used are or or where is the Lorentz factor, = / and is the speed of light. The energy of an ultrarelativistic particle is almost completely due to its kinetic energy E k = ( γ − 1 ) m c 2 {\displaystyle E_{k}=(\gamma -1)mc^{2}} .
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]
The defining property for the gamma matrices to generate a Clifford algebra is the anticommutation relation {,} = + = ,where the curly brackets {,} represent the anticommutator, is the Minkowski metric with signature (+ − − −), and is the 4 × 4 identity matrix.
Take, for example, the reciprocal electrodynamic action of a magnet and a conductor. The observable phenomenon here depends only on the relative motion of the conductor and the magnet, whereas the customary view draws a sharp distinction between the two cases in which either the one or the other of these bodies is in motion.