, or specifically, of which the velocity is comparable to the speed of light
Several approaches exist as a means of describing the motion of single and multiple relativistic particles, with a prominent example being postulations through the Dirac equation of single particle motion.
is the rest mass, when the rest mass tends to be zero, e.g. for a photon, or the momentum tends to be large, e.g. for a large-speed proton, this relation will collapses into a linear dispersion, i.e.
This is different from the parabolic energy-momentum relation for classical particles.
Thus, in practice, the linearity or the non-parabolicity of the energy-momentum relation is considered as a key feature for relativistic particles.
These two types of relativistic particles are remarked as massless and massive, respectively.
In other words, a massive particle is relativistic when its total mass-energy is at least twice its rest mass.
According to the Lorentz factor formula, this requires the particle to move at roughly 85% of the speed of light.
[b] In astrophysics, jets of relativistic plasma are produced by the centers of active galaxies and quasars.
[4] A charged relativistic particle crossing the interface of two media with different dielectric constants emits transition radiation.
This is exploited in the transition radiation detectors of high-velocity particles.
[5] Relativistic electrons can also exist in some solid state materials,[6][7][8][9] including semimetals such as graphene,[6] topological insulators,[10] bismuth antimony alloys,[11] and semiconductors such as transitional metal dichalcogenide [12] and black phosphorene layers.