Lorentz factor

The Lorentz factor is a convenient term to define in special relativity.

It is usually defined

<math>\gamma \equiv \frac{1}{\sqrt{1 - \beta^2}}<math>

where

<math>\beta = u/c<math>

is the velocity u in units of c, the speed of light. Sometimes (especially in discussion of superluminal motion) it is written as Γ rather than γ.

The Lorentz factor applies to time dilation, length contraction and relativistic mass relative to rest mass in Special Relativity. An object moving with respect to an observer moves in slow motion in accordance with multiplying its actual elapsed time by gamma. Its length is shorter as though its local length were divided by gamma. All seeming paradoxes of special relativity are resolved by the proper visualization of desynchronization.

Table

%c	Lorentz factor	reciprocal
0	1.000	1.000
10	1.005	0.995
50	1.155	0.867
90	2.294	0.436
99	7.089	0.141
99.9	22.366	0.045

See also

• special relativity
• Lorentz transformation