Oh-My-God particle

The Oh-My-God particle was an ultra-high-energy cosmic ray detected on 15 October 1991 by the Fly's Eye camera in Dugway Proving Ground, Utah, United States. , it is the highest-energy cosmic ray ever observed. Its energy was estimated as $3.2 eV$ (320 exa-eV). The particle's energy was unexpected and called into question prevailing theories about the origin and propagation of cosmic rays.

Speed
It is not known what kind of particle it was, but most cosmic rays are protons. If $$m_\mathrm{p}$$ is the rest mass of the particle and $$E_\mathrm{K}$$ is its kinetic energy (energy above the rest mass energy), then its speed was $\sqrt{1-[m_\mathrm{p}c^2/(E_\mathrm{K}+m_\mathrm{p}c^2)]^2}$ times the speed of light. Assuming it was a proton, for which $$m_\mathrm{p}c^2$$ is 938 MeV, this means it was traveling at $1$ times the speed of light, its Lorentz factor was $3.2$ and its rapidity was $27.1$. 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 billion light years, it would take approximately 1.71 days in the reference frame of the proton to travel that distance.

Collision energy
The energy of the particle was some 40 million times that of the highest-energy protons that have been produced in any terrestrial particle accelerator. However, only a small fraction of this energy was available for its interaction with a nucleus in the Earth's atmosphere, with most of the energy remaining in the form of kinetic energy of the center of mass of the products of the interaction. If $$m_\mathrm{t}$$ is the mass of the "target" nucleus, the energy available for such a collision is

$$\sqrt{ 2E_\mathrm{K}m_\mathrm{t}c^2+(m_\mathrm{p}+m_\mathrm{t})^2c^4 }-(m_\mathrm{p}+m_\mathrm{t})c^2$$

which for large $$E_\mathrm{K}$$ is approximately

$$\sqrt{ 2E_\mathrm{K}m_\mathrm{t}c^2}.$$

For the Oh-My-God particle hitting a nitrogen nucleus, this gives 2900 TeV, which is roughly 200 times higher than the highest collision energy of the Large Hadron Collider, in which two high-energy particles going opposite directions collide. In the center-of-mass frame of reference (which moved at almost the speed of light in our frame of reference), the products of the collision would therefore have had around 2900 TeV of energy, enough to transform the nucleus into many particles, moving apart at almost the speed of light even in this center-of-mass frame of reference. As with other cosmic rays, this generated a cascade of relativistic particles as the particles interacted with other nuclei.

Comparisons
The Oh-My-God particle's energy was estimated as $3.2 eV$, or $51 J$. Although this amount is phenomenally large for a single elementary particle – far outstripping the highest energy that human technology can generate in a particle – it is still far below the level of the Planck scale, where exotic physics is expected. Though a subatomic particle, its energy was comparable to the gravitational potential energy of a 1 kilogram object that could fall 5 meters off a two-story building.

The Oh-My-God particle had (100 quintillion) times the photon energy of visible light, equivalent to a 5 oz baseball travelling at about 28 m/s. Its energy was 20 million times greater than the highest photon energy measured in electromagnetic radiation emitted by an extragalactic object, the blazar Markarian 501.

High energy, but far below the Planck scale
While the particle's energy was higher than anything achieved in terrestrial accelerators, it was still about 40 million times lower than the Planck energy ($1.221 eV$). Particles of that energy would be required in order to expose effects on the Planck scale. A proton with that much energy would travel $1.665$ times closer to the speed of light than the Oh-My-God particle did. As viewed from Earth and observed in Earth's reference frame, it would take about $3.579 years$ ($2.59$ times the current age of the universe) for a photon to overtake a Planck energy proton with a 1 cm lead.

Later similar events
Since the first observation, hundreds of similar events (energy $5.7 eV$ or greater) have been recorded, confirming the phenomenon.  These ultra-high-energy cosmic ray particles are very rare; the energy of most cosmic ray particles is between eV and  eV.

More recent studies using the Telescope Array Project have suggested a source of the particles within a 20 degree radius "warm spot" in the direction of the constellation Ursa Major.

The Amaterasu particle, named after the sun goddess in Japanese mythology, was detected in 2021 and later identified in 2023, using the Telescope Array observatory in Utah, United States. It had an energy exceeding 240 exa-electron volts ($2.4$ eV). This particle appears to have emerged from the Local Void, an empty area of space bordering the Milky Way galaxy. It contained an amount of energy comparable to dropping a brick from the height of the waist. No promising astronomical object matching the direction from which the cosmic ray arrived has been identified.