Ultrarelativistic limit

In physics, a particle is called ultrarelativistic when its speed is very close to the speed of light . The expression for the relativistic energy of a particle with rest mass and momentum is given by The energy of an ultrarelativistic particle is almost completely due to its momentum (), and thus can be approximated by . This can result from holding the mass fixed and increasing to very large values (the usual case); or by holding the energy fixed and shrinking the mass to negligible values. The latter is used to derive orbits of massless particles such as the photon from those of massive particles (cf. Kepler problem in general relativity). In general, the ultrarelativistic limit of an expression is the resulting simplified expression when is assumed. Or, similarly, in the limit where the Lorentz factor is very large ().