Editing Oh-My-God particle (section)

==Speed==
It is not known what kind of [[particle]] it was, but most [[cosmic ray]]s are protons. If <math>m_\mathrm{p}</math> is the [[rest mass]] of the particle and <math>E_\mathrm{K}</math> is its [[kinetic energy]] (energy above the [[rest mass energy]]), then its speed was very close to <math display=inline>\sqrt{1-[m_\mathrm{p}c^2/(E_\mathrm{K}+m_\mathrm{p}c^2)]^2}</math> times the [[speed of light]]. Since <math display=inline>E_\mathrm{K} \gg m_\mathrm{p}c^2</math>, this ratio can be simplified to <math display=inline>1-\frac{1}{2}[m_\mathrm{p}c^2/E_\mathrm{K}]^2</math>. Assuming it was a proton, for which <math>m_\mathrm{p}c^2</math> is 938&nbsp;MeV, this means it was traveling at {{val|0.9999999999999999999999957}} times the speed of light, its [[Lorentz factor]] was {{val|3.2|e=11}} and its [[rapidity]] was {{val|27.1}}. This is 1.3 [[femtometers]] per second less than the speed of light, so if a [[photon]] were traveling alongside the proton, it would take over 245,000&nbsp;years for the photon to gain a 1&nbsp;cm lead, as seen from the Earth's reference frame. Due to [[special relativity]], the relativistic [[time dilation]] experienced by a proton traveling at this speed would be extreme. If the proton originated from a distance of 1.5&nbsp;billion light years, it would take approximately 1.71&nbsp;days in the [[reference frame]] of the proton to travel that distance.