Ultrarelativistic limit
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In physics, a particle is called ultrarelativistic when its speed is very close to the speed of light c, such that its total energy E2 = m2c4 + p2c2 is almost completely due to its momentum (
), and thus can be approximated by E = pc.
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 (
).
[edit] Accuracy of the Approximation
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 are usually above 106 (v very close to c), the approximation is essentially exact.
[edit] Other limits
The opposite case is a so-called classical particle, where its speed is much smaller than c and so its energy can be approximated by 
.
