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EP is a derived, as opposed to basic, Planck unit. It is defined by:
Substituting values for the various components in this definition gives the approximate equivalent value of this unit in terms of other units of energy:
An equivalent definition is:
where tP is the Planck time.
where mP is the Planck mass.
The ultra-high-energy cosmic ray observed in 1991 had a measured energy of about 50 joules, equivalent to about 2.5×10−8 EP. Theoretically, the highest energy photon carries precisely 1 EP of energy (see Ultra-high-energy gamma ray). Most Planck units are extremely small or extremely large, as in the case of Planck temperature and Planck acceleration. For comparison, the Planck energy is approximately equal to the energy stored in an automobile gas tank (57.2 L of gasoline at 34.2 MJ/L of chemical energy).
Planck units are designed to normalize the physical constants G, ћ and c to 1. Hence given Planck units, the mass-energy equivalence E = mc² simplifies to E = m, so that the Planck energy and mass are numerically identical. In the equations of general relativity, G is often multiplied by 4π. Hence writings in particle physics and physical cosmology often normalize 4πG to 1. This normalization results in the reduced Planck energy, defined as:
- "Planck Energy". Cosmos, The SAO Encyclopedia, Swinburne University of Technology. Retrieved 18 September 2015.
- "CODATA Value: Planck mass energy equivalent in GeV". physics.nist.gov. Retrieved 2016-12-21.
- "HiRes - The High Resolution Fly's Eye Ultra High Energy Cosmic Ray Observatory". www.cosmic-ray.org. Retrieved 2016-12-21.