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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 ...
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}} .
The Hafele–Keating experiment was a test of the theory of relativity. In 1971, [1] Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners.
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:
The two forces differ by the Lorentz factor γ. This difference is expected in a relativistic theory, however, due to the change in space-time between frames, as discussed next. Relativity takes the Lorentz transformation of space-time suggested by invariance of Maxwell's equations and imposes it upon dynamics as well (a revision of Newton's ...
This uncertainty corresponds to the undefined factor as described above. It was clear due to theoretical reasons (the group character of the Lorentz transformation as required by the relativity principle) that the individual values of length contraction and time dilation must assume their exact relativistic form. But a direct measurement of one ...
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′ .