In physics, a particle is called ultrarelativistic when its speed is very close to the speed of light c. Notations commonly used are
The total energy can also be approximated as
is the Lorentz invariant momentum.
This can result from holding the mass fixed and increasing the kinetic energy to very large values or by holding the energy E fixed and shrinking the mass m to very small values which also imply a very large
Particles with a very small mass do not need much energy to travel at a speed close to
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).
[citation needed] Below are few ultrarelativistic approximations when
: For calculations of the energy of a particle, the relative error of the ultrarelativistic limit for a speed v = 0.95c is about 10%, and for v = 0.99c it is just 2%.
For particles such as neutrinos, whose γ (Lorentz factor) are usually above 106 (v practically indistinguishable from c), the approximation is essentially exact.
The opposite case (v ≪ c) is a so-called classical particle, where its speed is much smaller than c. Its kinetic energy can be approximated by first term of the
binomial series: This relativity-related article is a stub.