In special relativity, gamma (γ) is the symbol for a very common quantity,
1/sqrt(1 - v^2/c^2)
where v is the velocity
of the reference frame, and c is the speed of light
. It is used in the Lorentz transformation
relating quantities in two inertial reference frames as a constant of proportionality
. As a function
of v, it begins at 1 for v=0 and increases with increasing v such that it is infinite at v=c.
There are many important uses of γ in relativity. It is the constant of proportionality in time dilation and length contraction. The mechanical energy of a body is E = γmc2, which reduces to the famous E=mc2 when the particle velocity is zero. Similarly, the relativistic momentum is p=γmv, which reduces to the familiar Newtonian momentum when v<<c. Along with β=v/c, γ appears in many other relativistic situations, including relativistic electromagnetism.