Ultrarelativistic limit

In physics, a particle is called ultrarelativistic when its speed is very close to the speed of light c. Notations commonly used are ${\displaystyle v\approx c}$ or ${\displaystyle \beta \approx 1}$ or ${\displaystyle \gamma \gg 1}$ where ${\displaystyle \gamma }$ is the Lorentz factor, ${\displaystyle \beta =v/c}$ and ${\displaystyle c}$ is the speed of light.

The energy of an ultrarelativistic particle is almost completely due to its kinetic energy ${\displaystyle E_{k}=(\gamma -1)mc^{2}}$. The total energy can also be approximated as ${\displaystyle E=\gamma mc^{2}\approx pc}$ where ${\displaystyle p=\gamma mv}$ 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 ${\displaystyle \gamma }$. Particles with a very small mass do not need much energy to travel at a speed close to c. 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]}