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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. Most Planck units are fantastically small and thus are unrelated to "macroscopic" phenomena (or fantastically large, as in the case of Planck temperature and Planck acceleration). Energy of 1 EP, on the other hand, is definitely macroscopic, approximately equaling 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.